Fit Generalized Estimating Equations (GEE)

The geeglm function fits generalized estimating equations using the 'geese.fit' function of the 'geepack' package for doing the actual computations. geeglm has a syntax similar to glm and returns an object similar to a glm object. An important feature of geeglm, is that an anova method exists for these models.

geeglm(
  formula,
  family = gaussian,
  data = parent.frame(),
  weights,
  subset,
  na.action,
  start = NULL,
  etastart,
  mustart,
  offset,
  control = geese.control(...),
  method = "glm.fit",
  contrasts = NULL,
  id,
  waves = NULL,
  zcor = NULL,
  corstr = "independence",
  scale.fix = FALSE,
  scale.value = 1,
  std.err = "san.se",
  ...
)

Arguments

formula

See corresponding documentation to glm

family

See corresponding documentation to glm

data

See corresponding documentation to glm

weights

See corresponding documentation to glm

subset

See corresponding documentation to glm

na.action

No action is taken. Indeed geeglm only works on complete data.

start

See corresponding documentation to glm

etastart

See corresponding documentation to glm

mustart

See corresponding documentation to glm

offset

See corresponding documentation to glm

control

See corresponding documentation to glm

method

See corresponding documentation to glm

contrasts

See corresponding documentation to glm

id

a vector which identifies the clusters. The length of `id' should be the same as the number of observations. Data are assumed to be sorted so that observations on each cluster appear as contiguous rows in data. If data is not sorted this way, the function will not identify the clusters correctly. If data is not sorted this way, a warning will be issued. Please consult the package vignette for details.

waves

Wariable specifying the ordering of repeated mesurements on the same unit. Also used in connection with missing values. Please consult the package vignette for details.

zcor

Used for entering a user defined working correlation structure.

corstr

a character string specifying the correlation structure. The following are permitted: '"independence"', '"exchangeable"', '"ar1"', '"unstructured"' and '"userdefined"'

scale.fix

a logical variable; if true, the scale parameter is fixed at the value of 'scale.value'.

scale.value

numeric variable giving the value to which the scale parameter should be fixed; used only if 'scale.fix = TRUE'.

std.err

Type of standard error to be calculated. Defualt 'san.se' is the usual robust estimate. Other options are 'jack': if approximate jackknife variance estimate should be computed. 'j1s': if 1-step jackknife variance estimate should be computed. 'fij': logical indicating if fully iterated jackknife variance estimate should be computed.

...

further arguments passed to or from other methods.

Value

An object of type 'geeglm'

Details

In the case of corstr="fixed" one must provide the zcor vector if the clusters have unequal sizes. Clusters with size one must not be represented in zcor.

Note

See the documentation for the 'geese' function for additional information. geeglm only works for complete data. Thus if there are NA's in data you can specify data=na.omit(mydata).

Warning

Use "unstructured" correlation structure only with great care. (It may cause R to crash).

References

Halekoh, U.; Højsgaard, S. and Yan, J (2006) The R Package geepack for Generalized Estimating Equations. Journal of Statistical Software, 15, 2, 1-11"

Liang, K.Y. and Zeger, S.L. (1986) Longitudinal data analysis using generalized linear models. Biometrika, 73 13-22.

Prentice, R.L. and Zhao, L.P. (1991). Estimating equations for parameters in means and covariances of multivariate discrete and continuous responses. Biometrics, 47 825-839.

See also

geese, glm, anova.geeglm

Author

Søren Højsgaard, sorenh@math.aau.dk

Examples

data(dietox)
dietox$Cu     <- as.factor(dietox$Cu)
mf <- formula(Weight ~ Cu * (Time + I(Time^2) + I(Time^3)))
gee1 <- geeglm(mf, data=dietox, id=Pig, family=poisson("identity"), corstr="ar1")
#> Warning: non-integer x = 26.500000
#> Warning: non-integer x = 27.599990
#> Warning: non-integer x = 36.500000
#> Warning: non-integer x = 40.299990
#> Warning: non-integer x = 49.099980
#> Warning: non-integer x = 55.399990
#> Warning: non-integer x = 59.599980
#> Warning: non-integer x = 76.599980
#> Warning: non-integer x = 86.500000
#> Warning: non-integer x = 91.599980
#> Warning: non-integer x = 98.599980
#> Warning: non-integer x = 28.299990
#> Warning: non-integer x = 30.099990
#> Warning: non-integer x = 38.299990
#> Warning: non-integer x = 44.500000
#> Warning: non-integer x = 51.599980
#> Warning: non-integer x = 57.599980
#> Warning: non-integer x = 82.299990
#> Warning: non-integer x = 99.699950
#> Warning: non-integer x = 106.699950
#> Warning: non-integer x = 27.599990
#> Warning: non-integer x = 30.599990
#> Warning: non-integer x = 38.699980
#> Warning: non-integer x = 47.199980
#> Warning: non-integer x = 54.099980
#> Warning: non-integer x = 61.500000
#> Warning: non-integer x = 68.500000
#> Warning: non-integer x = 75.199950
#> Warning: non-integer x = 81.699950
#> Warning: non-integer x = 90.199950
#> Warning: non-integer x = 98.399960
#> Warning: non-integer x = 105.399960
#> Warning: non-integer x = 31.500000
#> Warning: non-integer x = 34.799990
#> Warning: non-integer x = 40.699980
#> Warning: non-integer x = 47.699980
#> Warning: non-integer x = 55.899990
#> Warning: non-integer x = 62.199980
#> Warning: non-integer x = 70.699950
#> Warning: non-integer x = 86.199950
#> Warning: non-integer x = 94.699950
#> Warning: non-integer x = 109.199950
#> Warning: non-integer x = 27.099990
#> Warning: non-integer x = 42.500000
#> Warning: non-integer x = 50.099980
#> Warning: non-integer x = 56.500000
#> Warning: non-integer x = 72.500000
#> Warning: non-integer x = 80.500000
#> Warning: non-integer x = 108.399960
#> Warning: non-integer x = 31.799990
#> Warning: non-integer x = 44.799990
#> Warning: non-integer x = 50.899990
#> Warning: non-integer x = 57.399990
#> Warning: non-integer x = 62.500000
#> Warning: non-integer x = 71.699950
#> Warning: non-integer x = 78.199950
#> Warning: non-integer x = 85.799990
#> Warning: non-integer x = 91.799990
#> Warning: non-integer x = 100.199950
#> Warning: non-integer x = 27.700000
#> Warning: non-integer x = 33.599980
#> Warning: non-integer x = 46.699980
#> Warning: non-integer x = 54.799990
#> Warning: non-integer x = 69.799990
#> Warning: non-integer x = 83.599980
#> Warning: non-integer x = 88.199950
#> Warning: non-integer x = 96.799990
#> Warning: non-integer x = 102.299990
#> Warning: non-integer x = 23.599990
#> Warning: non-integer x = 36.299990
#> Warning: non-integer x = 42.399990
#> Warning: non-integer x = 50.500000
#> Warning: non-integer x = 57.599980
#> Warning: non-integer x = 66.599980
#> Warning: non-integer x = 74.199950
#> Warning: non-integer x = 89.299990
#> Warning: non-integer x = 26.899990
#> Warning: non-integer x = 32.299990
#> Warning: non-integer x = 38.599980
#> Warning: non-integer x = 57.799990
#> Warning: non-integer x = 58.599980
#> Warning: non-integer x = 65.899960
#> Warning: non-integer x = 71.199950
#> Warning: non-integer x = 79.399960
#> Warning: non-integer x = 91.699950
#> Warning: non-integer x = 22.599990
#> Warning: non-integer x = 28.500000
#> Warning: non-integer x = 32.699980
#> Warning: non-integer x = 39.899990
#> Warning: non-integer x = 47.599980
#> Warning: non-integer x = 53.799990
#> Warning: non-integer x = 67.199950
#> Warning: non-integer x = 74.099980
#> Warning: non-integer x = 89.399960
#> Warning: non-integer x = 93.500000
#> Warning: non-integer x = 19.399990
#> Warning: non-integer x = 21.399990
#> Warning: non-integer x = 25.299990
#> Warning: non-integer x = 31.899990
#> Warning: non-integer x = 37.599980
#> Warning: non-integer x = 43.699980
#> Warning: non-integer x = 48.899990
#> Warning: non-integer x = 53.699980
#> Warning: non-integer x = 59.299990
#> Warning: non-integer x = 64.899960
#> Warning: non-integer x = 65.799990
#> Warning: non-integer x = 27.299990
#> Warning: non-integer x = 32.399990
#> Warning: non-integer x = 38.299990
#> Warning: non-integer x = 45.799990
#> Warning: non-integer x = 53.799990
#> Warning: non-integer x = 68.699950
#> Warning: non-integer x = 75.799990
#> Warning: non-integer x = 80.799990
#> Warning: non-integer x = 86.799990
#> Warning: non-integer x = 91.399960
#> Warning: non-integer x = 99.799990
#> Warning: non-integer x = 26.200000
#> Warning: non-integer x = 31.099990
#> Warning: non-integer x = 34.599980
#> Warning: non-integer x = 41.199980
#> Warning: non-integer x = 49.199980
#> Warning: non-integer x = 55.599980
#> Warning: non-integer x = 62.599980
#> Warning: non-integer x = 72.099980
#> Warning: non-integer x = 77.500000
#> Warning: non-integer x = 83.799990
#> Warning: non-integer x = 93.399960
#> Warning: non-integer x = 98.399960
#> Warning: non-integer x = 24.899990
#> Warning: non-integer x = 29.700000
#> Warning: non-integer x = 33.799990
#> Warning: non-integer x = 38.799990
#> Warning: non-integer x = 48.299990
#> Warning: non-integer x = 52.899990
#> Warning: non-integer x = 70.399960
#> Warning: non-integer x = 76.799990
#> Warning: non-integer x = 83.299990
#> Warning: non-integer x = 102.699950
#> Warning: non-integer x = 24.599990
#> Warning: non-integer x = 34.599980
#> Warning: non-integer x = 41.500000
#> Warning: non-integer x = 49.699980
#> Warning: non-integer x = 56.500000
#> Warning: non-integer x = 66.899960
#> Warning: non-integer x = 75.799990
#> Warning: non-integer x = 84.599980
#> Warning: non-integer x = 98.799990
#> Warning: non-integer x = 107.199950
#> Warning: non-integer x = 32.699980
#> Warning: non-integer x = 38.299990
#> Warning: non-integer x = 45.500000
#> Warning: non-integer x = 48.599980
#> Warning: non-integer x = 62.599980
#> Warning: non-integer x = 70.199950
#> Warning: non-integer x = 73.799990
#> Warning: non-integer x = 80.299990
#> Warning: non-integer x = 85.500000
#> Warning: non-integer x = 93.099980
#> Warning: non-integer x = 35.199980
#> Warning: non-integer x = 41.500000
#> Warning: non-integer x = 47.699980
#> Warning: non-integer x = 53.799990
#> Warning: non-integer x = 61.599980
#> Warning: non-integer x = 79.099980
#> Warning: non-integer x = 85.699950
#> Warning: non-integer x = 92.500000
#> Warning: non-integer x = 101.099980
#> Warning: non-integer x = 34.500000
#> Warning: non-integer x = 40.399990
#> Warning: non-integer x = 53.500000
#> Warning: non-integer x = 60.199980
#> Warning: non-integer x = 68.599980
#> Warning: non-integer x = 73.399960
#> Warning: non-integer x = 78.500000
#> Warning: non-integer x = 90.599980
#> Warning: non-integer x = 97.199950
#> Warning: non-integer x = 31.200000
#> Warning: non-integer x = 38.799990
#> Warning: non-integer x = 44.699980
#> Warning: non-integer x = 53.599980
#> Warning: non-integer x = 59.199980
#> Warning: non-integer x = 67.099980
#> Warning: non-integer x = 76.399960
#> Warning: non-integer x = 83.799990
#> Warning: non-integer x = 71.599980
#> Warning: non-integer x = 97.399960
#> Warning: non-integer x = 107.099980
#> Warning: non-integer x = 24.299990
#> Warning: non-integer x = 28.399990
#> Warning: non-integer x = 40.299990
#> Warning: non-integer x = 46.199980
#> Warning: non-integer x = 51.899990
#> Warning: non-integer x = 58.099980
#> Warning: non-integer x = 62.599980
#> Warning: non-integer x = 68.199950
#> Warning: non-integer x = 78.399960
#> Warning: non-integer x = 87.500000
#> Warning: non-integer x = 90.399960
#> Warning: non-integer x = 24.599990
#> Warning: non-integer x = 25.799990
#> Warning: non-integer x = 28.599990
#> Warning: non-integer x = 30.399990
#> Warning: non-integer x = 36.099980
#> Warning: non-integer x = 36.099980
#> Warning: non-integer x = 49.299990
#> Warning: non-integer x = 57.899990
#> Warning: non-integer x = 75.699950
#> Warning: non-integer x = 81.399960
#> Warning: non-integer x = 88.699950
#> Warning: non-integer x = 21.200000
#> Warning: non-integer x = 25.799990
#> Warning: non-integer x = 29.399990
#> Warning: non-integer x = 36.799990
#> Warning: non-integer x = 43.199980
#> Warning: non-integer x = 51.099980
#> Warning: non-integer x = 59.299990
#> Warning: non-integer x = 72.799990
#> Warning: non-integer x = 78.599980
#> Warning: non-integer x = 93.799990
#> Warning: non-integer x = 95.199950
#> Warning: non-integer x = 29.399990
#> Warning: non-integer x = 34.599980
#> Warning: non-integer x = 40.599980
#> Warning: non-integer x = 46.599980
#> Warning: non-integer x = 62.500000
#> Warning: non-integer x = 78.299990
#> Warning: non-integer x = 83.199950
#> Warning: non-integer x = 34.699980
#> Warning: non-integer x = 42.799990
#> Warning: non-integer x = 48.399990
#> Warning: non-integer x = 53.299990
#> Warning: non-integer x = 71.099980
#> Warning: non-integer x = 77.399960
#> Warning: non-integer x = 94.500000
#> Warning: non-integer x = 104.599980
#> Warning: non-integer x = 29.599990
#> Warning: non-integer x = 34.199980
#> Warning: non-integer x = 63.500000
#> Warning: non-integer x = 72.699950
#> Warning: non-integer x = 78.699950
#> Warning: non-integer x = 84.899960
#> Warning: non-integer x = 96.399960
#> Warning: non-integer x = 100.199950
#> Warning: non-integer x = 22.399990
#> Warning: non-integer x = 25.200000
#> Warning: non-integer x = 36.500000
#> Warning: non-integer x = 43.299990
#> Warning: non-integer x = 58.099980
#> Warning: non-integer x = 70.699950
#> Warning: non-integer x = 78.099980
#> Warning: non-integer x = 83.500000
#> Warning: non-integer x = 26.599990
#> Warning: non-integer x = 28.200000
#> Warning: non-integer x = 38.399990
#> Warning: non-integer x = 45.799990
#> Warning: non-integer x = 54.899990
#> Warning: non-integer x = 60.099980
#> Warning: non-integer x = 56.899990
#> Warning: non-integer x = 64.899960
#> Warning: non-integer x = 81.899960
#> Warning: non-integer x = 90.899960
#> Warning: non-integer x = 28.200000
#> Warning: non-integer x = 35.299990
#> Warning: non-integer x = 42.699980
#> Warning: non-integer x = 48.199980
#> Warning: non-integer x = 53.199980
#> Warning: non-integer x = 64.799990
#> Warning: non-integer x = 71.500000
#> Warning: non-integer x = 76.099980
#> Warning: non-integer x = 86.099980
#> Warning: non-integer x = 92.500000
#> Warning: non-integer x = 27.099990
#> Warning: non-integer x = 34.699980
#> Warning: non-integer x = 40.699980
#> Warning: non-integer x = 47.599980
#> Warning: non-integer x = 56.500000
#> Warning: non-integer x = 72.299990
#> Warning: non-integer x = 95.099980
#> Warning: non-integer x = 105.699950
#> Warning: non-integer x = 37.799990
#> Warning: non-integer x = 43.299990
#> Warning: non-integer x = 51.500000
#> Warning: non-integer x = 63.699980
#> Warning: non-integer x = 70.500000
#> Warning: non-integer x = 80.399960
#> Warning: non-integer x = 106.099980
#> Warning: non-integer x = 29.500000
#> Warning: non-integer x = 31.399990
#> Warning: non-integer x = 39.399990
#> Warning: non-integer x = 44.799990
#> Warning: non-integer x = 50.299990
#> Warning: non-integer x = 65.599980
#> Warning: non-integer x = 72.399960
#> Warning: non-integer x = 80.199950
#> Warning: non-integer x = 90.399960
#> Warning: non-integer x = 99.099980
#> Warning: non-integer x = 22.799990
#> Warning: non-integer x = 33.899990
#> Warning: non-integer x = 37.699980
#> Warning: non-integer x = 41.399990
#> Warning: non-integer x = 48.199980
#> Warning: non-integer x = 53.699980
#> Warning: non-integer x = 62.599980
#> Warning: non-integer x = 70.399960
#> Warning: non-integer x = 78.500000
#> Warning: non-integer x = 85.899960
#> Warning: non-integer x = 22.299990
#> Warning: non-integer x = 24.700000
#> Warning: non-integer x = 30.399990
#> Warning: non-integer x = 36.899990
#> Warning: non-integer x = 44.099980
#> Warning: non-integer x = 52.799990
#> Warning: non-integer x = 60.299990
#> Warning: non-integer x = 67.799990
#> Warning: non-integer x = 75.399960
#> Warning: non-integer x = 87.599980
#> Warning: non-integer x = 101.399960
#> Warning: non-integer x = 23.799990
#> Warning: non-integer x = 37.099980
#> Warning: non-integer x = 43.199980
#> Warning: non-integer x = 50.399990
#> Warning: non-integer x = 60.199980
#> Warning: non-integer x = 82.399960
#> Warning: non-integer x = 91.199950
#> Warning: non-integer x = 101.799990
#> Warning: non-integer x = 109.599980
#> Warning: non-integer x = 25.799990
#> Warning: non-integer x = 29.200000
#> Warning: non-integer x = 35.799990
#> Warning: non-integer x = 41.099980
#> Warning: non-integer x = 55.199980
#> Warning: non-integer x = 62.199980
#> Warning: non-integer x = 69.799990
#> Warning: non-integer x = 76.399960
#> Warning: non-integer x = 83.199950
#> Warning: non-integer x = 93.199950
#> Warning: non-integer x = 32.899990
#> Warning: non-integer x = 46.199980
#> Warning: non-integer x = 53.500000
#> Warning: non-integer x = 58.599980
#> Warning: non-integer x = 68.199950
#> Warning: non-integer x = 80.799990
#> Warning: non-integer x = 84.500000
#> Warning: non-integer x = 24.799990
#> Warning: non-integer x = 35.799990
#> Warning: non-integer x = 42.299990
#> Warning: non-integer x = 50.899990
#> Warning: non-integer x = 57.799990
#> Warning: non-integer x = 64.799990
#> Warning: non-integer x = 71.799990
#> Warning: non-integer x = 83.799990
#> Warning: non-integer x = 92.099980
#> Warning: non-integer x = 26.200000
#> Warning: non-integer x = 30.399990
#> Warning: non-integer x = 37.399990
#> Warning: non-integer x = 49.500000
#> Warning: non-integer x = 55.099980
#> Warning: non-integer x = 64.199950
#> Warning: non-integer x = 75.599980
#> Warning: non-integer x = 83.299990
#> Warning: non-integer x = 87.399960
#> Warning: non-integer x = 94.699950
#> Warning: non-integer x = 98.399960
#> Warning: non-integer x = 32.500000
#> Warning: non-integer x = 38.799990
#> Warning: non-integer x = 47.799990
#> Warning: non-integer x = 54.500000
#> Warning: non-integer x = 70.099980
#> Warning: non-integer x = 76.599980
#> Warning: non-integer x = 86.199950
#> Warning: non-integer x = 95.799990
#> Warning: non-integer x = 101.399960
#> Warning: non-integer x = 112.299990
#> Warning: non-integer x = 32.399990
#> Warning: non-integer x = 38.199980
#> Warning: non-integer x = 44.699980
#> Warning: non-integer x = 53.199980
#> Warning: non-integer x = 62.399990
#> Warning: non-integer x = 70.500000
#> Warning: non-integer x = 72.799990
#> Warning: non-integer x = 86.599980
#> Warning: non-integer x = 93.299990
#> Warning: non-integer x = 104.199950
#> Warning: non-integer x = 27.399990
#> Warning: non-integer x = 32.199980
#> Warning: non-integer x = 37.899990
#> Warning: non-integer x = 45.899990
#> Warning: non-integer x = 51.199980
#> Warning: non-integer x = 57.099980
#> Warning: non-integer x = 76.799990
#> Warning: non-integer x = 83.099980
#> Warning: non-integer x = 91.599980
#> Warning: non-integer x = 100.500000
#> Warning: non-integer x = 105.299990
#> Warning: non-integer x = 27.099990
#> Warning: non-integer x = 30.299990
#> Warning: non-integer x = 38.199980
#> Warning: non-integer x = 43.199980
#> Warning: non-integer x = 52.500000
#> Warning: non-integer x = 67.299990
#> Warning: non-integer x = 74.199950
#> Warning: non-integer x = 81.199950
#> Warning: non-integer x = 87.500000
#> Warning: non-integer x = 94.399960
#> Warning: non-integer x = 101.399960
#> Warning: non-integer x = 26.799990
#> Warning: non-integer x = 31.099990
#> Warning: non-integer x = 37.799990
#> Warning: non-integer x = 44.599980
#> Warning: non-integer x = 50.500000
#> Warning: non-integer x = 58.299990
#> Warning: non-integer x = 68.299990
#> Warning: non-integer x = 75.099980
#> Warning: non-integer x = 84.399960
#> Warning: non-integer x = 87.299990
#> Warning: non-integer x = 96.399960
#> Warning: non-integer x = 104.399960
#> Warning: non-integer x = 24.500000
#> Warning: non-integer x = 31.599990
#> Warning: non-integer x = 37.399990
#> Warning: non-integer x = 46.399990
#> Warning: non-integer x = 53.599980
#> Warning: non-integer x = 61.199980
#> Warning: non-integer x = 70.099980
#> Warning: non-integer x = 77.500000
#> Warning: non-integer x = 86.199950
#> Warning: non-integer x = 89.199950
#> Warning: non-integer x = 96.899960
#> Warning: non-integer x = 104.500000
#> Warning: non-integer x = 23.099990
#> Warning: non-integer x = 30.099990
#> Warning: non-integer x = 40.699980
#> Warning: non-integer x = 46.599980
#> Warning: non-integer x = 52.099980
#> Warning: non-integer x = 60.500000
#> Warning: non-integer x = 73.500000
#> Warning: non-integer x = 77.299990
#> Warning: non-integer x = 86.899960
#> Warning: non-integer x = 96.399960
#> Warning: non-integer x = 21.500000
#> Warning: non-integer x = 24.599990
#> Warning: non-integer x = 28.500000
#> Warning: non-integer x = 39.099980
#> Warning: non-integer x = 45.299990
#> Warning: non-integer x = 59.599980
#> Warning: non-integer x = 69.500000
#> Warning: non-integer x = 75.199950
#> Warning: non-integer x = 84.899960
#> Warning: non-integer x = 93.399960
#> Warning: non-integer x = 99.299990
#> Warning: non-integer x = 24.099990
#> Warning: non-integer x = 28.099990
#> Warning: non-integer x = 32.500000
#> Warning: non-integer x = 40.599980
#> Warning: non-integer x = 53.799990
#> Warning: non-integer x = 61.199980
#> Warning: non-integer x = 71.899960
#> Warning: non-integer x = 79.500000
#> Warning: non-integer x = 87.399960
#> Warning: non-integer x = 93.299990
#> Warning: non-integer x = 101.599980
#> Warning: non-integer x = 34.199980
#> Warning: non-integer x = 42.099980
#> Warning: non-integer x = 50.099980
#> Warning: non-integer x = 57.599980
#> Warning: non-integer x = 62.299990
#> Warning: non-integer x = 76.099980
#> Warning: non-integer x = 81.500000
#> Warning: non-integer x = 84.299990
#> Warning: non-integer x = 97.899960
#> Warning: non-integer x = 108.599980
#> Warning: non-integer x = 25.099990
#> Warning: non-integer x = 23.200000
#> Warning: non-integer x = 28.899990
#> Warning: non-integer x = 36.799990
#> Warning: non-integer x = 44.199980
#> Warning: non-integer x = 52.799990
#> Warning: non-integer x = 62.199980
#> Warning: non-integer x = 69.399960
#> Warning: non-integer x = 78.099980
#> Warning: non-integer x = 88.799990
#> Warning: non-integer x = 102.399960
#> Warning: non-integer x = 106.799990
#> Warning: non-integer x = 32.199980
#> Warning: non-integer x = 36.399990
#> Warning: non-integer x = 41.799990
#> Warning: non-integer x = 48.199980
#> Warning: non-integer x = 55.899990
#> Warning: non-integer x = 60.099980
#> Warning: non-integer x = 68.500000
#> Warning: non-integer x = 77.799990
#> Warning: non-integer x = 86.399960
#> Warning: non-integer x = 96.699950
#> Warning: non-integer x = 111.099980
#> Warning: non-integer x = 115.399960
#> Warning: non-integer x = 24.700000
#> Warning: non-integer x = 28.899990
#> Warning: non-integer x = 34.599980
#> Warning: non-integer x = 42.199980
#> Warning: non-integer x = 48.199980
#> Warning: non-integer x = 54.399990
#> Warning: non-integer x = 62.500000
#> Warning: non-integer x = 69.799990
#> Warning: non-integer x = 78.599980
#> Warning: non-integer x = 96.399960
#> Warning: non-integer x = 103.199950
#> Warning: non-integer x = 24.200000
#> Warning: non-integer x = 29.200000
#> Warning: non-integer x = 36.199980
#> Warning: non-integer x = 43.099980
#> Warning: non-integer x = 49.199980
#> Warning: non-integer x = 70.899960
#> Warning: non-integer x = 87.199950
#> Warning: non-integer x = 94.699950
#> Warning: non-integer x = 100.599980
#> Warning: non-integer x = 24.500000
#> Warning: non-integer x = 28.399990
#> Warning: non-integer x = 41.899990
#> Warning: non-integer x = 55.599980
#> Warning: non-integer x = 64.099980
#> Warning: non-integer x = 71.199950
#> Warning: non-integer x = 80.500000
#> Warning: non-integer x = 90.199950
#> Warning: non-integer x = 98.899960
#> Warning: non-integer x = 103.799990
#> Warning: non-integer x = 26.599990
#> Warning: non-integer x = 33.099980
#> Warning: non-integer x = 38.399990
#> Warning: non-integer x = 46.599980
#> Warning: non-integer x = 52.299990
#> Warning: non-integer x = 61.500000
#> Warning: non-integer x = 69.299990
#> Warning: non-integer x = 74.199950
#> Warning: non-integer x = 80.199950
#> Warning: non-integer x = 87.199950
#> Warning: non-integer x = 94.799990
#> Warning: non-integer x = 26.799990
#> Warning: non-integer x = 33.599980
#> Warning: non-integer x = 42.099980
#> Warning: non-integer x = 47.899990
#> Warning: non-integer x = 56.199980
#> Warning: non-integer x = 63.399990
#> Warning: non-integer x = 71.799990
#> Warning: non-integer x = 87.599980
#> Warning: non-integer x = 94.899960
#> Warning: non-integer x = 30.599990
#> Warning: non-integer x = 37.599980
#> Warning: non-integer x = 42.799990
#> Warning: non-integer x = 47.399990
#> Warning: non-integer x = 56.599980
#> Warning: non-integer x = 62.399990
#> Warning: non-integer x = 71.799990
#> Warning: non-integer x = 86.799990
#> Warning: non-integer x = 94.199950
#> Warning: non-integer x = 101.899960
#> Warning: non-integer x = 112.500000
#> Warning: non-integer x = 21.899990
#> Warning: non-integer x = 26.799990
#> Warning: non-integer x = 34.699980
#> Warning: non-integer x = 41.299990
#> Warning: non-integer x = 48.699980
#> Warning: non-integer x = 57.899990
#> Warning: non-integer x = 65.399960
#> Warning: non-integer x = 71.299990
#> Warning: non-integer x = 80.599980
#> Warning: non-integer x = 88.399960
#> Warning: non-integer x = 96.299990
#> Warning: non-integer x = 103.500000
#> Warning: non-integer x = 26.799990
#> Warning: non-integer x = 39.099980
#> Warning: non-integer x = 46.399990
#> Warning: non-integer x = 61.599980
#> Warning: non-integer x = 68.799990
#> Warning: non-integer x = 72.199950
#> Warning: non-integer x = 77.199950
#> Warning: non-integer x = 83.799990
#> Warning: non-integer x = 90.799990
#> Warning: non-integer x = 24.200000
#> Warning: non-integer x = 25.399990
#> Warning: non-integer x = 30.700000
#> Warning: non-integer x = 35.599980
#> Warning: non-integer x = 42.799990
#> Warning: non-integer x = 49.500000
#> Warning: non-integer x = 57.199980
#> Warning: non-integer x = 65.599980
#> Warning: non-integer x = 72.399960
#> Warning: non-integer x = 81.199950
#> Warning: non-integer x = 85.199950
#> Warning: non-integer x = 90.199950
#> Warning: non-integer x = 25.200000
#> Warning: non-integer x = 29.799990
#> Warning: non-integer x = 35.699980
#> Warning: non-integer x = 55.899990
#> Warning: non-integer x = 63.500000
#> Warning: non-integer x = 79.500000
#> Warning: non-integer x = 83.599980
#> Warning: non-integer x = 89.399960
#> Warning: non-integer x = 98.500000
#> Warning: non-integer x = 23.500000
#> Warning: non-integer x = 25.899990
#> Warning: non-integer x = 32.199980
#> Warning: non-integer x = 32.399990
#> Warning: non-integer x = 29.799990
#> Warning: non-integer x = 32.799990
#> Warning: non-integer x = 56.899990
#> Warning: non-integer x = 64.799990
#> Warning: non-integer x = 72.099980
#> Warning: non-integer x = 81.399960
#> Warning: non-integer x = 26.599990
#> Warning: non-integer x = 38.199980
#> Warning: non-integer x = 46.399990
#> Warning: non-integer x = 53.199980
#> Warning: non-integer x = 59.599980
#> Warning: non-integer x = 66.199950
#> Warning: non-integer x = 72.599980
#> Warning: non-integer x = 80.099980
#> Warning: non-integer x = 97.699950
#> Warning: non-integer x = 35.399990
#> Warning: non-integer x = 42.299990
#> Warning: non-integer x = 49.500000
#> Warning: non-integer x = 58.699980
#> Warning: non-integer x = 66.599980
#> Warning: non-integer x = 71.399960
#> Warning: non-integer x = 78.799990
#> Warning: non-integer x = 85.500000
#> Warning: non-integer x = 91.299990
#> Warning: non-integer x = 97.799990
#> Warning: non-integer x = 29.299990
#> Warning: non-integer x = 45.399990
#> Warning: non-integer x = 51.799990
#> Warning: non-integer x = 58.799990
#> Warning: non-integer x = 62.599980
#> Warning: non-integer x = 71.599980
#> Warning: non-integer x = 76.699950
#> Warning: non-integer x = 81.699950
#> Warning: non-integer x = 86.399960
#> Warning: non-integer x = 92.099980
#> Warning: non-integer x = 25.299990
#> Warning: non-integer x = 31.599990
#> Warning: non-integer x = 35.199980
#> Warning: non-integer x = 37.299990
#> Warning: non-integer x = 40.799990
#> Warning: non-integer x = 47.699980
#> Warning: non-integer x = 64.599980
#> Warning: non-integer x = 71.199950
#> Warning: non-integer x = 80.500000
#> Warning: non-integer x = 85.899960
#> Warning: non-integer x = 22.099990
#> Warning: non-integer x = 26.299990
#> Warning: non-integer x = 33.299990
#> Warning: non-integer x = 39.599980
#> Warning: non-integer x = 41.399990
#> Warning: non-integer x = 46.299990
#> Warning: non-integer x = 52.399990
#> Warning: non-integer x = 59.399990
#> Warning: non-integer x = 66.699950
#> Warning: non-integer x = 73.899960
#> Warning: non-integer x = 76.799990
#> Warning: non-integer x = 23.700000
#> Warning: non-integer x = 28.799990
#> Warning: non-integer x = 35.099980
#> Warning: non-integer x = 49.099980
#> Warning: non-integer x = 58.799990
#> Warning: non-integer x = 65.399960
#> Warning: non-integer x = 68.500000
#> Warning: non-integer x = 90.699950
#> Warning: non-integer x = 28.899990
#> Warning: non-integer x = 35.799990
#> Warning: non-integer x = 47.500000
#> Warning: non-integer x = 56.399990
#> Warning: non-integer x = 63.699980
#> Warning: non-integer x = 70.299990
#> Warning: non-integer x = 89.199950
#> Warning: non-integer x = 96.299990
#> Warning: non-integer x = 99.799990
#> Warning: non-integer x = 30.099990
#> Warning: non-integer x = 37.099980
#> Warning: non-integer x = 53.599980
#> Warning: non-integer x = 61.099980
#> Warning: non-integer x = 78.199950
#> Warning: non-integer x = 87.099980
#> Warning: non-integer x = 94.399960
#> Warning: non-integer x = 102.500000
#> Warning: non-integer x = 107.500000
#> Warning: non-integer x = 35.399990
#> Warning: non-integer x = 48.599980
#> Warning: non-integer x = 56.399990
#> Warning: non-integer x = 75.500000
#> Warning: non-integer x = 77.799990
#> Warning: non-integer x = 85.799990
#> Warning: non-integer x = 101.399960
#> Warning: non-integer x = 27.299990
#> Warning: non-integer x = 31.200000
#> Warning: non-integer x = 43.899990
#> Warning: non-integer x = 49.799990
#> Warning: non-integer x = 57.199980
#> Warning: non-integer x = 65.199950
#> Warning: non-integer x = 73.199950
#> Warning: non-integer x = 78.799990
#> Warning: non-integer x = 87.399960
#> Warning: non-integer x = 100.500000
#> Warning: non-integer x = 25.700000
#> Warning: non-integer x = 28.700000
#> Warning: non-integer x = 33.399990
#> Warning: non-integer x = 46.699980
#> Warning: non-integer x = 56.599980
#> Warning: non-integer x = 65.199950
#> Warning: non-integer x = 73.199950
#> Warning: non-integer x = 81.699950
#> Warning: non-integer x = 90.299990
#> Warning: non-integer x = 103.500000
gee1
#> 
#> Call:
#> geeglm(formula = mf, family = poisson("identity"), data = dietox, 
#>     id = Pig, corstr = "ar1")
#> 
#> Coefficients:
#>       (Intercept)           CuCu035           CuCu175              Time 
#>     21.8578677803      0.5267336747      0.0427835423      2.8851574386 
#>         I(Time^2)         I(Time^3)      CuCu035:Time      CuCu175:Time 
#>      0.6140424145     -0.0262947719     -0.4054242617      0.8569406775 
#> CuCu035:I(Time^2) CuCu175:I(Time^2) CuCu035:I(Time^3) CuCu175:I(Time^3) 
#>      0.0182862906     -0.0960713285      0.0005466981      0.0026996115 
#> 
#> Degrees of Freedom: 861 Total (i.e. Null);  849 Residual
#> 
#> Scale Link:                   identity
#> Estimated Scale Parameters:  [1] 0.7752475
#> 
#> Correlation:  Structure = ar1    Link = identity 
#> Estimated Correlation Parameters:
#>     alpha 
#> 0.9572319 
#> 
#> Number of clusters:   72   Maximum cluster size: 12 
#> 
coef(gee1)
#>       (Intercept)           CuCu035           CuCu175              Time 
#>     21.8578677803      0.5267336747      0.0427835423      2.8851574386 
#>         I(Time^2)         I(Time^3)      CuCu035:Time      CuCu175:Time 
#>      0.6140424145     -0.0262947719     -0.4054242617      0.8569406775 
#> CuCu035:I(Time^2) CuCu175:I(Time^2) CuCu035:I(Time^3) CuCu175:I(Time^3) 
#>      0.0182862906     -0.0960713285      0.0005466981      0.0026996115 
vcov(gee1)
#>                     (Intercept)       CuCu035       CuCu175          Time
#> (Intercept)        0.4804492833 -0.4804492833 -0.4804492833 -0.0379583612
#> CuCu035           -0.4804492833  0.8861597346  0.4804492833  0.0379583612
#> CuCu175           -0.4804492833  0.4804492833  1.0396808258  0.0379583612
#> Time              -0.0379583612  0.0379583612  0.0379583612  0.1297852777
#> I(Time^2)          0.0064482049 -0.0064482049 -0.0064482049 -0.0218859094
#> I(Time^3)         -0.0002843285  0.0002843285  0.0002843285  0.0009913586
#> CuCu035:Time       0.0379583612 -0.1826073981 -0.0379583612 -0.1297852777
#> CuCu175:Time       0.0379583612 -0.0379583612 -0.0454849148 -0.1297852777
#> CuCu035:I(Time^2) -0.0064482049  0.0324190156  0.0064482049  0.0218859094
#> CuCu175:I(Time^2) -0.0064482049  0.0064482049  0.0208669227  0.0218859094
#> CuCu035:I(Time^3)  0.0002843285 -0.0014000132 -0.0002843285 -0.0009913586
#> CuCu175:I(Time^3)  0.0002843285 -0.0002843285 -0.0011476694 -0.0009913586
#>                       I(Time^2)     I(Time^3)  CuCu035:Time  CuCu175:Time
#> (Intercept)        0.0064482049 -2.843285e-04  0.0379583612  0.0379583612
#> CuCu035           -0.0064482049  2.843285e-04 -0.1826073981 -0.0379583612
#> CuCu175           -0.0064482049  2.843285e-04 -0.0379583612 -0.0454849148
#> Time              -0.0218859094  9.913586e-04 -0.1297852777 -0.1297852777
#> I(Time^2)          0.0049230324 -2.575246e-04  0.0218859094  0.0218859094
#> I(Time^3)         -0.0002575246  1.460603e-05 -0.0009913586 -0.0009913586
#> CuCu035:Time       0.0218859094 -9.913586e-04  0.4059283136  0.1297852777
#> CuCu175:Time       0.0218859094 -9.913586e-04  0.1297852777  0.3789933839
#> CuCu035:I(Time^2) -0.0049230324  2.575246e-04 -0.0652565891 -0.0218859094
#> CuCu175:I(Time^2) -0.0049230324  2.575246e-04 -0.0218859094 -0.0612973102
#> CuCu035:I(Time^3)  0.0002575246 -1.460603e-05  0.0028757555  0.0009913586
#> CuCu175:I(Time^3)  0.0002575246 -1.460603e-05  0.0009913586  0.0027682832
#>                   CuCu035:I(Time^2) CuCu175:I(Time^2) CuCu035:I(Time^3)
#> (Intercept)           -0.0064482049     -0.0064482049      2.843285e-04
#> CuCu035                0.0324190156      0.0064482049     -1.400013e-03
#> CuCu175                0.0064482049      0.0208669227     -2.843285e-04
#> Time                   0.0218859094      0.0218859094     -9.913586e-04
#> I(Time^2)             -0.0049230324     -0.0049230324      2.575246e-04
#> I(Time^3)              0.0002575246      0.0002575246     -1.460603e-05
#> CuCu035:Time          -0.0652565891     -0.0218859094      2.875755e-03
#> CuCu175:Time          -0.0218859094     -0.0612973102      9.913586e-04
#> CuCu035:I(Time^2)      0.0133246877      0.0049230324     -6.670129e-04
#> CuCu175:I(Time^2)      0.0049230324      0.0122765730     -2.575246e-04
#> CuCu035:I(Time^3)     -0.0006670129     -0.0002575246      3.587529e-05
#> CuCu175:I(Time^3)     -0.0002575246     -0.0006069731      1.460603e-05
#>                   CuCu175:I(Time^3)
#> (Intercept)            2.843285e-04
#> CuCu035               -2.843285e-04
#> CuCu175               -1.147669e-03
#> Time                  -9.913586e-04
#> I(Time^2)              2.575246e-04
#> I(Time^3)             -1.460603e-05
#> CuCu035:Time           9.913586e-04
#> CuCu175:Time           2.768283e-03
#> CuCu035:I(Time^2)     -2.575246e-04
#> CuCu175:I(Time^2)     -6.069731e-04
#> CuCu035:I(Time^3)      1.460603e-05
#> CuCu175:I(Time^3)      3.192473e-05
summary(gee1)
#> 
#> Call:
#> geeglm(formula = mf, family = poisson("identity"), data = dietox, 
#>     id = Pig, corstr = "ar1")
#> 
#>  Coefficients:
#>                     Estimate    Std.err    Wald Pr(>|W|)    
#> (Intercept)       21.8578678  0.6931445 994.416  < 2e-16 ***
#> CuCu035            0.5267337  0.9413606   0.313    0.576    
#> CuCu175            0.0427835  1.0196474   0.002    0.967    
#> Time               2.8851574  0.3602572  64.138 1.11e-15 ***
#> I(Time^2)          0.6140424  0.0701643  76.589  < 2e-16 ***
#> I(Time^3)         -0.0262948  0.0038218  47.338 5.98e-12 ***
#> CuCu035:Time      -0.4054243  0.6371250   0.405    0.525    
#> CuCu175:Time       0.8569407  0.6156244   1.938    0.164    
#> CuCu035:I(Time^2)  0.0182863  0.1154326   0.025    0.874    
#> CuCu175:I(Time^2) -0.0960713  0.1107997   0.752    0.386    
#> CuCu035:I(Time^3)  0.0005467  0.0059896   0.008    0.927    
#> CuCu175:I(Time^3)  0.0026996  0.0056502   0.228    0.633    
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#> 
#> Correlation structure = ar1 
#> Estimated Scale Parameters:
#> 
#>             Estimate Std.err
#> (Intercept)   0.7752  0.1416
#>   Link = identity 
#> 
#> Estimated Correlation Parameters:
#>       Estimate  Std.err
#> alpha   0.9572 0.009788
#> Number of clusters:   72  Maximum cluster size: 12 
coef(summary(gee1))
#>                     Estimate  Std.err      Wald  Pr(>|W|)
#> (Intercept)       21.8578678 0.693144 9.944e+02 0.000e+00
#> CuCu035            0.5267337 0.941361 3.131e-01 5.758e-01
#> CuCu175            0.0427835 1.019647 1.761e-03 9.665e-01
#> Time               2.8851574 0.360257 6.414e+01 1.110e-15
#> I(Time^2)          0.6140424 0.070164 7.659e+01 0.000e+00
#> I(Time^3)         -0.0262948 0.003822 4.734e+01 5.975e-12
#> CuCu035:Time      -0.4054243 0.637125 4.049e-01 5.246e-01
#> CuCu175:Time       0.8569407 0.615624 1.938e+00 1.639e-01
#> CuCu035:I(Time^2)  0.0182863 0.115433 2.510e-02 8.741e-01
#> CuCu175:I(Time^2) -0.0960713 0.110800 7.518e-01 3.859e-01
#> CuCu035:I(Time^3)  0.0005467 0.005990 8.331e-03 9.273e-01
#> CuCu175:I(Time^3)  0.0026996 0.005650 2.283e-01 6.328e-01

mf2 <- formula(Weight ~ Cu * Time + I(Time^2) + I(Time^3))
gee2 <- geeglm(mf2, data=dietox, id=Pig, family=poisson("identity"), corstr="ar1")
#> Warning: non-integer x = 26.500000
#> Warning: non-integer x = 27.599990
#> Warning: non-integer x = 36.500000
#> Warning: non-integer x = 40.299990
#> Warning: non-integer x = 49.099980
#> Warning: non-integer x = 55.399990
#> Warning: non-integer x = 59.599980
#> Warning: non-integer x = 76.599980
#> Warning: non-integer x = 86.500000
#> Warning: non-integer x = 91.599980
#> Warning: non-integer x = 98.599980
#> Warning: non-integer x = 28.299990
#> Warning: non-integer x = 30.099990
#> Warning: non-integer x = 38.299990
#> Warning: non-integer x = 44.500000
#> Warning: non-integer x = 51.599980
#> Warning: non-integer x = 57.599980
#> Warning: non-integer x = 82.299990
#> Warning: non-integer x = 99.699950
#> Warning: non-integer x = 106.699950
#> Warning: non-integer x = 27.599990
#> Warning: non-integer x = 30.599990
#> Warning: non-integer x = 38.699980
#> Warning: non-integer x = 47.199980
#> Warning: non-integer x = 54.099980
#> Warning: non-integer x = 61.500000
#> Warning: non-integer x = 68.500000
#> Warning: non-integer x = 75.199950
#> Warning: non-integer x = 81.699950
#> Warning: non-integer x = 90.199950
#> Warning: non-integer x = 98.399960
#> Warning: non-integer x = 105.399960
#> Warning: non-integer x = 31.500000
#> Warning: non-integer x = 34.799990
#> Warning: non-integer x = 40.699980
#> Warning: non-integer x = 47.699980
#> Warning: non-integer x = 55.899990
#> Warning: non-integer x = 62.199980
#> Warning: non-integer x = 70.699950
#> Warning: non-integer x = 86.199950
#> Warning: non-integer x = 94.699950
#> Warning: non-integer x = 109.199950
#> Warning: non-integer x = 27.099990
#> Warning: non-integer x = 42.500000
#> Warning: non-integer x = 50.099980
#> Warning: non-integer x = 56.500000
#> Warning: non-integer x = 72.500000
#> Warning: non-integer x = 80.500000
#> Warning: non-integer x = 108.399960
#> Warning: non-integer x = 31.799990
#> Warning: non-integer x = 44.799990
#> Warning: non-integer x = 50.899990
#> Warning: non-integer x = 57.399990
#> Warning: non-integer x = 62.500000
#> Warning: non-integer x = 71.699950
#> Warning: non-integer x = 78.199950
#> Warning: non-integer x = 85.799990
#> Warning: non-integer x = 91.799990
#> Warning: non-integer x = 100.199950
#> Warning: non-integer x = 27.700000
#> Warning: non-integer x = 33.599980
#> Warning: non-integer x = 46.699980
#> Warning: non-integer x = 54.799990
#> Warning: non-integer x = 69.799990
#> Warning: non-integer x = 83.599980
#> Warning: non-integer x = 88.199950
#> Warning: non-integer x = 96.799990
#> Warning: non-integer x = 102.299990
#> Warning: non-integer x = 23.599990
#> Warning: non-integer x = 36.299990
#> Warning: non-integer x = 42.399990
#> Warning: non-integer x = 50.500000
#> Warning: non-integer x = 57.599980
#> Warning: non-integer x = 66.599980
#> Warning: non-integer x = 74.199950
#> Warning: non-integer x = 89.299990
#> Warning: non-integer x = 26.899990
#> Warning: non-integer x = 32.299990
#> Warning: non-integer x = 38.599980
#> Warning: non-integer x = 57.799990
#> Warning: non-integer x = 58.599980
#> Warning: non-integer x = 65.899960
#> Warning: non-integer x = 71.199950
#> Warning: non-integer x = 79.399960
#> Warning: non-integer x = 91.699950
#> Warning: non-integer x = 22.599990
#> Warning: non-integer x = 28.500000
#> Warning: non-integer x = 32.699980
#> Warning: non-integer x = 39.899990
#> Warning: non-integer x = 47.599980
#> Warning: non-integer x = 53.799990
#> Warning: non-integer x = 67.199950
#> Warning: non-integer x = 74.099980
#> Warning: non-integer x = 89.399960
#> Warning: non-integer x = 93.500000
#> Warning: non-integer x = 19.399990
#> Warning: non-integer x = 21.399990
#> Warning: non-integer x = 25.299990
#> Warning: non-integer x = 31.899990
#> Warning: non-integer x = 37.599980
#> Warning: non-integer x = 43.699980
#> Warning: non-integer x = 48.899990
#> Warning: non-integer x = 53.699980
#> Warning: non-integer x = 59.299990
#> Warning: non-integer x = 64.899960
#> Warning: non-integer x = 65.799990
#> Warning: non-integer x = 27.299990
#> Warning: non-integer x = 32.399990
#> Warning: non-integer x = 38.299990
#> Warning: non-integer x = 45.799990
#> Warning: non-integer x = 53.799990
#> Warning: non-integer x = 68.699950
#> Warning: non-integer x = 75.799990
#> Warning: non-integer x = 80.799990
#> Warning: non-integer x = 86.799990
#> Warning: non-integer x = 91.399960
#> Warning: non-integer x = 99.799990
#> Warning: non-integer x = 26.200000
#> Warning: non-integer x = 31.099990
#> Warning: non-integer x = 34.599980
#> Warning: non-integer x = 41.199980
#> Warning: non-integer x = 49.199980
#> Warning: non-integer x = 55.599980
#> Warning: non-integer x = 62.599980
#> Warning: non-integer x = 72.099980
#> Warning: non-integer x = 77.500000
#> Warning: non-integer x = 83.799990
#> Warning: non-integer x = 93.399960
#> Warning: non-integer x = 98.399960
#> Warning: non-integer x = 24.899990
#> Warning: non-integer x = 29.700000
#> Warning: non-integer x = 33.799990
#> Warning: non-integer x = 38.799990
#> Warning: non-integer x = 48.299990
#> Warning: non-integer x = 52.899990
#> Warning: non-integer x = 70.399960
#> Warning: non-integer x = 76.799990
#> Warning: non-integer x = 83.299990
#> Warning: non-integer x = 102.699950
#> Warning: non-integer x = 24.599990
#> Warning: non-integer x = 34.599980
#> Warning: non-integer x = 41.500000
#> Warning: non-integer x = 49.699980
#> Warning: non-integer x = 56.500000
#> Warning: non-integer x = 66.899960
#> Warning: non-integer x = 75.799990
#> Warning: non-integer x = 84.599980
#> Warning: non-integer x = 98.799990
#> Warning: non-integer x = 107.199950
#> Warning: non-integer x = 32.699980
#> Warning: non-integer x = 38.299990
#> Warning: non-integer x = 45.500000
#> Warning: non-integer x = 48.599980
#> Warning: non-integer x = 62.599980
#> Warning: non-integer x = 70.199950
#> Warning: non-integer x = 73.799990
#> Warning: non-integer x = 80.299990
#> Warning: non-integer x = 85.500000
#> Warning: non-integer x = 93.099980
#> Warning: non-integer x = 35.199980
#> Warning: non-integer x = 41.500000
#> Warning: non-integer x = 47.699980
#> Warning: non-integer x = 53.799990
#> Warning: non-integer x = 61.599980
#> Warning: non-integer x = 79.099980
#> Warning: non-integer x = 85.699950
#> Warning: non-integer x = 92.500000
#> Warning: non-integer x = 101.099980
#> Warning: non-integer x = 34.500000
#> Warning: non-integer x = 40.399990
#> Warning: non-integer x = 53.500000
#> Warning: non-integer x = 60.199980
#> Warning: non-integer x = 68.599980
#> Warning: non-integer x = 73.399960
#> Warning: non-integer x = 78.500000
#> Warning: non-integer x = 90.599980
#> Warning: non-integer x = 97.199950
#> Warning: non-integer x = 31.200000
#> Warning: non-integer x = 38.799990
#> Warning: non-integer x = 44.699980
#> Warning: non-integer x = 53.599980
#> Warning: non-integer x = 59.199980
#> Warning: non-integer x = 67.099980
#> Warning: non-integer x = 76.399960
#> Warning: non-integer x = 83.799990
#> Warning: non-integer x = 71.599980
#> Warning: non-integer x = 97.399960
#> Warning: non-integer x = 107.099980
#> Warning: non-integer x = 24.299990
#> Warning: non-integer x = 28.399990
#> Warning: non-integer x = 40.299990
#> Warning: non-integer x = 46.199980
#> Warning: non-integer x = 51.899990
#> Warning: non-integer x = 58.099980
#> Warning: non-integer x = 62.599980
#> Warning: non-integer x = 68.199950
#> Warning: non-integer x = 78.399960
#> Warning: non-integer x = 87.500000
#> Warning: non-integer x = 90.399960
#> Warning: non-integer x = 24.599990
#> Warning: non-integer x = 25.799990
#> Warning: non-integer x = 28.599990
#> Warning: non-integer x = 30.399990
#> Warning: non-integer x = 36.099980
#> Warning: non-integer x = 36.099980
#> Warning: non-integer x = 49.299990
#> Warning: non-integer x = 57.899990
#> Warning: non-integer x = 75.699950
#> Warning: non-integer x = 81.399960
#> Warning: non-integer x = 88.699950
#> Warning: non-integer x = 21.200000
#> Warning: non-integer x = 25.799990
#> Warning: non-integer x = 29.399990
#> Warning: non-integer x = 36.799990
#> Warning: non-integer x = 43.199980
#> Warning: non-integer x = 51.099980
#> Warning: non-integer x = 59.299990
#> Warning: non-integer x = 72.799990
#> Warning: non-integer x = 78.599980
#> Warning: non-integer x = 93.799990
#> Warning: non-integer x = 95.199950
#> Warning: non-integer x = 29.399990
#> Warning: non-integer x = 34.599980
#> Warning: non-integer x = 40.599980
#> Warning: non-integer x = 46.599980
#> Warning: non-integer x = 62.500000
#> Warning: non-integer x = 78.299990
#> Warning: non-integer x = 83.199950
#> Warning: non-integer x = 34.699980
#> Warning: non-integer x = 42.799990
#> Warning: non-integer x = 48.399990
#> Warning: non-integer x = 53.299990
#> Warning: non-integer x = 71.099980
#> Warning: non-integer x = 77.399960
#> Warning: non-integer x = 94.500000
#> Warning: non-integer x = 104.599980
#> Warning: non-integer x = 29.599990
#> Warning: non-integer x = 34.199980
#> Warning: non-integer x = 63.500000
#> Warning: non-integer x = 72.699950
#> Warning: non-integer x = 78.699950
#> Warning: non-integer x = 84.899960
#> Warning: non-integer x = 96.399960
#> Warning: non-integer x = 100.199950
#> Warning: non-integer x = 22.399990
#> Warning: non-integer x = 25.200000
#> Warning: non-integer x = 36.500000
#> Warning: non-integer x = 43.299990
#> Warning: non-integer x = 58.099980
#> Warning: non-integer x = 70.699950
#> Warning: non-integer x = 78.099980
#> Warning: non-integer x = 83.500000
#> Warning: non-integer x = 26.599990
#> Warning: non-integer x = 28.200000
#> Warning: non-integer x = 38.399990
#> Warning: non-integer x = 45.799990
#> Warning: non-integer x = 54.899990
#> Warning: non-integer x = 60.099980
#> Warning: non-integer x = 56.899990
#> Warning: non-integer x = 64.899960
#> Warning: non-integer x = 81.899960
#> Warning: non-integer x = 90.899960
#> Warning: non-integer x = 28.200000
#> Warning: non-integer x = 35.299990
#> Warning: non-integer x = 42.699980
#> Warning: non-integer x = 48.199980
#> Warning: non-integer x = 53.199980
#> Warning: non-integer x = 64.799990
#> Warning: non-integer x = 71.500000
#> Warning: non-integer x = 76.099980
#> Warning: non-integer x = 86.099980
#> Warning: non-integer x = 92.500000
#> Warning: non-integer x = 27.099990
#> Warning: non-integer x = 34.699980
#> Warning: non-integer x = 40.699980
#> Warning: non-integer x = 47.599980
#> Warning: non-integer x = 56.500000
#> Warning: non-integer x = 72.299990
#> Warning: non-integer x = 95.099980
#> Warning: non-integer x = 105.699950
#> Warning: non-integer x = 37.799990
#> Warning: non-integer x = 43.299990
#> Warning: non-integer x = 51.500000
#> Warning: non-integer x = 63.699980
#> Warning: non-integer x = 70.500000
#> Warning: non-integer x = 80.399960
#> Warning: non-integer x = 106.099980
#> Warning: non-integer x = 29.500000
#> Warning: non-integer x = 31.399990
#> Warning: non-integer x = 39.399990
#> Warning: non-integer x = 44.799990
#> Warning: non-integer x = 50.299990
#> Warning: non-integer x = 65.599980
#> Warning: non-integer x = 72.399960
#> Warning: non-integer x = 80.199950
#> Warning: non-integer x = 90.399960
#> Warning: non-integer x = 99.099980
#> Warning: non-integer x = 22.799990
#> Warning: non-integer x = 33.899990
#> Warning: non-integer x = 37.699980
#> Warning: non-integer x = 41.399990
#> Warning: non-integer x = 48.199980
#> Warning: non-integer x = 53.699980
#> Warning: non-integer x = 62.599980
#> Warning: non-integer x = 70.399960
#> Warning: non-integer x = 78.500000
#> Warning: non-integer x = 85.899960
#> Warning: non-integer x = 22.299990
#> Warning: non-integer x = 24.700000
#> Warning: non-integer x = 30.399990
#> Warning: non-integer x = 36.899990
#> Warning: non-integer x = 44.099980
#> Warning: non-integer x = 52.799990
#> Warning: non-integer x = 60.299990
#> Warning: non-integer x = 67.799990
#> Warning: non-integer x = 75.399960
#> Warning: non-integer x = 87.599980
#> Warning: non-integer x = 101.399960
#> Warning: non-integer x = 23.799990
#> Warning: non-integer x = 37.099980
#> Warning: non-integer x = 43.199980
#> Warning: non-integer x = 50.399990
#> Warning: non-integer x = 60.199980
#> Warning: non-integer x = 82.399960
#> Warning: non-integer x = 91.199950
#> Warning: non-integer x = 101.799990
#> Warning: non-integer x = 109.599980
#> Warning: non-integer x = 25.799990
#> Warning: non-integer x = 29.200000
#> Warning: non-integer x = 35.799990
#> Warning: non-integer x = 41.099980
#> Warning: non-integer x = 55.199980
#> Warning: non-integer x = 62.199980
#> Warning: non-integer x = 69.799990
#> Warning: non-integer x = 76.399960
#> Warning: non-integer x = 83.199950
#> Warning: non-integer x = 93.199950
#> Warning: non-integer x = 32.899990
#> Warning: non-integer x = 46.199980
#> Warning: non-integer x = 53.500000
#> Warning: non-integer x = 58.599980
#> Warning: non-integer x = 68.199950
#> Warning: non-integer x = 80.799990
#> Warning: non-integer x = 84.500000
#> Warning: non-integer x = 24.799990
#> Warning: non-integer x = 35.799990
#> Warning: non-integer x = 42.299990
#> Warning: non-integer x = 50.899990
#> Warning: non-integer x = 57.799990
#> Warning: non-integer x = 64.799990
#> Warning: non-integer x = 71.799990
#> Warning: non-integer x = 83.799990
#> Warning: non-integer x = 92.099980
#> Warning: non-integer x = 26.200000
#> Warning: non-integer x = 30.399990
#> Warning: non-integer x = 37.399990
#> Warning: non-integer x = 49.500000
#> Warning: non-integer x = 55.099980
#> Warning: non-integer x = 64.199950
#> Warning: non-integer x = 75.599980
#> Warning: non-integer x = 83.299990
#> Warning: non-integer x = 87.399960
#> Warning: non-integer x = 94.699950
#> Warning: non-integer x = 98.399960
#> Warning: non-integer x = 32.500000
#> Warning: non-integer x = 38.799990
#> Warning: non-integer x = 47.799990
#> Warning: non-integer x = 54.500000
#> Warning: non-integer x = 70.099980
#> Warning: non-integer x = 76.599980
#> Warning: non-integer x = 86.199950
#> Warning: non-integer x = 95.799990
#> Warning: non-integer x = 101.399960
#> Warning: non-integer x = 112.299990
#> Warning: non-integer x = 32.399990
#> Warning: non-integer x = 38.199980
#> Warning: non-integer x = 44.699980
#> Warning: non-integer x = 53.199980
#> Warning: non-integer x = 62.399990
#> Warning: non-integer x = 70.500000
#> Warning: non-integer x = 72.799990
#> Warning: non-integer x = 86.599980
#> Warning: non-integer x = 93.299990
#> Warning: non-integer x = 104.199950
#> Warning: non-integer x = 27.399990
#> Warning: non-integer x = 32.199980
#> Warning: non-integer x = 37.899990
#> Warning: non-integer x = 45.899990
#> Warning: non-integer x = 51.199980
#> Warning: non-integer x = 57.099980
#> Warning: non-integer x = 76.799990
#> Warning: non-integer x = 83.099980
#> Warning: non-integer x = 91.599980
#> Warning: non-integer x = 100.500000
#> Warning: non-integer x = 105.299990
#> Warning: non-integer x = 27.099990
#> Warning: non-integer x = 30.299990
#> Warning: non-integer x = 38.199980
#> Warning: non-integer x = 43.199980
#> Warning: non-integer x = 52.500000
#> Warning: non-integer x = 67.299990
#> Warning: non-integer x = 74.199950
#> Warning: non-integer x = 81.199950
#> Warning: non-integer x = 87.500000
#> Warning: non-integer x = 94.399960
#> Warning: non-integer x = 101.399960
#> Warning: non-integer x = 26.799990
#> Warning: non-integer x = 31.099990
#> Warning: non-integer x = 37.799990
#> Warning: non-integer x = 44.599980
#> Warning: non-integer x = 50.500000
#> Warning: non-integer x = 58.299990
#> Warning: non-integer x = 68.299990
#> Warning: non-integer x = 75.099980
#> Warning: non-integer x = 84.399960
#> Warning: non-integer x = 87.299990
#> Warning: non-integer x = 96.399960
#> Warning: non-integer x = 104.399960
#> Warning: non-integer x = 24.500000
#> Warning: non-integer x = 31.599990
#> Warning: non-integer x = 37.399990
#> Warning: non-integer x = 46.399990
#> Warning: non-integer x = 53.599980
#> Warning: non-integer x = 61.199980
#> Warning: non-integer x = 70.099980
#> Warning: non-integer x = 77.500000
#> Warning: non-integer x = 86.199950
#> Warning: non-integer x = 89.199950
#> Warning: non-integer x = 96.899960
#> Warning: non-integer x = 104.500000
#> Warning: non-integer x = 23.099990
#> Warning: non-integer x = 30.099990
#> Warning: non-integer x = 40.699980
#> Warning: non-integer x = 46.599980
#> Warning: non-integer x = 52.099980
#> Warning: non-integer x = 60.500000
#> Warning: non-integer x = 73.500000
#> Warning: non-integer x = 77.299990
#> Warning: non-integer x = 86.899960
#> Warning: non-integer x = 96.399960
#> Warning: non-integer x = 21.500000
#> Warning: non-integer x = 24.599990
#> Warning: non-integer x = 28.500000
#> Warning: non-integer x = 39.099980
#> Warning: non-integer x = 45.299990
#> Warning: non-integer x = 59.599980
#> Warning: non-integer x = 69.500000
#> Warning: non-integer x = 75.199950
#> Warning: non-integer x = 84.899960
#> Warning: non-integer x = 93.399960
#> Warning: non-integer x = 99.299990
#> Warning: non-integer x = 24.099990
#> Warning: non-integer x = 28.099990
#> Warning: non-integer x = 32.500000
#> Warning: non-integer x = 40.599980
#> Warning: non-integer x = 53.799990
#> Warning: non-integer x = 61.199980
#> Warning: non-integer x = 71.899960
#> Warning: non-integer x = 79.500000
#> Warning: non-integer x = 87.399960
#> Warning: non-integer x = 93.299990
#> Warning: non-integer x = 101.599980
#> Warning: non-integer x = 34.199980
#> Warning: non-integer x = 42.099980
#> Warning: non-integer x = 50.099980
#> Warning: non-integer x = 57.599980
#> Warning: non-integer x = 62.299990
#> Warning: non-integer x = 76.099980
#> Warning: non-integer x = 81.500000
#> Warning: non-integer x = 84.299990
#> Warning: non-integer x = 97.899960
#> Warning: non-integer x = 108.599980
#> Warning: non-integer x = 25.099990
#> Warning: non-integer x = 23.200000
#> Warning: non-integer x = 28.899990
#> Warning: non-integer x = 36.799990
#> Warning: non-integer x = 44.199980
#> Warning: non-integer x = 52.799990
#> Warning: non-integer x = 62.199980
#> Warning: non-integer x = 69.399960
#> Warning: non-integer x = 78.099980
#> Warning: non-integer x = 88.799990
#> Warning: non-integer x = 102.399960
#> Warning: non-integer x = 106.799990
#> Warning: non-integer x = 32.199980
#> Warning: non-integer x = 36.399990
#> Warning: non-integer x = 41.799990
#> Warning: non-integer x = 48.199980
#> Warning: non-integer x = 55.899990
#> Warning: non-integer x = 60.099980
#> Warning: non-integer x = 68.500000
#> Warning: non-integer x = 77.799990
#> Warning: non-integer x = 86.399960
#> Warning: non-integer x = 96.699950
#> Warning: non-integer x = 111.099980
#> Warning: non-integer x = 115.399960
#> Warning: non-integer x = 24.700000
#> Warning: non-integer x = 28.899990
#> Warning: non-integer x = 34.599980
#> Warning: non-integer x = 42.199980
#> Warning: non-integer x = 48.199980
#> Warning: non-integer x = 54.399990
#> Warning: non-integer x = 62.500000
#> Warning: non-integer x = 69.799990
#> Warning: non-integer x = 78.599980
#> Warning: non-integer x = 96.399960
#> Warning: non-integer x = 103.199950
#> Warning: non-integer x = 24.200000
#> Warning: non-integer x = 29.200000
#> Warning: non-integer x = 36.199980
#> Warning: non-integer x = 43.099980
#> Warning: non-integer x = 49.199980
#> Warning: non-integer x = 70.899960
#> Warning: non-integer x = 87.199950
#> Warning: non-integer x = 94.699950
#> Warning: non-integer x = 100.599980
#> Warning: non-integer x = 24.500000
#> Warning: non-integer x = 28.399990
#> Warning: non-integer x = 41.899990
#> Warning: non-integer x = 55.599980
#> Warning: non-integer x = 64.099980
#> Warning: non-integer x = 71.199950
#> Warning: non-integer x = 80.500000
#> Warning: non-integer x = 90.199950
#> Warning: non-integer x = 98.899960
#> Warning: non-integer x = 103.799990
#> Warning: non-integer x = 26.599990
#> Warning: non-integer x = 33.099980
#> Warning: non-integer x = 38.399990
#> Warning: non-integer x = 46.599980
#> Warning: non-integer x = 52.299990
#> Warning: non-integer x = 61.500000
#> Warning: non-integer x = 69.299990
#> Warning: non-integer x = 74.199950
#> Warning: non-integer x = 80.199950
#> Warning: non-integer x = 87.199950
#> Warning: non-integer x = 94.799990
#> Warning: non-integer x = 26.799990
#> Warning: non-integer x = 33.599980
#> Warning: non-integer x = 42.099980
#> Warning: non-integer x = 47.899990
#> Warning: non-integer x = 56.199980
#> Warning: non-integer x = 63.399990
#> Warning: non-integer x = 71.799990
#> Warning: non-integer x = 87.599980
#> Warning: non-integer x = 94.899960
#> Warning: non-integer x = 30.599990
#> Warning: non-integer x = 37.599980
#> Warning: non-integer x = 42.799990
#> Warning: non-integer x = 47.399990
#> Warning: non-integer x = 56.599980
#> Warning: non-integer x = 62.399990
#> Warning: non-integer x = 71.799990
#> Warning: non-integer x = 86.799990
#> Warning: non-integer x = 94.199950
#> Warning: non-integer x = 101.899960
#> Warning: non-integer x = 112.500000
#> Warning: non-integer x = 21.899990
#> Warning: non-integer x = 26.799990
#> Warning: non-integer x = 34.699980
#> Warning: non-integer x = 41.299990
#> Warning: non-integer x = 48.699980
#> Warning: non-integer x = 57.899990
#> Warning: non-integer x = 65.399960
#> Warning: non-integer x = 71.299990
#> Warning: non-integer x = 80.599980
#> Warning: non-integer x = 88.399960
#> Warning: non-integer x = 96.299990
#> Warning: non-integer x = 103.500000
#> Warning: non-integer x = 26.799990
#> Warning: non-integer x = 39.099980
#> Warning: non-integer x = 46.399990
#> Warning: non-integer x = 61.599980
#> Warning: non-integer x = 68.799990
#> Warning: non-integer x = 72.199950
#> Warning: non-integer x = 77.199950
#> Warning: non-integer x = 83.799990
#> Warning: non-integer x = 90.799990
#> Warning: non-integer x = 24.200000
#> Warning: non-integer x = 25.399990
#> Warning: non-integer x = 30.700000
#> Warning: non-integer x = 35.599980
#> Warning: non-integer x = 42.799990
#> Warning: non-integer x = 49.500000
#> Warning: non-integer x = 57.199980
#> Warning: non-integer x = 65.599980
#> Warning: non-integer x = 72.399960
#> Warning: non-integer x = 81.199950
#> Warning: non-integer x = 85.199950
#> Warning: non-integer x = 90.199950
#> Warning: non-integer x = 25.200000
#> Warning: non-integer x = 29.799990
#> Warning: non-integer x = 35.699980
#> Warning: non-integer x = 55.899990
#> Warning: non-integer x = 63.500000
#> Warning: non-integer x = 79.500000
#> Warning: non-integer x = 83.599980
#> Warning: non-integer x = 89.399960
#> Warning: non-integer x = 98.500000
#> Warning: non-integer x = 23.500000
#> Warning: non-integer x = 25.899990
#> Warning: non-integer x = 32.199980
#> Warning: non-integer x = 32.399990
#> Warning: non-integer x = 29.799990
#> Warning: non-integer x = 32.799990
#> Warning: non-integer x = 56.899990
#> Warning: non-integer x = 64.799990
#> Warning: non-integer x = 72.099980
#> Warning: non-integer x = 81.399960
#> Warning: non-integer x = 26.599990
#> Warning: non-integer x = 38.199980
#> Warning: non-integer x = 46.399990
#> Warning: non-integer x = 53.199980
#> Warning: non-integer x = 59.599980
#> Warning: non-integer x = 66.199950
#> Warning: non-integer x = 72.599980
#> Warning: non-integer x = 80.099980
#> Warning: non-integer x = 97.699950
#> Warning: non-integer x = 35.399990
#> Warning: non-integer x = 42.299990
#> Warning: non-integer x = 49.500000
#> Warning: non-integer x = 58.699980
#> Warning: non-integer x = 66.599980
#> Warning: non-integer x = 71.399960
#> Warning: non-integer x = 78.799990
#> Warning: non-integer x = 85.500000
#> Warning: non-integer x = 91.299990
#> Warning: non-integer x = 97.799990
#> Warning: non-integer x = 29.299990
#> Warning: non-integer x = 45.399990
#> Warning: non-integer x = 51.799990
#> Warning: non-integer x = 58.799990
#> Warning: non-integer x = 62.599980
#> Warning: non-integer x = 71.599980
#> Warning: non-integer x = 76.699950
#> Warning: non-integer x = 81.699950
#> Warning: non-integer x = 86.399960
#> Warning: non-integer x = 92.099980
#> Warning: non-integer x = 25.299990
#> Warning: non-integer x = 31.599990
#> Warning: non-integer x = 35.199980
#> Warning: non-integer x = 37.299990
#> Warning: non-integer x = 40.799990
#> Warning: non-integer x = 47.699980
#> Warning: non-integer x = 64.599980
#> Warning: non-integer x = 71.199950
#> Warning: non-integer x = 80.500000
#> Warning: non-integer x = 85.899960
#> Warning: non-integer x = 22.099990
#> Warning: non-integer x = 26.299990
#> Warning: non-integer x = 33.299990
#> Warning: non-integer x = 39.599980
#> Warning: non-integer x = 41.399990
#> Warning: non-integer x = 46.299990
#> Warning: non-integer x = 52.399990
#> Warning: non-integer x = 59.399990
#> Warning: non-integer x = 66.699950
#> Warning: non-integer x = 73.899960
#> Warning: non-integer x = 76.799990
#> Warning: non-integer x = 23.700000
#> Warning: non-integer x = 28.799990
#> Warning: non-integer x = 35.099980
#> Warning: non-integer x = 49.099980
#> Warning: non-integer x = 58.799990
#> Warning: non-integer x = 65.399960
#> Warning: non-integer x = 68.500000
#> Warning: non-integer x = 90.699950
#> Warning: non-integer x = 28.899990
#> Warning: non-integer x = 35.799990
#> Warning: non-integer x = 47.500000
#> Warning: non-integer x = 56.399990
#> Warning: non-integer x = 63.699980
#> Warning: non-integer x = 70.299990
#> Warning: non-integer x = 89.199950
#> Warning: non-integer x = 96.299990
#> Warning: non-integer x = 99.799990
#> Warning: non-integer x = 30.099990
#> Warning: non-integer x = 37.099980
#> Warning: non-integer x = 53.599980
#> Warning: non-integer x = 61.099980
#> Warning: non-integer x = 78.199950
#> Warning: non-integer x = 87.099980
#> Warning: non-integer x = 94.399960
#> Warning: non-integer x = 102.500000
#> Warning: non-integer x = 107.500000
#> Warning: non-integer x = 35.399990
#> Warning: non-integer x = 48.599980
#> Warning: non-integer x = 56.399990
#> Warning: non-integer x = 75.500000
#> Warning: non-integer x = 77.799990
#> Warning: non-integer x = 85.799990
#> Warning: non-integer x = 101.399960
#> Warning: non-integer x = 27.299990
#> Warning: non-integer x = 31.200000
#> Warning: non-integer x = 43.899990
#> Warning: non-integer x = 49.799990
#> Warning: non-integer x = 57.199980
#> Warning: non-integer x = 65.199950
#> Warning: non-integer x = 73.199950
#> Warning: non-integer x = 78.799990
#> Warning: non-integer x = 87.399960
#> Warning: non-integer x = 100.500000
#> Warning: non-integer x = 25.700000
#> Warning: non-integer x = 28.700000
#> Warning: non-integer x = 33.399990
#> Warning: non-integer x = 46.699980
#> Warning: non-integer x = 56.599980
#> Warning: non-integer x = 65.199950
#> Warning: non-integer x = 73.199950
#> Warning: non-integer x = 81.699950
#> Warning: non-integer x = 90.299990
#> Warning: non-integer x = 103.500000
anova(gee2)
#> Warning: non-integer x = 26.500000
#> Warning: non-integer x = 27.599990
#> Warning: non-integer x = 36.500000
#> Warning: non-integer x = 40.299990
#> Warning: non-integer x = 49.099980
#> Warning: non-integer x = 55.399990
#> Warning: non-integer x = 59.599980
#> Warning: non-integer x = 76.599980
#> Warning: non-integer x = 86.500000
#> Warning: non-integer x = 91.599980
#> Warning: non-integer x = 98.599980
#> Warning: non-integer x = 28.299990
#> Warning: non-integer x = 30.099990
#> Warning: non-integer x = 38.299990
#> Warning: non-integer x = 44.500000
#> Warning: non-integer x = 51.599980
#> Warning: non-integer x = 57.599980
#> Warning: non-integer x = 82.299990
#> Warning: non-integer x = 99.699950
#> Warning: non-integer x = 106.699950
#> Warning: non-integer x = 27.599990
#> Warning: non-integer x = 30.599990
#> Warning: non-integer x = 38.699980
#> Warning: non-integer x = 47.199980
#> Warning: non-integer x = 54.099980
#> Warning: non-integer x = 61.500000
#> Warning: non-integer x = 68.500000
#> Warning: non-integer x = 75.199950
#> Warning: non-integer x = 81.699950
#> Warning: non-integer x = 90.199950
#> Warning: non-integer x = 98.399960
#> Warning: non-integer x = 105.399960
#> Warning: non-integer x = 31.500000
#> Warning: non-integer x = 34.799990
#> Warning: non-integer x = 40.699980
#> Warning: non-integer x = 47.699980
#> Warning: non-integer x = 55.899990
#> Warning: non-integer x = 62.199980
#> Warning: non-integer x = 70.699950
#> Warning: non-integer x = 86.199950
#> Warning: non-integer x = 94.699950
#> Warning: non-integer x = 109.199950
#> Warning: non-integer x = 27.099990
#> Warning: non-integer x = 42.500000
#> Warning: non-integer x = 50.099980
#> Warning: non-integer x = 56.500000
#> Warning: non-integer x = 72.500000
#> Warning: non-integer x = 80.500000
#> Warning: non-integer x = 108.399960
#> Warning: non-integer x = 31.799990
#> Warning: non-integer x = 44.799990
#> Warning: non-integer x = 50.899990
#> Warning: non-integer x = 57.399990
#> Warning: non-integer x = 62.500000
#> Warning: non-integer x = 71.699950
#> Warning: non-integer x = 78.199950
#> Warning: non-integer x = 85.799990
#> Warning: non-integer x = 91.799990
#> Warning: non-integer x = 100.199950
#> Warning: non-integer x = 27.700000
#> Warning: non-integer x = 33.599980
#> Warning: non-integer x = 46.699980
#> Warning: non-integer x = 54.799990
#> Warning: non-integer x = 69.799990
#> Warning: non-integer x = 83.599980
#> Warning: non-integer x = 88.199950
#> Warning: non-integer x = 96.799990
#> Warning: non-integer x = 102.299990
#> Warning: non-integer x = 23.599990
#> Warning: non-integer x = 36.299990
#> Warning: non-integer x = 42.399990
#> Warning: non-integer x = 50.500000
#> Warning: non-integer x = 57.599980
#> Warning: non-integer x = 66.599980
#> Warning: non-integer x = 74.199950
#> Warning: non-integer x = 89.299990
#> Warning: non-integer x = 26.899990
#> Warning: non-integer x = 32.299990
#> Warning: non-integer x = 38.599980
#> Warning: non-integer x = 57.799990
#> Warning: non-integer x = 58.599980
#> Warning: non-integer x = 65.899960
#> Warning: non-integer x = 71.199950
#> Warning: non-integer x = 79.399960
#> Warning: non-integer x = 91.699950
#> Warning: non-integer x = 22.599990
#> Warning: non-integer x = 28.500000
#> Warning: non-integer x = 32.699980
#> Warning: non-integer x = 39.899990
#> Warning: non-integer x = 47.599980
#> Warning: non-integer x = 53.799990
#> Warning: non-integer x = 67.199950
#> Warning: non-integer x = 74.099980
#> Warning: non-integer x = 89.399960
#> Warning: non-integer x = 93.500000
#> Warning: non-integer x = 19.399990
#> Warning: non-integer x = 21.399990
#> Warning: non-integer x = 25.299990
#> Warning: non-integer x = 31.899990
#> Warning: non-integer x = 37.599980
#> Warning: non-integer x = 43.699980
#> Warning: non-integer x = 48.899990
#> Warning: non-integer x = 53.699980
#> Warning: non-integer x = 59.299990
#> Warning: non-integer x = 64.899960
#> Warning: non-integer x = 65.799990
#> Warning: non-integer x = 27.299990
#> Warning: non-integer x = 32.399990
#> Warning: non-integer x = 38.299990
#> Warning: non-integer x = 45.799990
#> Warning: non-integer x = 53.799990
#> Warning: non-integer x = 68.699950
#> Warning: non-integer x = 75.799990
#> Warning: non-integer x = 80.799990
#> Warning: non-integer x = 86.799990
#> Warning: non-integer x = 91.399960
#> Warning: non-integer x = 99.799990
#> Warning: non-integer x = 26.200000
#> Warning: non-integer x = 31.099990
#> Warning: non-integer x = 34.599980
#> Warning: non-integer x = 41.199980
#> Warning: non-integer x = 49.199980
#> Warning: non-integer x = 55.599980
#> Warning: non-integer x = 62.599980
#> Warning: non-integer x = 72.099980
#> Warning: non-integer x = 77.500000
#> Warning: non-integer x = 83.799990
#> Warning: non-integer x = 93.399960
#> Warning: non-integer x = 98.399960
#> Warning: non-integer x = 24.899990
#> Warning: non-integer x = 29.700000
#> Warning: non-integer x = 33.799990
#> Warning: non-integer x = 38.799990
#> Warning: non-integer x = 48.299990
#> Warning: non-integer x = 52.899990
#> Warning: non-integer x = 70.399960
#> Warning: non-integer x = 76.799990
#> Warning: non-integer x = 83.299990
#> Warning: non-integer x = 102.699950
#> Warning: non-integer x = 24.599990
#> Warning: non-integer x = 34.599980
#> Warning: non-integer x = 41.500000
#> Warning: non-integer x = 49.699980
#> Warning: non-integer x = 56.500000
#> Warning: non-integer x = 66.899960
#> Warning: non-integer x = 75.799990
#> Warning: non-integer x = 84.599980
#> Warning: non-integer x = 98.799990
#> Warning: non-integer x = 107.199950
#> Warning: non-integer x = 32.699980
#> Warning: non-integer x = 38.299990
#> Warning: non-integer x = 45.500000
#> Warning: non-integer x = 48.599980
#> Warning: non-integer x = 62.599980
#> Warning: non-integer x = 70.199950
#> Warning: non-integer x = 73.799990
#> Warning: non-integer x = 80.299990
#> Warning: non-integer x = 85.500000
#> Warning: non-integer x = 93.099980
#> Warning: non-integer x = 35.199980
#> Warning: non-integer x = 41.500000
#> Warning: non-integer x = 47.699980
#> Warning: non-integer x = 53.799990
#> Warning: non-integer x = 61.599980
#> Warning: non-integer x = 79.099980
#> Warning: non-integer x = 85.699950
#> Warning: non-integer x = 92.500000
#> Warning: non-integer x = 101.099980
#> Warning: non-integer x = 34.500000
#> Warning: non-integer x = 40.399990
#> Warning: non-integer x = 53.500000
#> Warning: non-integer x = 60.199980
#> Warning: non-integer x = 68.599980
#> Warning: non-integer x = 73.399960
#> Warning: non-integer x = 78.500000
#> Warning: non-integer x = 90.599980
#> Warning: non-integer x = 97.199950
#> Warning: non-integer x = 31.200000
#> Warning: non-integer x = 38.799990
#> Warning: non-integer x = 44.699980
#> Warning: non-integer x = 53.599980
#> Warning: non-integer x = 59.199980
#> Warning: non-integer x = 67.099980
#> Warning: non-integer x = 76.399960
#> Warning: non-integer x = 83.799990
#> Warning: non-integer x = 71.599980
#> Warning: non-integer x = 97.399960
#> Warning: non-integer x = 107.099980
#> Warning: non-integer x = 24.299990
#> Warning: non-integer x = 28.399990
#> Warning: non-integer x = 40.299990
#> Warning: non-integer x = 46.199980
#> Warning: non-integer x = 51.899990
#> Warning: non-integer x = 58.099980
#> Warning: non-integer x = 62.599980
#> Warning: non-integer x = 68.199950
#> Warning: non-integer x = 78.399960
#> Warning: non-integer x = 87.500000
#> Warning: non-integer x = 90.399960
#> Warning: non-integer x = 24.599990
#> Warning: non-integer x = 25.799990
#> Warning: non-integer x = 28.599990
#> Warning: non-integer x = 30.399990
#> Warning: non-integer x = 36.099980
#> Warning: non-integer x = 36.099980
#> Warning: non-integer x = 49.299990
#> Warning: non-integer x = 57.899990
#> Warning: non-integer x = 75.699950
#> Warning: non-integer x = 81.399960
#> Warning: non-integer x = 88.699950
#> Warning: non-integer x = 21.200000
#> Warning: non-integer x = 25.799990
#> Warning: non-integer x = 29.399990
#> Warning: non-integer x = 36.799990
#> Warning: non-integer x = 43.199980
#> Warning: non-integer x = 51.099980
#> Warning: non-integer x = 59.299990
#> Warning: non-integer x = 72.799990
#> Warning: non-integer x = 78.599980
#> Warning: non-integer x = 93.799990
#> Warning: non-integer x = 95.199950
#> Warning: non-integer x = 29.399990
#> Warning: non-integer x = 34.599980
#> Warning: non-integer x = 40.599980
#> Warning: non-integer x = 46.599980
#> Warning: non-integer x = 62.500000
#> Warning: non-integer x = 78.299990
#> Warning: non-integer x = 83.199950
#> Warning: non-integer x = 34.699980
#> Warning: non-integer x = 42.799990
#> Warning: non-integer x = 48.399990
#> Warning: non-integer x = 53.299990
#> Warning: non-integer x = 71.099980
#> Warning: non-integer x = 77.399960
#> Warning: non-integer x = 94.500000
#> Warning: non-integer x = 104.599980
#> Warning: non-integer x = 29.599990
#> Warning: non-integer x = 34.199980
#> Warning: non-integer x = 63.500000
#> Warning: non-integer x = 72.699950
#> Warning: non-integer x = 78.699950
#> Warning: non-integer x = 84.899960
#> Warning: non-integer x = 96.399960
#> Warning: non-integer x = 100.199950
#> Warning: non-integer x = 22.399990
#> Warning: non-integer x = 25.200000
#> Warning: non-integer x = 36.500000
#> Warning: non-integer x = 43.299990
#> Warning: non-integer x = 58.099980
#> Warning: non-integer x = 70.699950
#> Warning: non-integer x = 78.099980
#> Warning: non-integer x = 83.500000
#> Warning: non-integer x = 26.599990
#> Warning: non-integer x = 28.200000
#> Warning: non-integer x = 38.399990
#> Warning: non-integer x = 45.799990
#> Warning: non-integer x = 54.899990
#> Warning: non-integer x = 60.099980
#> Warning: non-integer x = 56.899990
#> Warning: non-integer x = 64.899960
#> Warning: non-integer x = 81.899960
#> Warning: non-integer x = 90.899960
#> Warning: non-integer x = 28.200000
#> Warning: non-integer x = 35.299990
#> Warning: non-integer x = 42.699980
#> Warning: non-integer x = 48.199980
#> Warning: non-integer x = 53.199980
#> Warning: non-integer x = 64.799990
#> Warning: non-integer x = 71.500000
#> Warning: non-integer x = 76.099980
#> Warning: non-integer x = 86.099980
#> Warning: non-integer x = 92.500000
#> Warning: non-integer x = 27.099990
#> Warning: non-integer x = 34.699980
#> Warning: non-integer x = 40.699980
#> Warning: non-integer x = 47.599980
#> Warning: non-integer x = 56.500000
#> Warning: non-integer x = 72.299990
#> Warning: non-integer x = 95.099980
#> Warning: non-integer x = 105.699950
#> Warning: non-integer x = 37.799990
#> Warning: non-integer x = 43.299990
#> Warning: non-integer x = 51.500000
#> Warning: non-integer x = 63.699980
#> Warning: non-integer x = 70.500000
#> Warning: non-integer x = 80.399960
#> Warning: non-integer x = 106.099980
#> Warning: non-integer x = 29.500000
#> Warning: non-integer x = 31.399990
#> Warning: non-integer x = 39.399990
#> Warning: non-integer x = 44.799990
#> Warning: non-integer x = 50.299990
#> Warning: non-integer x = 65.599980
#> Warning: non-integer x = 72.399960
#> Warning: non-integer x = 80.199950
#> Warning: non-integer x = 90.399960
#> Warning: non-integer x = 99.099980
#> Warning: non-integer x = 22.799990
#> Warning: non-integer x = 33.899990
#> Warning: non-integer x = 37.699980
#> Warning: non-integer x = 41.399990
#> Warning: non-integer x = 48.199980
#> Warning: non-integer x = 53.699980
#> Warning: non-integer x = 62.599980
#> Warning: non-integer x = 70.399960
#> Warning: non-integer x = 78.500000
#> Warning: non-integer x = 85.899960
#> Warning: non-integer x = 22.299990
#> Warning: non-integer x = 24.700000
#> Warning: non-integer x = 30.399990
#> Warning: non-integer x = 36.899990
#> Warning: non-integer x = 44.099980
#> Warning: non-integer x = 52.799990
#> Warning: non-integer x = 60.299990
#> Warning: non-integer x = 67.799990
#> Warning: non-integer x = 75.399960
#> Warning: non-integer x = 87.599980
#> Warning: non-integer x = 101.399960
#> Warning: non-integer x = 23.799990
#> Warning: non-integer x = 37.099980
#> Warning: non-integer x = 43.199980
#> Warning: non-integer x = 50.399990
#> Warning: non-integer x = 60.199980
#> Warning: non-integer x = 82.399960
#> Warning: non-integer x = 91.199950
#> Warning: non-integer x = 101.799990
#> Warning: non-integer x = 109.599980
#> Warning: non-integer x = 25.799990
#> Warning: non-integer x = 29.200000
#> Warning: non-integer x = 35.799990
#> Warning: non-integer x = 41.099980
#> Warning: non-integer x = 55.199980
#> Warning: non-integer x = 62.199980
#> Warning: non-integer x = 69.799990
#> Warning: non-integer x = 76.399960
#> Warning: non-integer x = 83.199950
#> Warning: non-integer x = 93.199950
#> Warning: non-integer x = 32.899990
#> Warning: non-integer x = 46.199980
#> Warning: non-integer x = 53.500000
#> Warning: non-integer x = 58.599980
#> Warning: non-integer x = 68.199950
#> Warning: non-integer x = 80.799990
#> Warning: non-integer x = 84.500000
#> Warning: non-integer x = 24.799990
#> Warning: non-integer x = 35.799990
#> Warning: non-integer x = 42.299990
#> Warning: non-integer x = 50.899990
#> Warning: non-integer x = 57.799990
#> Warning: non-integer x = 64.799990
#> Warning: non-integer x = 71.799990
#> Warning: non-integer x = 83.799990
#> Warning: non-integer x = 92.099980
#> Warning: non-integer x = 26.200000
#> Warning: non-integer x = 30.399990
#> Warning: non-integer x = 37.399990
#> Warning: non-integer x = 49.500000
#> Warning: non-integer x = 55.099980
#> Warning: non-integer x = 64.199950
#> Warning: non-integer x = 75.599980
#> Warning: non-integer x = 83.299990
#> Warning: non-integer x = 87.399960
#> Warning: non-integer x = 94.699950
#> Warning: non-integer x = 98.399960
#> Warning: non-integer x = 32.500000
#> Warning: non-integer x = 38.799990
#> Warning: non-integer x = 47.799990
#> Warning: non-integer x = 54.500000
#> Warning: non-integer x = 70.099980
#> Warning: non-integer x = 76.599980
#> Warning: non-integer x = 86.199950
#> Warning: non-integer x = 95.799990
#> Warning: non-integer x = 101.399960
#> Warning: non-integer x = 112.299990
#> Warning: non-integer x = 32.399990
#> Warning: non-integer x = 38.199980
#> Warning: non-integer x = 44.699980
#> Warning: non-integer x = 53.199980
#> Warning: non-integer x = 62.399990
#> Warning: non-integer x = 70.500000
#> Warning: non-integer x = 72.799990
#> Warning: non-integer x = 86.599980
#> Warning: non-integer x = 93.299990
#> Warning: non-integer x = 104.199950
#> Warning: non-integer x = 27.399990
#> Warning: non-integer x = 32.199980
#> Warning: non-integer x = 37.899990
#> Warning: non-integer x = 45.899990
#> Warning: non-integer x = 51.199980
#> Warning: non-integer x = 57.099980
#> Warning: non-integer x = 76.799990
#> Warning: non-integer x = 83.099980
#> Warning: non-integer x = 91.599980
#> Warning: non-integer x = 100.500000
#> Warning: non-integer x = 105.299990
#> Warning: non-integer x = 27.099990
#> Warning: non-integer x = 30.299990
#> Warning: non-integer x = 38.199980
#> Warning: non-integer x = 43.199980
#> Warning: non-integer x = 52.500000
#> Warning: non-integer x = 67.299990
#> Warning: non-integer x = 74.199950
#> Warning: non-integer x = 81.199950
#> Warning: non-integer x = 87.500000
#> Warning: non-integer x = 94.399960
#> Warning: non-integer x = 101.399960
#> Warning: non-integer x = 26.799990
#> Warning: non-integer x = 31.099990
#> Warning: non-integer x = 37.799990
#> Warning: non-integer x = 44.599980
#> Warning: non-integer x = 50.500000
#> Warning: non-integer x = 58.299990
#> Warning: non-integer x = 68.299990
#> Warning: non-integer x = 75.099980
#> Warning: non-integer x = 84.399960
#> Warning: non-integer x = 87.299990
#> Warning: non-integer x = 96.399960
#> Warning: non-integer x = 104.399960
#> Warning: non-integer x = 24.500000
#> Warning: non-integer x = 31.599990
#> Warning: non-integer x = 37.399990
#> Warning: non-integer x = 46.399990
#> Warning: non-integer x = 53.599980
#> Warning: non-integer x = 61.199980
#> Warning: non-integer x = 70.099980
#> Warning: non-integer x = 77.500000
#> Warning: non-integer x = 86.199950
#> Warning: non-integer x = 89.199950
#> Warning: non-integer x = 96.899960
#> Warning: non-integer x = 104.500000
#> Warning: non-integer x = 23.099990
#> Warning: non-integer x = 30.099990
#> Warning: non-integer x = 40.699980
#> Warning: non-integer x = 46.599980
#> Warning: non-integer x = 52.099980
#> Warning: non-integer x = 60.500000
#> Warning: non-integer x = 73.500000
#> Warning: non-integer x = 77.299990
#> Warning: non-integer x = 86.899960
#> Warning: non-integer x = 96.399960
#> Warning: non-integer x = 21.500000
#> Warning: non-integer x = 24.599990
#> Warning: non-integer x = 28.500000
#> Warning: non-integer x = 39.099980
#> Warning: non-integer x = 45.299990
#> Warning: non-integer x = 59.599980
#> Warning: non-integer x = 69.500000
#> Warning: non-integer x = 75.199950
#> Warning: non-integer x = 84.899960
#> Warning: non-integer x = 93.399960
#> Warning: non-integer x = 99.299990
#> Warning: non-integer x = 24.099990
#> Warning: non-integer x = 28.099990
#> Warning: non-integer x = 32.500000
#> Warning: non-integer x = 40.599980
#> Warning: non-integer x = 53.799990
#> Warning: non-integer x = 61.199980
#> Warning: non-integer x = 71.899960
#> Warning: non-integer x = 79.500000
#> Warning: non-integer x = 87.399960
#> Warning: non-integer x = 93.299990
#> Warning: non-integer x = 101.599980
#> Warning: non-integer x = 34.199980
#> Warning: non-integer x = 42.099980
#> Warning: non-integer x = 50.099980
#> Warning: non-integer x = 57.599980
#> Warning: non-integer x = 62.299990
#> Warning: non-integer x = 76.099980
#> Warning: non-integer x = 81.500000
#> Warning: non-integer x = 84.299990
#> Warning: non-integer x = 97.899960
#> Warning: non-integer x = 108.599980
#> Warning: non-integer x = 25.099990
#> Warning: non-integer x = 23.200000
#> Warning: non-integer x = 28.899990
#> Warning: non-integer x = 36.799990
#> Warning: non-integer x = 44.199980
#> Warning: non-integer x = 52.799990
#> Warning: non-integer x = 62.199980
#> Warning: non-integer x = 69.399960
#> Warning: non-integer x = 78.099980
#> Warning: non-integer x = 88.799990
#> Warning: non-integer x = 102.399960
#> Warning: non-integer x = 106.799990
#> Warning: non-integer x = 32.199980
#> Warning: non-integer x = 36.399990
#> Warning: non-integer x = 41.799990
#> Warning: non-integer x = 48.199980
#> Warning: non-integer x = 55.899990
#> Warning: non-integer x = 60.099980
#> Warning: non-integer x = 68.500000
#> Warning: non-integer x = 77.799990
#> Warning: non-integer x = 86.399960
#> Warning: non-integer x = 96.699950
#> Warning: non-integer x = 111.099980
#> Warning: non-integer x = 115.399960
#> Warning: non-integer x = 24.700000
#> Warning: non-integer x = 28.899990
#> Warning: non-integer x = 34.599980
#> Warning: non-integer x = 42.199980
#> Warning: non-integer x = 48.199980
#> Warning: non-integer x = 54.399990
#> Warning: non-integer x = 62.500000
#> Warning: non-integer x = 69.799990
#> Warning: non-integer x = 78.599980
#> Warning: non-integer x = 96.399960
#> Warning: non-integer x = 103.199950
#> Warning: non-integer x = 24.200000
#> Warning: non-integer x = 29.200000
#> Warning: non-integer x = 36.199980
#> Warning: non-integer x = 43.099980
#> Warning: non-integer x = 49.199980
#> Warning: non-integer x = 70.899960
#> Warning: non-integer x = 87.199950
#> Warning: non-integer x = 94.699950
#> Warning: non-integer x = 100.599980
#> Warning: non-integer x = 24.500000
#> Warning: non-integer x = 28.399990
#> Warning: non-integer x = 41.899990
#> Warning: non-integer x = 55.599980
#> Warning: non-integer x = 64.099980
#> Warning: non-integer x = 71.199950
#> Warning: non-integer x = 80.500000
#> Warning: non-integer x = 90.199950
#> Warning: non-integer x = 98.899960
#> Warning: non-integer x = 103.799990
#> Warning: non-integer x = 26.599990
#> Warning: non-integer x = 33.099980
#> Warning: non-integer x = 38.399990
#> Warning: non-integer x = 46.599980
#> Warning: non-integer x = 52.299990
#> Warning: non-integer x = 61.500000
#> Warning: non-integer x = 69.299990
#> Warning: non-integer x = 74.199950
#> Warning: non-integer x = 80.199950
#> Warning: non-integer x = 87.199950
#> Warning: non-integer x = 94.799990
#> Warning: non-integer x = 26.799990
#> Warning: non-integer x = 33.599980
#> Warning: non-integer x = 42.099980
#> Warning: non-integer x = 47.899990
#> Warning: non-integer x = 56.199980
#> Warning: non-integer x = 63.399990
#> Warning: non-integer x = 71.799990
#> Warning: non-integer x = 87.599980
#> Warning: non-integer x = 94.899960
#> Warning: non-integer x = 30.599990
#> Warning: non-integer x = 37.599980
#> Warning: non-integer x = 42.799990
#> Warning: non-integer x = 47.399990
#> Warning: non-integer x = 56.599980
#> Warning: non-integer x = 62.399990
#> Warning: non-integer x = 71.799990
#> Warning: non-integer x = 86.799990
#> Warning: non-integer x = 94.199950
#> Warning: non-integer x = 101.899960
#> Warning: non-integer x = 112.500000
#> Warning: non-integer x = 21.899990
#> Warning: non-integer x = 26.799990
#> Warning: non-integer x = 34.699980
#> Warning: non-integer x = 41.299990
#> Warning: non-integer x = 48.699980
#> Warning: non-integer x = 57.899990
#> Warning: non-integer x = 65.399960
#> Warning: non-integer x = 71.299990
#> Warning: non-integer x = 80.599980
#> Warning: non-integer x = 88.399960
#> Warning: non-integer x = 96.299990
#> Warning: non-integer x = 103.500000
#> Warning: non-integer x = 26.799990
#> Warning: non-integer x = 39.099980
#> Warning: non-integer x = 46.399990
#> Warning: non-integer x = 61.599980
#> Warning: non-integer x = 68.799990
#> Warning: non-integer x = 72.199950
#> Warning: non-integer x = 77.199950
#> Warning: non-integer x = 83.799990
#> Warning: non-integer x = 90.799990
#> Warning: non-integer x = 24.200000
#> Warning: non-integer x = 25.399990
#> Warning: non-integer x = 30.700000
#> Warning: non-integer x = 35.599980
#> Warning: non-integer x = 42.799990
#> Warning: non-integer x = 49.500000
#> Warning: non-integer x = 57.199980
#> Warning: non-integer x = 65.599980
#> Warning: non-integer x = 72.399960
#> Warning: non-integer x = 81.199950
#> Warning: non-integer x = 85.199950
#> Warning: non-integer x = 90.199950
#> Warning: non-integer x = 25.200000
#> Warning: non-integer x = 29.799990
#> Warning: non-integer x = 35.699980
#> Warning: non-integer x = 55.899990
#> Warning: non-integer x = 63.500000
#> Warning: non-integer x = 79.500000
#> Warning: non-integer x = 83.599980
#> Warning: non-integer x = 89.399960
#> Warning: non-integer x = 98.500000
#> Warning: non-integer x = 23.500000
#> Warning: non-integer x = 25.899990
#> Warning: non-integer x = 32.199980
#> Warning: non-integer x = 32.399990
#> Warning: non-integer x = 29.799990
#> Warning: non-integer x = 32.799990
#> Warning: non-integer x = 56.899990
#> Warning: non-integer x = 64.799990
#> Warning: non-integer x = 72.099980
#> Warning: non-integer x = 81.399960
#> Warning: non-integer x = 26.599990
#> Warning: non-integer x = 38.199980
#> Warning: non-integer x = 46.399990
#> Warning: non-integer x = 53.199980
#> Warning: non-integer x = 59.599980
#> Warning: non-integer x = 66.199950
#> Warning: non-integer x = 72.599980
#> Warning: non-integer x = 80.099980
#> Warning: non-integer x = 97.699950
#> Warning: non-integer x = 35.399990
#> Warning: non-integer x = 42.299990
#> Warning: non-integer x = 49.500000
#> Warning: non-integer x = 58.699980
#> Warning: non-integer x = 66.599980
#> Warning: non-integer x = 71.399960
#> Warning: non-integer x = 78.799990
#> Warning: non-integer x = 85.500000
#> Warning: non-integer x = 91.299990
#> Warning: non-integer x = 97.799990
#> Warning: non-integer x = 29.299990
#> Warning: non-integer x = 45.399990
#> Warning: non-integer x = 51.799990
#> Warning: non-integer x = 58.799990
#> Warning: non-integer x = 62.599980
#> Warning: non-integer x = 71.599980
#> Warning: non-integer x = 76.699950
#> Warning: non-integer x = 81.699950
#> Warning: non-integer x = 86.399960
#> Warning: non-integer x = 92.099980
#> Warning: non-integer x = 25.299990
#> Warning: non-integer x = 31.599990
#> Warning: non-integer x = 35.199980
#> Warning: non-integer x = 37.299990
#> Warning: non-integer x = 40.799990
#> Warning: non-integer x = 47.699980
#> Warning: non-integer x = 64.599980
#> Warning: non-integer x = 71.199950
#> Warning: non-integer x = 80.500000
#> Warning: non-integer x = 85.899960
#> Warning: non-integer x = 22.099990
#> Warning: non-integer x = 26.299990
#> Warning: non-integer x = 33.299990
#> Warning: non-integer x = 39.599980
#> Warning: non-integer x = 41.399990
#> Warning: non-integer x = 46.299990
#> Warning: non-integer x = 52.399990
#> Warning: non-integer x = 59.399990
#> Warning: non-integer x = 66.699950
#> Warning: non-integer x = 73.899960
#> Warning: non-integer x = 76.799990
#> Warning: non-integer x = 23.700000
#> Warning: non-integer x = 28.799990
#> Warning: non-integer x = 35.099980
#> Warning: non-integer x = 49.099980
#> Warning: non-integer x = 58.799990
#> Warning: non-integer x = 65.399960
#> Warning: non-integer x = 68.500000
#> Warning: non-integer x = 90.699950
#> Warning: non-integer x = 28.899990
#> Warning: non-integer x = 35.799990
#> Warning: non-integer x = 47.500000
#> Warning: non-integer x = 56.399990
#> Warning: non-integer x = 63.699980
#> Warning: non-integer x = 70.299990
#> Warning: non-integer x = 89.199950
#> Warning: non-integer x = 96.299990
#> Warning: non-integer x = 99.799990
#> Warning: non-integer x = 30.099990
#> Warning: non-integer x = 37.099980
#> Warning: non-integer x = 53.599980
#> Warning: non-integer x = 61.099980
#> Warning: non-integer x = 78.199950
#> Warning: non-integer x = 87.099980
#> Warning: non-integer x = 94.399960
#> Warning: non-integer x = 102.500000
#> Warning: non-integer x = 107.500000
#> Warning: non-integer x = 35.399990
#> Warning: non-integer x = 48.599980
#> Warning: non-integer x = 56.399990
#> Warning: non-integer x = 75.500000
#> Warning: non-integer x = 77.799990
#> Warning: non-integer x = 85.799990
#> Warning: non-integer x = 101.399960
#> Warning: non-integer x = 27.299990
#> Warning: non-integer x = 31.200000
#> Warning: non-integer x = 43.899990
#> Warning: non-integer x = 49.799990
#> Warning: non-integer x = 57.199980
#> Warning: non-integer x = 65.199950
#> Warning: non-integer x = 73.199950
#> Warning: non-integer x = 78.799990
#> Warning: non-integer x = 87.399960
#> Warning: non-integer x = 100.500000
#> Warning: non-integer x = 25.700000
#> Warning: non-integer x = 28.700000
#> Warning: non-integer x = 33.399990
#> Warning: non-integer x = 46.699980
#> Warning: non-integer x = 56.599980
#> Warning: non-integer x = 65.199950
#> Warning: non-integer x = 73.199950
#> Warning: non-integer x = 81.699950
#> Warning: non-integer x = 90.299990
#> Warning: non-integer x = 103.500000
#> Warning: non-integer x = 26.500000
#> Warning: non-integer x = 27.599990
#> Warning: non-integer x = 36.500000
#> Warning: non-integer x = 40.299990
#> Warning: non-integer x = 49.099980
#> Warning: non-integer x = 55.399990
#> Warning: non-integer x = 59.599980
#> Warning: non-integer x = 76.599980
#> Warning: non-integer x = 86.500000
#> Warning: non-integer x = 91.599980
#> Warning: non-integer x = 98.599980
#> Warning: non-integer x = 28.299990
#> Warning: non-integer x = 30.099990
#> Warning: non-integer x = 38.299990
#> Warning: non-integer x = 44.500000
#> Warning: non-integer x = 51.599980
#> Warning: non-integer x = 57.599980
#> Warning: non-integer x = 82.299990
#> Warning: non-integer x = 99.699950
#> Warning: non-integer x = 106.699950
#> Warning: non-integer x = 27.599990
#> Warning: non-integer x = 30.599990
#> Warning: non-integer x = 38.699980
#> Warning: non-integer x = 47.199980
#> Warning: non-integer x = 54.099980
#> Warning: non-integer x = 61.500000
#> Warning: non-integer x = 68.500000
#> Warning: non-integer x = 75.199950
#> Warning: non-integer x = 81.699950
#> Warning: non-integer x = 90.199950
#> Warning: non-integer x = 98.399960
#> Warning: non-integer x = 105.399960
#> Warning: non-integer x = 31.500000
#> Warning: non-integer x = 34.799990
#> Warning: non-integer x = 40.699980
#> Warning: non-integer x = 47.699980
#> Warning: non-integer x = 55.899990
#> Warning: non-integer x = 62.199980
#> Warning: non-integer x = 70.699950
#> Warning: non-integer x = 86.199950
#> Warning: non-integer x = 94.699950
#> Warning: non-integer x = 109.199950
#> Warning: non-integer x = 27.099990
#> Warning: non-integer x = 42.500000
#> Warning: non-integer x = 50.099980
#> Warning: non-integer x = 56.500000
#> Warning: non-integer x = 72.500000
#> Warning: non-integer x = 80.500000
#> Warning: non-integer x = 108.399960
#> Warning: non-integer x = 31.799990
#> Warning: non-integer x = 44.799990
#> Warning: non-integer x = 50.899990
#> Warning: non-integer x = 57.399990
#> Warning: non-integer x = 62.500000
#> Warning: non-integer x = 71.699950
#> Warning: non-integer x = 78.199950
#> Warning: non-integer x = 85.799990
#> Warning: non-integer x = 91.799990
#> Warning: non-integer x = 100.199950
#> Warning: non-integer x = 27.700000
#> Warning: non-integer x = 33.599980
#> Warning: non-integer x = 46.699980
#> Warning: non-integer x = 54.799990
#> Warning: non-integer x = 69.799990
#> Warning: non-integer x = 83.599980
#> Warning: non-integer x = 88.199950
#> Warning: non-integer x = 96.799990
#> Warning: non-integer x = 102.299990
#> Warning: non-integer x = 23.599990
#> Warning: non-integer x = 36.299990
#> Warning: non-integer x = 42.399990
#> Warning: non-integer x = 50.500000
#> Warning: non-integer x = 57.599980
#> Warning: non-integer x = 66.599980
#> Warning: non-integer x = 74.199950
#> Warning: non-integer x = 89.299990
#> Warning: non-integer x = 26.899990
#> Warning: non-integer x = 32.299990
#> Warning: non-integer x = 38.599980
#> Warning: non-integer x = 57.799990
#> Warning: non-integer x = 58.599980
#> Warning: non-integer x = 65.899960
#> Warning: non-integer x = 71.199950
#> Warning: non-integer x = 79.399960
#> Warning: non-integer x = 91.699950
#> Warning: non-integer x = 22.599990
#> Warning: non-integer x = 28.500000
#> Warning: non-integer x = 32.699980
#> Warning: non-integer x = 39.899990
#> Warning: non-integer x = 47.599980
#> Warning: non-integer x = 53.799990
#> Warning: non-integer x = 67.199950
#> Warning: non-integer x = 74.099980
#> Warning: non-integer x = 89.399960
#> Warning: non-integer x = 93.500000
#> Warning: non-integer x = 19.399990
#> Warning: non-integer x = 21.399990
#> Warning: non-integer x = 25.299990
#> Warning: non-integer x = 31.899990
#> Warning: non-integer x = 37.599980
#> Warning: non-integer x = 43.699980
#> Warning: non-integer x = 48.899990
#> Warning: non-integer x = 53.699980
#> Warning: non-integer x = 59.299990
#> Warning: non-integer x = 64.899960
#> Warning: non-integer x = 65.799990
#> Warning: non-integer x = 27.299990
#> Warning: non-integer x = 32.399990
#> Warning: non-integer x = 38.299990
#> Warning: non-integer x = 45.799990
#> Warning: non-integer x = 53.799990
#> Warning: non-integer x = 68.699950
#> Warning: non-integer x = 75.799990
#> Warning: non-integer x = 80.799990
#> Warning: non-integer x = 86.799990
#> Warning: non-integer x = 91.399960
#> Warning: non-integer x = 99.799990
#> Warning: non-integer x = 26.200000
#> Warning: non-integer x = 31.099990
#> Warning: non-integer x = 34.599980
#> Warning: non-integer x = 41.199980
#> Warning: non-integer x = 49.199980
#> Warning: non-integer x = 55.599980
#> Warning: non-integer x = 62.599980
#> Warning: non-integer x = 72.099980
#> Warning: non-integer x = 77.500000
#> Warning: non-integer x = 83.799990
#> Warning: non-integer x = 93.399960
#> Warning: non-integer x = 98.399960
#> Warning: non-integer x = 24.899990
#> Warning: non-integer x = 29.700000
#> Warning: non-integer x = 33.799990
#> Warning: non-integer x = 38.799990
#> Warning: non-integer x = 48.299990
#> Warning: non-integer x = 52.899990
#> Warning: non-integer x = 70.399960
#> Warning: non-integer x = 76.799990
#> Warning: non-integer x = 83.299990
#> Warning: non-integer x = 102.699950
#> Warning: non-integer x = 24.599990
#> Warning: non-integer x = 34.599980
#> Warning: non-integer x = 41.500000
#> Warning: non-integer x = 49.699980
#> Warning: non-integer x = 56.500000
#> Warning: non-integer x = 66.899960
#> Warning: non-integer x = 75.799990
#> Warning: non-integer x = 84.599980
#> Warning: non-integer x = 98.799990
#> Warning: non-integer x = 107.199950
#> Warning: non-integer x = 32.699980
#> Warning: non-integer x = 38.299990
#> Warning: non-integer x = 45.500000
#> Warning: non-integer x = 48.599980
#> Warning: non-integer x = 62.599980
#> Warning: non-integer x = 70.199950
#> Warning: non-integer x = 73.799990
#> Warning: non-integer x = 80.299990
#> Warning: non-integer x = 85.500000
#> Warning: non-integer x = 93.099980
#> Warning: non-integer x = 35.199980
#> Warning: non-integer x = 41.500000
#> Warning: non-integer x = 47.699980
#> Warning: non-integer x = 53.799990
#> Warning: non-integer x = 61.599980
#> Warning: non-integer x = 79.099980
#> Warning: non-integer x = 85.699950
#> Warning: non-integer x = 92.500000
#> Warning: non-integer x = 101.099980
#> Warning: non-integer x = 34.500000
#> Warning: non-integer x = 40.399990
#> Warning: non-integer x = 53.500000
#> Warning: non-integer x = 60.199980
#> Warning: non-integer x = 68.599980
#> Warning: non-integer x = 73.399960
#> Warning: non-integer x = 78.500000
#> Warning: non-integer x = 90.599980
#> Warning: non-integer x = 97.199950
#> Warning: non-integer x = 31.200000
#> Warning: non-integer x = 38.799990
#> Warning: non-integer x = 44.699980
#> Warning: non-integer x = 53.599980
#> Warning: non-integer x = 59.199980
#> Warning: non-integer x = 67.099980
#> Warning: non-integer x = 76.399960
#> Warning: non-integer x = 83.799990
#> Warning: non-integer x = 71.599980
#> Warning: non-integer x = 97.399960
#> Warning: non-integer x = 107.099980
#> Warning: non-integer x = 24.299990
#> Warning: non-integer x = 28.399990
#> Warning: non-integer x = 40.299990
#> Warning: non-integer x = 46.199980
#> Warning: non-integer x = 51.899990
#> Warning: non-integer x = 58.099980
#> Warning: non-integer x = 62.599980
#> Warning: non-integer x = 68.199950
#> Warning: non-integer x = 78.399960
#> Warning: non-integer x = 87.500000
#> Warning: non-integer x = 90.399960
#> Warning: non-integer x = 24.599990
#> Warning: non-integer x = 25.799990
#> Warning: non-integer x = 28.599990
#> Warning: non-integer x = 30.399990
#> Warning: non-integer x = 36.099980
#> Warning: non-integer x = 36.099980
#> Warning: non-integer x = 49.299990
#> Warning: non-integer x = 57.899990
#> Warning: non-integer x = 75.699950
#> Warning: non-integer x = 81.399960
#> Warning: non-integer x = 88.699950
#> Warning: non-integer x = 21.200000
#> Warning: non-integer x = 25.799990
#> Warning: non-integer x = 29.399990
#> Warning: non-integer x = 36.799990
#> Warning: non-integer x = 43.199980
#> Warning: non-integer x = 51.099980
#> Warning: non-integer x = 59.299990
#> Warning: non-integer x = 72.799990
#> Warning: non-integer x = 78.599980
#> Warning: non-integer x = 93.799990
#> Warning: non-integer x = 95.199950
#> Warning: non-integer x = 29.399990
#> Warning: non-integer x = 34.599980
#> Warning: non-integer x = 40.599980
#> Warning: non-integer x = 46.599980
#> Warning: non-integer x = 62.500000
#> Warning: non-integer x = 78.299990
#> Warning: non-integer x = 83.199950
#> Warning: non-integer x = 34.699980
#> Warning: non-integer x = 42.799990
#> Warning: non-integer x = 48.399990
#> Warning: non-integer x = 53.299990
#> Warning: non-integer x = 71.099980
#> Warning: non-integer x = 77.399960
#> Warning: non-integer x = 94.500000
#> Warning: non-integer x = 104.599980
#> Warning: non-integer x = 29.599990
#> Warning: non-integer x = 34.199980
#> Warning: non-integer x = 63.500000
#> Warning: non-integer x = 72.699950
#> Warning: non-integer x = 78.699950
#> Warning: non-integer x = 84.899960
#> Warning: non-integer x = 96.399960
#> Warning: non-integer x = 100.199950
#> Warning: non-integer x = 22.399990
#> Warning: non-integer x = 25.200000
#> Warning: non-integer x = 36.500000
#> Warning: non-integer x = 43.299990
#> Warning: non-integer x = 58.099980
#> Warning: non-integer x = 70.699950
#> Warning: non-integer x = 78.099980
#> Warning: non-integer x = 83.500000
#> Warning: non-integer x = 26.599990
#> Warning: non-integer x = 28.200000
#> Warning: non-integer x = 38.399990
#> Warning: non-integer x = 45.799990
#> Warning: non-integer x = 54.899990
#> Warning: non-integer x = 60.099980
#> Warning: non-integer x = 56.899990
#> Warning: non-integer x = 64.899960
#> Warning: non-integer x = 81.899960
#> Warning: non-integer x = 90.899960
#> Warning: non-integer x = 28.200000
#> Warning: non-integer x = 35.299990
#> Warning: non-integer x = 42.699980
#> Warning: non-integer x = 48.199980
#> Warning: non-integer x = 53.199980
#> Warning: non-integer x = 64.799990
#> Warning: non-integer x = 71.500000
#> Warning: non-integer x = 76.099980
#> Warning: non-integer x = 86.099980
#> Warning: non-integer x = 92.500000
#> Warning: non-integer x = 27.099990
#> Warning: non-integer x = 34.699980
#> Warning: non-integer x = 40.699980
#> Warning: non-integer x = 47.599980
#> Warning: non-integer x = 56.500000
#> Warning: non-integer x = 72.299990
#> Warning: non-integer x = 95.099980
#> Warning: non-integer x = 105.699950
#> Warning: non-integer x = 37.799990
#> Warning: non-integer x = 43.299990
#> Warning: non-integer x = 51.500000
#> Warning: non-integer x = 63.699980
#> Warning: non-integer x = 70.500000
#> Warning: non-integer x = 80.399960
#> Warning: non-integer x = 106.099980
#> Warning: non-integer x = 29.500000
#> Warning: non-integer x = 31.399990
#> Warning: non-integer x = 39.399990
#> Warning: non-integer x = 44.799990
#> Warning: non-integer x = 50.299990
#> Warning: non-integer x = 65.599980
#> Warning: non-integer x = 72.399960
#> Warning: non-integer x = 80.199950
#> Warning: non-integer x = 90.399960
#> Warning: non-integer x = 99.099980
#> Warning: non-integer x = 22.799990
#> Warning: non-integer x = 33.899990
#> Warning: non-integer x = 37.699980
#> Warning: non-integer x = 41.399990
#> Warning: non-integer x = 48.199980
#> Warning: non-integer x = 53.699980
#> Warning: non-integer x = 62.599980
#> Warning: non-integer x = 70.399960
#> Warning: non-integer x = 78.500000
#> Warning: non-integer x = 85.899960
#> Warning: non-integer x = 22.299990
#> Warning: non-integer x = 24.700000
#> Warning: non-integer x = 30.399990
#> Warning: non-integer x = 36.899990
#> Warning: non-integer x = 44.099980
#> Warning: non-integer x = 52.799990
#> Warning: non-integer x = 60.299990
#> Warning: non-integer x = 67.799990
#> Warning: non-integer x = 75.399960
#> Warning: non-integer x = 87.599980
#> Warning: non-integer x = 101.399960
#> Warning: non-integer x = 23.799990
#> Warning: non-integer x = 37.099980
#> Warning: non-integer x = 43.199980
#> Warning: non-integer x = 50.399990
#> Warning: non-integer x = 60.199980
#> Warning: non-integer x = 82.399960
#> Warning: non-integer x = 91.199950
#> Warning: non-integer x = 101.799990
#> Warning: non-integer x = 109.599980
#> Warning: non-integer x = 25.799990
#> Warning: non-integer x = 29.200000
#> Warning: non-integer x = 35.799990
#> Warning: non-integer x = 41.099980
#> Warning: non-integer x = 55.199980
#> Warning: non-integer x = 62.199980
#> Warning: non-integer x = 69.799990
#> Warning: non-integer x = 76.399960
#> Warning: non-integer x = 83.199950
#> Warning: non-integer x = 93.199950
#> Warning: non-integer x = 32.899990
#> Warning: non-integer x = 46.199980
#> Warning: non-integer x = 53.500000
#> Warning: non-integer x = 58.599980
#> Warning: non-integer x = 68.199950
#> Warning: non-integer x = 80.799990
#> Warning: non-integer x = 84.500000
#> Warning: non-integer x = 24.799990
#> Warning: non-integer x = 35.799990
#> Warning: non-integer x = 42.299990
#> Warning: non-integer x = 50.899990
#> Warning: non-integer x = 57.799990
#> Warning: non-integer x = 64.799990
#> Warning: non-integer x = 71.799990
#> Warning: non-integer x = 83.799990
#> Warning: non-integer x = 92.099980
#> Warning: non-integer x = 26.200000
#> Warning: non-integer x = 30.399990
#> Warning: non-integer x = 37.399990
#> Warning: non-integer x = 49.500000
#> Warning: non-integer x = 55.099980
#> Warning: non-integer x = 64.199950
#> Warning: non-integer x = 75.599980
#> Warning: non-integer x = 83.299990
#> Warning: non-integer x = 87.399960
#> Warning: non-integer x = 94.699950
#> Warning: non-integer x = 98.399960
#> Warning: non-integer x = 32.500000
#> Warning: non-integer x = 38.799990
#> Warning: non-integer x = 47.799990
#> Warning: non-integer x = 54.500000
#> Warning: non-integer x = 70.099980
#> Warning: non-integer x = 76.599980
#> Warning: non-integer x = 86.199950
#> Warning: non-integer x = 95.799990
#> Warning: non-integer x = 101.399960
#> Warning: non-integer x = 112.299990
#> Warning: non-integer x = 32.399990
#> Warning: non-integer x = 38.199980
#> Warning: non-integer x = 44.699980
#> Warning: non-integer x = 53.199980
#> Warning: non-integer x = 62.399990
#> Warning: non-integer x = 70.500000
#> Warning: non-integer x = 72.799990
#> Warning: non-integer x = 86.599980
#> Warning: non-integer x = 93.299990
#> Warning: non-integer x = 104.199950
#> Warning: non-integer x = 27.399990
#> Warning: non-integer x = 32.199980
#> Warning: non-integer x = 37.899990
#> Warning: non-integer x = 45.899990
#> Warning: non-integer x = 51.199980
#> Warning: non-integer x = 57.099980
#> Warning: non-integer x = 76.799990
#> Warning: non-integer x = 83.099980
#> Warning: non-integer x = 91.599980
#> Warning: non-integer x = 100.500000
#> Warning: non-integer x = 105.299990
#> Warning: non-integer x = 27.099990
#> Warning: non-integer x = 30.299990
#> Warning: non-integer x = 38.199980
#> Warning: non-integer x = 43.199980
#> Warning: non-integer x = 52.500000
#> Warning: non-integer x = 67.299990
#> Warning: non-integer x = 74.199950
#> Warning: non-integer x = 81.199950
#> Warning: non-integer x = 87.500000
#> Warning: non-integer x = 94.399960
#> Warning: non-integer x = 101.399960
#> Warning: non-integer x = 26.799990
#> Warning: non-integer x = 31.099990
#> Warning: non-integer x = 37.799990
#> Warning: non-integer x = 44.599980
#> Warning: non-integer x = 50.500000
#> Warning: non-integer x = 58.299990
#> Warning: non-integer x = 68.299990
#> Warning: non-integer x = 75.099980
#> Warning: non-integer x = 84.399960
#> Warning: non-integer x = 87.299990
#> Warning: non-integer x = 96.399960
#> Warning: non-integer x = 104.399960
#> Warning: non-integer x = 24.500000
#> Warning: non-integer x = 31.599990
#> Warning: non-integer x = 37.399990
#> Warning: non-integer x = 46.399990
#> Warning: non-integer x = 53.599980
#> Warning: non-integer x = 61.199980
#> Warning: non-integer x = 70.099980
#> Warning: non-integer x = 77.500000
#> Warning: non-integer x = 86.199950
#> Warning: non-integer x = 89.199950
#> Warning: non-integer x = 96.899960
#> Warning: non-integer x = 104.500000
#> Warning: non-integer x = 23.099990
#> Warning: non-integer x = 30.099990
#> Warning: non-integer x = 40.699980
#> Warning: non-integer x = 46.599980
#> Warning: non-integer x = 52.099980
#> Warning: non-integer x = 60.500000
#> Warning: non-integer x = 73.500000
#> Warning: non-integer x = 77.299990
#> Warning: non-integer x = 86.899960
#> Warning: non-integer x = 96.399960
#> Warning: non-integer x = 21.500000
#> Warning: non-integer x = 24.599990
#> Warning: non-integer x = 28.500000
#> Warning: non-integer x = 39.099980
#> Warning: non-integer x = 45.299990
#> Warning: non-integer x = 59.599980
#> Warning: non-integer x = 69.500000
#> Warning: non-integer x = 75.199950
#> Warning: non-integer x = 84.899960
#> Warning: non-integer x = 93.399960
#> Warning: non-integer x = 99.299990
#> Warning: non-integer x = 24.099990
#> Warning: non-integer x = 28.099990
#> Warning: non-integer x = 32.500000
#> Warning: non-integer x = 40.599980
#> Warning: non-integer x = 53.799990
#> Warning: non-integer x = 61.199980
#> Warning: non-integer x = 71.899960
#> Warning: non-integer x = 79.500000
#> Warning: non-integer x = 87.399960
#> Warning: non-integer x = 93.299990
#> Warning: non-integer x = 101.599980
#> Warning: non-integer x = 34.199980
#> Warning: non-integer x = 42.099980
#> Warning: non-integer x = 50.099980
#> Warning: non-integer x = 57.599980
#> Warning: non-integer x = 62.299990
#> Warning: non-integer x = 76.099980
#> Warning: non-integer x = 81.500000
#> Warning: non-integer x = 84.299990
#> Warning: non-integer x = 97.899960
#> Warning: non-integer x = 108.599980
#> Warning: non-integer x = 25.099990
#> Warning: non-integer x = 23.200000
#> Warning: non-integer x = 28.899990
#> Warning: non-integer x = 36.799990
#> Warning: non-integer x = 44.199980
#> Warning: non-integer x = 52.799990
#> Warning: non-integer x = 62.199980
#> Warning: non-integer x = 69.399960
#> Warning: non-integer x = 78.099980
#> Warning: non-integer x = 88.799990
#> Warning: non-integer x = 102.399960
#> Warning: non-integer x = 106.799990
#> Warning: non-integer x = 32.199980
#> Warning: non-integer x = 36.399990
#> Warning: non-integer x = 41.799990
#> Warning: non-integer x = 48.199980
#> Warning: non-integer x = 55.899990
#> Warning: non-integer x = 60.099980
#> Warning: non-integer x = 68.500000
#> Warning: non-integer x = 77.799990
#> Warning: non-integer x = 86.399960
#> Warning: non-integer x = 96.699950
#> Warning: non-integer x = 111.099980
#> Warning: non-integer x = 115.399960
#> Warning: non-integer x = 24.700000
#> Warning: non-integer x = 28.899990
#> Warning: non-integer x = 34.599980
#> Warning: non-integer x = 42.199980
#> Warning: non-integer x = 48.199980
#> Warning: non-integer x = 54.399990
#> Warning: non-integer x = 62.500000
#> Warning: non-integer x = 69.799990
#> Warning: non-integer x = 78.599980
#> Warning: non-integer x = 96.399960
#> Warning: non-integer x = 103.199950
#> Warning: non-integer x = 24.200000
#> Warning: non-integer x = 29.200000
#> Warning: non-integer x = 36.199980
#> Warning: non-integer x = 43.099980
#> Warning: non-integer x = 49.199980
#> Warning: non-integer x = 70.899960
#> Warning: non-integer x = 87.199950
#> Warning: non-integer x = 94.699950
#> Warning: non-integer x = 100.599980
#> Warning: non-integer x = 24.500000
#> Warning: non-integer x = 28.399990
#> Warning: non-integer x = 41.899990
#> Warning: non-integer x = 55.599980
#> Warning: non-integer x = 64.099980
#> Warning: non-integer x = 71.199950
#> Warning: non-integer x = 80.500000
#> Warning: non-integer x = 90.199950
#> Warning: non-integer x = 98.899960
#> Warning: non-integer x = 103.799990
#> Warning: non-integer x = 26.599990
#> Warning: non-integer x = 33.099980
#> Warning: non-integer x = 38.399990
#> Warning: non-integer x = 46.599980
#> Warning: non-integer x = 52.299990
#> Warning: non-integer x = 61.500000
#> Warning: non-integer x = 69.299990
#> Warning: non-integer x = 74.199950
#> Warning: non-integer x = 80.199950
#> Warning: non-integer x = 87.199950
#> Warning: non-integer x = 94.799990
#> Warning: non-integer x = 26.799990
#> Warning: non-integer x = 33.599980
#> Warning: non-integer x = 42.099980
#> Warning: non-integer x = 47.899990
#> Warning: non-integer x = 56.199980
#> Warning: non-integer x = 63.399990
#> Warning: non-integer x = 71.799990
#> Warning: non-integer x = 87.599980
#> Warning: non-integer x = 94.899960
#> Warning: non-integer x = 30.599990
#> Warning: non-integer x = 37.599980
#> Warning: non-integer x = 42.799990
#> Warning: non-integer x = 47.399990
#> Warning: non-integer x = 56.599980
#> Warning: non-integer x = 62.399990
#> Warning: non-integer x = 71.799990
#> Warning: non-integer x = 86.799990
#> Warning: non-integer x = 94.199950
#> Warning: non-integer x = 101.899960
#> Warning: non-integer x = 112.500000
#> Warning: non-integer x = 21.899990
#> Warning: non-integer x = 26.799990
#> Warning: non-integer x = 34.699980
#> Warning: non-integer x = 41.299990
#> Warning: non-integer x = 48.699980
#> Warning: non-integer x = 57.899990
#> Warning: non-integer x = 65.399960
#> Warning: non-integer x = 71.299990
#> Warning: non-integer x = 80.599980
#> Warning: non-integer x = 88.399960
#> Warning: non-integer x = 96.299990
#> Warning: non-integer x = 103.500000
#> Warning: non-integer x = 26.799990
#> Warning: non-integer x = 39.099980
#> Warning: non-integer x = 46.399990
#> Warning: non-integer x = 61.599980
#> Warning: non-integer x = 68.799990
#> Warning: non-integer x = 72.199950
#> Warning: non-integer x = 77.199950
#> Warning: non-integer x = 83.799990
#> Warning: non-integer x = 90.799990
#> Warning: non-integer x = 24.200000
#> Warning: non-integer x = 25.399990
#> Warning: non-integer x = 30.700000
#> Warning: non-integer x = 35.599980
#> Warning: non-integer x = 42.799990
#> Warning: non-integer x = 49.500000
#> Warning: non-integer x = 57.199980
#> Warning: non-integer x = 65.599980
#> Warning: non-integer x = 72.399960
#> Warning: non-integer x = 81.199950
#> Warning: non-integer x = 85.199950
#> Warning: non-integer x = 90.199950
#> Warning: non-integer x = 25.200000
#> Warning: non-integer x = 29.799990
#> Warning: non-integer x = 35.699980
#> Warning: non-integer x = 55.899990
#> Warning: non-integer x = 63.500000
#> Warning: non-integer x = 79.500000
#> Warning: non-integer x = 83.599980
#> Warning: non-integer x = 89.399960
#> Warning: non-integer x = 98.500000
#> Warning: non-integer x = 23.500000
#> Warning: non-integer x = 25.899990
#> Warning: non-integer x = 32.199980
#> Warning: non-integer x = 32.399990
#> Warning: non-integer x = 29.799990
#> Warning: non-integer x = 32.799990
#> Warning: non-integer x = 56.899990
#> Warning: non-integer x = 64.799990
#> Warning: non-integer x = 72.099980
#> Warning: non-integer x = 81.399960
#> Warning: non-integer x = 26.599990
#> Warning: non-integer x = 38.199980
#> Warning: non-integer x = 46.399990
#> Warning: non-integer x = 53.199980
#> Warning: non-integer x = 59.599980
#> Warning: non-integer x = 66.199950
#> Warning: non-integer x = 72.599980
#> Warning: non-integer x = 80.099980
#> Warning: non-integer x = 97.699950
#> Warning: non-integer x = 35.399990
#> Warning: non-integer x = 42.299990
#> Warning: non-integer x = 49.500000
#> Warning: non-integer x = 58.699980
#> Warning: non-integer x = 66.599980
#> Warning: non-integer x = 71.399960
#> Warning: non-integer x = 78.799990
#> Warning: non-integer x = 85.500000
#> Warning: non-integer x = 91.299990
#> Warning: non-integer x = 97.799990
#> Warning: non-integer x = 29.299990
#> Warning: non-integer x = 45.399990
#> Warning: non-integer x = 51.799990
#> Warning: non-integer x = 58.799990
#> Warning: non-integer x = 62.599980
#> Warning: non-integer x = 71.599980
#> Warning: non-integer x = 76.699950
#> Warning: non-integer x = 81.699950
#> Warning: non-integer x = 86.399960
#> Warning: non-integer x = 92.099980
#> Warning: non-integer x = 25.299990
#> Warning: non-integer x = 31.599990
#> Warning: non-integer x = 35.199980
#> Warning: non-integer x = 37.299990
#> Warning: non-integer x = 40.799990
#> Warning: non-integer x = 47.699980
#> Warning: non-integer x = 64.599980
#> Warning: non-integer x = 71.199950
#> Warning: non-integer x = 80.500000
#> Warning: non-integer x = 85.899960
#> Warning: non-integer x = 22.099990
#> Warning: non-integer x = 26.299990
#> Warning: non-integer x = 33.299990
#> Warning: non-integer x = 39.599980
#> Warning: non-integer x = 41.399990
#> Warning: non-integer x = 46.299990
#> Warning: non-integer x = 52.399990
#> Warning: non-integer x = 59.399990
#> Warning: non-integer x = 66.699950
#> Warning: non-integer x = 73.899960
#> Warning: non-integer x = 76.799990
#> Warning: non-integer x = 23.700000
#> Warning: non-integer x = 28.799990
#> Warning: non-integer x = 35.099980
#> Warning: non-integer x = 49.099980
#> Warning: non-integer x = 58.799990
#> Warning: non-integer x = 65.399960
#> Warning: non-integer x = 68.500000
#> Warning: non-integer x = 90.699950
#> Warning: non-integer x = 28.899990
#> Warning: non-integer x = 35.799990
#> Warning: non-integer x = 47.500000
#> Warning: non-integer x = 56.399990
#> Warning: non-integer x = 63.699980
#> Warning: non-integer x = 70.299990
#> Warning: non-integer x = 89.199950
#> Warning: non-integer x = 96.299990
#> Warning: non-integer x = 99.799990
#> Warning: non-integer x = 30.099990
#> Warning: non-integer x = 37.099980
#> Warning: non-integer x = 53.599980
#> Warning: non-integer x = 61.099980
#> Warning: non-integer x = 78.199950
#> Warning: non-integer x = 87.099980
#> Warning: non-integer x = 94.399960
#> Warning: non-integer x = 102.500000
#> Warning: non-integer x = 107.500000
#> Warning: non-integer x = 35.399990
#> Warning: non-integer x = 48.599980
#> Warning: non-integer x = 56.399990
#> Warning: non-integer x = 75.500000
#> Warning: non-integer x = 77.799990
#> Warning: non-integer x = 85.799990
#> Warning: non-integer x = 101.399960
#> Warning: non-integer x = 27.299990
#> Warning: non-integer x = 31.200000
#> Warning: non-integer x = 43.899990
#> Warning: non-integer x = 49.799990
#> Warning: non-integer x = 57.199980
#> Warning: non-integer x = 65.199950
#> Warning: non-integer x = 73.199950
#> Warning: non-integer x = 78.799990
#> Warning: non-integer x = 87.399960
#> Warning: non-integer x = 100.500000
#> Warning: non-integer x = 25.700000
#> Warning: non-integer x = 28.700000
#> Warning: non-integer x = 33.399990
#> Warning: non-integer x = 46.699980
#> Warning: non-integer x = 56.599980
#> Warning: non-integer x = 65.199950
#> Warning: non-integer x = 73.199950
#> Warning: non-integer x = 81.699950
#> Warning: non-integer x = 90.299990
#> Warning: non-integer x = 103.500000
#> Warning: non-integer x = 26.500000
#> Warning: non-integer x = 27.599990
#> Warning: non-integer x = 36.500000
#> Warning: non-integer x = 40.299990
#> Warning: non-integer x = 49.099980
#> Warning: non-integer x = 55.399990
#> Warning: non-integer x = 59.599980
#> Warning: non-integer x = 76.599980
#> Warning: non-integer x = 86.500000
#> Warning: non-integer x = 91.599980
#> Warning: non-integer x = 98.599980
#> Warning: non-integer x = 28.299990
#> Warning: non-integer x = 30.099990
#> Warning: non-integer x = 38.299990
#> Warning: non-integer x = 44.500000
#> Warning: non-integer x = 51.599980
#> Warning: non-integer x = 57.599980
#> Warning: non-integer x = 82.299990
#> Warning: non-integer x = 99.699950
#> Warning: non-integer x = 106.699950
#> Warning: non-integer x = 27.599990
#> Warning: non-integer x = 30.599990
#> Warning: non-integer x = 38.699980
#> Warning: non-integer x = 47.199980
#> Warning: non-integer x = 54.099980
#> Warning: non-integer x = 61.500000
#> Warning: non-integer x = 68.500000
#> Warning: non-integer x = 75.199950
#> Warning: non-integer x = 81.699950
#> Warning: non-integer x = 90.199950
#> Warning: non-integer x = 98.399960
#> Warning: non-integer x = 105.399960
#> Warning: non-integer x = 31.500000
#> Warning: non-integer x = 34.799990
#> Warning: non-integer x = 40.699980
#> Warning: non-integer x = 47.699980
#> Warning: non-integer x = 55.899990
#> Warning: non-integer x = 62.199980
#> Warning: non-integer x = 70.699950
#> Warning: non-integer x = 86.199950
#> Warning: non-integer x = 94.699950
#> Warning: non-integer x = 109.199950
#> Warning: non-integer x = 27.099990
#> Warning: non-integer x = 42.500000
#> Warning: non-integer x = 50.099980
#> Warning: non-integer x = 56.500000
#> Warning: non-integer x = 72.500000
#> Warning: non-integer x = 80.500000
#> Warning: non-integer x = 108.399960
#> Warning: non-integer x = 31.799990
#> Warning: non-integer x = 44.799990
#> Warning: non-integer x = 50.899990
#> Warning: non-integer x = 57.399990
#> Warning: non-integer x = 62.500000
#> Warning: non-integer x = 71.699950
#> Warning: non-integer x = 78.199950
#> Warning: non-integer x = 85.799990
#> Warning: non-integer x = 91.799990
#> Warning: non-integer x = 100.199950
#> Warning: non-integer x = 27.700000
#> Warning: non-integer x = 33.599980
#> Warning: non-integer x = 46.699980
#> Warning: non-integer x = 54.799990
#> Warning: non-integer x = 69.799990
#> Warning: non-integer x = 83.599980
#> Warning: non-integer x = 88.199950
#> Warning: non-integer x = 96.799990
#> Warning: non-integer x = 102.299990
#> Warning: non-integer x = 23.599990
#> Warning: non-integer x = 36.299990
#> Warning: non-integer x = 42.399990
#> Warning: non-integer x = 50.500000
#> Warning: non-integer x = 57.599980
#> Warning: non-integer x = 66.599980
#> Warning: non-integer x = 74.199950
#> Warning: non-integer x = 89.299990
#> Warning: non-integer x = 26.899990
#> Warning: non-integer x = 32.299990
#> Warning: non-integer x = 38.599980
#> Warning: non-integer x = 57.799990
#> Warning: non-integer x = 58.599980
#> Warning: non-integer x = 65.899960
#> Warning: non-integer x = 71.199950
#> Warning: non-integer x = 79.399960
#> Warning: non-integer x = 91.699950
#> Warning: non-integer x = 22.599990
#> Warning: non-integer x = 28.500000
#> Warning: non-integer x = 32.699980
#> Warning: non-integer x = 39.899990
#> Warning: non-integer x = 47.599980
#> Warning: non-integer x = 53.799990
#> Warning: non-integer x = 67.199950
#> Warning: non-integer x = 74.099980
#> Warning: non-integer x = 89.399960
#> Warning: non-integer x = 93.500000
#> Warning: non-integer x = 19.399990
#> Warning: non-integer x = 21.399990
#> Warning: non-integer x = 25.299990
#> Warning: non-integer x = 31.899990
#> Warning: non-integer x = 37.599980
#> Warning: non-integer x = 43.699980
#> Warning: non-integer x = 48.899990
#> Warning: non-integer x = 53.699980
#> Warning: non-integer x = 59.299990
#> Warning: non-integer x = 64.899960
#> Warning: non-integer x = 65.799990
#> Warning: non-integer x = 27.299990
#> Warning: non-integer x = 32.399990
#> Warning: non-integer x = 38.299990
#> Warning: non-integer x = 45.799990
#> Warning: non-integer x = 53.799990
#> Warning: non-integer x = 68.699950
#> Warning: non-integer x = 75.799990
#> Warning: non-integer x = 80.799990
#> Warning: non-integer x = 86.799990
#> Warning: non-integer x = 91.399960
#> Warning: non-integer x = 99.799990
#> Warning: non-integer x = 26.200000
#> Warning: non-integer x = 31.099990
#> Warning: non-integer x = 34.599980
#> Warning: non-integer x = 41.199980
#> Warning: non-integer x = 49.199980
#> Warning: non-integer x = 55.599980
#> Warning: non-integer x = 62.599980
#> Warning: non-integer x = 72.099980
#> Warning: non-integer x = 77.500000
#> Warning: non-integer x = 83.799990
#> Warning: non-integer x = 93.399960
#> Warning: non-integer x = 98.399960
#> Warning: non-integer x = 24.899990
#> Warning: non-integer x = 29.700000
#> Warning: non-integer x = 33.799990
#> Warning: non-integer x = 38.799990
#> Warning: non-integer x = 48.299990
#> Warning: non-integer x = 52.899990
#> Warning: non-integer x = 70.399960
#> Warning: non-integer x = 76.799990
#> Warning: non-integer x = 83.299990
#> Warning: non-integer x = 102.699950
#> Warning: non-integer x = 24.599990
#> Warning: non-integer x = 34.599980
#> Warning: non-integer x = 41.500000
#> Warning: non-integer x = 49.699980
#> Warning: non-integer x = 56.500000
#> Warning: non-integer x = 66.899960
#> Warning: non-integer x = 75.799990
#> Warning: non-integer x = 84.599980
#> Warning: non-integer x = 98.799990
#> Warning: non-integer x = 107.199950
#> Warning: non-integer x = 32.699980
#> Warning: non-integer x = 38.299990
#> Warning: non-integer x = 45.500000
#> Warning: non-integer x = 48.599980
#> Warning: non-integer x = 62.599980
#> Warning: non-integer x = 70.199950
#> Warning: non-integer x = 73.799990
#> Warning: non-integer x = 80.299990
#> Warning: non-integer x = 85.500000
#> Warning: non-integer x = 93.099980
#> Warning: non-integer x = 35.199980
#> Warning: non-integer x = 41.500000
#> Warning: non-integer x = 47.699980
#> Warning: non-integer x = 53.799990
#> Warning: non-integer x = 61.599980
#> Warning: non-integer x = 79.099980
#> Warning: non-integer x = 85.699950
#> Warning: non-integer x = 92.500000
#> Warning: non-integer x = 101.099980
#> Warning: non-integer x = 34.500000
#> Warning: non-integer x = 40.399990
#> Warning: non-integer x = 53.500000
#> Warning: non-integer x = 60.199980
#> Warning: non-integer x = 68.599980
#> Warning: non-integer x = 73.399960
#> Warning: non-integer x = 78.500000
#> Warning: non-integer x = 90.599980
#> Warning: non-integer x = 97.199950
#> Warning: non-integer x = 31.200000
#> Warning: non-integer x = 38.799990
#> Warning: non-integer x = 44.699980
#> Warning: non-integer x = 53.599980
#> Warning: non-integer x = 59.199980
#> Warning: non-integer x = 67.099980
#> Warning: non-integer x = 76.399960
#> Warning: non-integer x = 83.799990
#> Warning: non-integer x = 71.599980
#> Warning: non-integer x = 97.399960
#> Warning: non-integer x = 107.099980
#> Warning: non-integer x = 24.299990
#> Warning: non-integer x = 28.399990
#> Warning: non-integer x = 40.299990
#> Warning: non-integer x = 46.199980
#> Warning: non-integer x = 51.899990
#> Warning: non-integer x = 58.099980
#> Warning: non-integer x = 62.599980
#> Warning: non-integer x = 68.199950
#> Warning: non-integer x = 78.399960
#> Warning: non-integer x = 87.500000
#> Warning: non-integer x = 90.399960
#> Warning: non-integer x = 24.599990
#> Warning: non-integer x = 25.799990
#> Warning: non-integer x = 28.599990
#> Warning: non-integer x = 30.399990
#> Warning: non-integer x = 36.099980
#> Warning: non-integer x = 36.099980
#> Warning: non-integer x = 49.299990
#> Warning: non-integer x = 57.899990
#> Warning: non-integer x = 75.699950
#> Warning: non-integer x = 81.399960
#> Warning: non-integer x = 88.699950
#> Warning: non-integer x = 21.200000
#> Warning: non-integer x = 25.799990
#> Warning: non-integer x = 29.399990
#> Warning: non-integer x = 36.799990
#> Warning: non-integer x = 43.199980
#> Warning: non-integer x = 51.099980
#> Warning: non-integer x = 59.299990
#> Warning: non-integer x = 72.799990
#> Warning: non-integer x = 78.599980
#> Warning: non-integer x = 93.799990
#> Warning: non-integer x = 95.199950
#> Warning: non-integer x = 29.399990
#> Warning: non-integer x = 34.599980
#> Warning: non-integer x = 40.599980
#> Warning: non-integer x = 46.599980
#> Warning: non-integer x = 62.500000
#> Warning: non-integer x = 78.299990
#> Warning: non-integer x = 83.199950
#> Warning: non-integer x = 34.699980
#> Warning: non-integer x = 42.799990
#> Warning: non-integer x = 48.399990
#> Warning: non-integer x = 53.299990
#> Warning: non-integer x = 71.099980
#> Warning: non-integer x = 77.399960
#> Warning: non-integer x = 94.500000
#> Warning: non-integer x = 104.599980
#> Warning: non-integer x = 29.599990
#> Warning: non-integer x = 34.199980
#> Warning: non-integer x = 63.500000
#> Warning: non-integer x = 72.699950
#> Warning: non-integer x = 78.699950
#> Warning: non-integer x = 84.899960
#> Warning: non-integer x = 96.399960
#> Warning: non-integer x = 100.199950
#> Warning: non-integer x = 22.399990
#> Warning: non-integer x = 25.200000
#> Warning: non-integer x = 36.500000
#> Warning: non-integer x = 43.299990
#> Warning: non-integer x = 58.099980
#> Warning: non-integer x = 70.699950
#> Warning: non-integer x = 78.099980
#> Warning: non-integer x = 83.500000
#> Warning: non-integer x = 26.599990
#> Warning: non-integer x = 28.200000
#> Warning: non-integer x = 38.399990
#> Warning: non-integer x = 45.799990
#> Warning: non-integer x = 54.899990
#> Warning: non-integer x = 60.099980
#> Warning: non-integer x = 56.899990
#> Warning: non-integer x = 64.899960
#> Warning: non-integer x = 81.899960
#> Warning: non-integer x = 90.899960
#> Warning: non-integer x = 28.200000
#> Warning: non-integer x = 35.299990
#> Warning: non-integer x = 42.699980
#> Warning: non-integer x = 48.199980
#> Warning: non-integer x = 53.199980
#> Warning: non-integer x = 64.799990
#> Warning: non-integer x = 71.500000
#> Warning: non-integer x = 76.099980
#> Warning: non-integer x = 86.099980
#> Warning: non-integer x = 92.500000
#> Warning: non-integer x = 27.099990
#> Warning: non-integer x = 34.699980
#> Warning: non-integer x = 40.699980
#> Warning: non-integer x = 47.599980
#> Warning: non-integer x = 56.500000
#> Warning: non-integer x = 72.299990
#> Warning: non-integer x = 95.099980
#> Warning: non-integer x = 105.699950
#> Warning: non-integer x = 37.799990
#> Warning: non-integer x = 43.299990
#> Warning: non-integer x = 51.500000
#> Warning: non-integer x = 63.699980
#> Warning: non-integer x = 70.500000
#> Warning: non-integer x = 80.399960
#> Warning: non-integer x = 106.099980
#> Warning: non-integer x = 29.500000
#> Warning: non-integer x = 31.399990
#> Warning: non-integer x = 39.399990
#> Warning: non-integer x = 44.799990
#> Warning: non-integer x = 50.299990
#> Warning: non-integer x = 65.599980
#> Warning: non-integer x = 72.399960
#> Warning: non-integer x = 80.199950
#> Warning: non-integer x = 90.399960
#> Warning: non-integer x = 99.099980
#> Warning: non-integer x = 22.799990
#> Warning: non-integer x = 33.899990
#> Warning: non-integer x = 37.699980
#> Warning: non-integer x = 41.399990
#> Warning: non-integer x = 48.199980
#> Warning: non-integer x = 53.699980
#> Warning: non-integer x = 62.599980
#> Warning: non-integer x = 70.399960
#> Warning: non-integer x = 78.500000
#> Warning: non-integer x = 85.899960
#> Warning: non-integer x = 22.299990
#> Warning: non-integer x = 24.700000
#> Warning: non-integer x = 30.399990
#> Warning: non-integer x = 36.899990
#> Warning: non-integer x = 44.099980
#> Warning: non-integer x = 52.799990
#> Warning: non-integer x = 60.299990
#> Warning: non-integer x = 67.799990
#> Warning: non-integer x = 75.399960
#> Warning: non-integer x = 87.599980
#> Warning: non-integer x = 101.399960
#> Warning: non-integer x = 23.799990
#> Warning: non-integer x = 37.099980
#> Warning: non-integer x = 43.199980
#> Warning: non-integer x = 50.399990
#> Warning: non-integer x = 60.199980
#> Warning: non-integer x = 82.399960
#> Warning: non-integer x = 91.199950
#> Warning: non-integer x = 101.799990
#> Warning: non-integer x = 109.599980
#> Warning: non-integer x = 25.799990
#> Warning: non-integer x = 29.200000
#> Warning: non-integer x = 35.799990
#> Warning: non-integer x = 41.099980
#> Warning: non-integer x = 55.199980
#> Warning: non-integer x = 62.199980
#> Warning: non-integer x = 69.799990
#> Warning: non-integer x = 76.399960
#> Warning: non-integer x = 83.199950
#> Warning: non-integer x = 93.199950
#> Warning: non-integer x = 32.899990
#> Warning: non-integer x = 46.199980
#> Warning: non-integer x = 53.500000
#> Warning: non-integer x = 58.599980
#> Warning: non-integer x = 68.199950
#> Warning: non-integer x = 80.799990
#> Warning: non-integer x = 84.500000
#> Warning: non-integer x = 24.799990
#> Warning: non-integer x = 35.799990
#> Warning: non-integer x = 42.299990
#> Warning: non-integer x = 50.899990
#> Warning: non-integer x = 57.799990
#> Warning: non-integer x = 64.799990
#> Warning: non-integer x = 71.799990
#> Warning: non-integer x = 83.799990
#> Warning: non-integer x = 92.099980
#> Warning: non-integer x = 26.200000
#> Warning: non-integer x = 30.399990
#> Warning: non-integer x = 37.399990
#> Warning: non-integer x = 49.500000
#> Warning: non-integer x = 55.099980
#> Warning: non-integer x = 64.199950
#> Warning: non-integer x = 75.599980
#> Warning: non-integer x = 83.299990
#> Warning: non-integer x = 87.399960
#> Warning: non-integer x = 94.699950
#> Warning: non-integer x = 98.399960
#> Warning: non-integer x = 32.500000
#> Warning: non-integer x = 38.799990
#> Warning: non-integer x = 47.799990
#> Warning: non-integer x = 54.500000
#> Warning: non-integer x = 70.099980
#> Warning: non-integer x = 76.599980
#> Warning: non-integer x = 86.199950
#> Warning: non-integer x = 95.799990
#> Warning: non-integer x = 101.399960
#> Warning: non-integer x = 112.299990
#> Warning: non-integer x = 32.399990
#> Warning: non-integer x = 38.199980
#> Warning: non-integer x = 44.699980
#> Warning: non-integer x = 53.199980
#> Warning: non-integer x = 62.399990
#> Warning: non-integer x = 70.500000
#> Warning: non-integer x = 72.799990
#> Warning: non-integer x = 86.599980
#> Warning: non-integer x = 93.299990
#> Warning: non-integer x = 104.199950
#> Warning: non-integer x = 27.399990
#> Warning: non-integer x = 32.199980
#> Warning: non-integer x = 37.899990
#> Warning: non-integer x = 45.899990
#> Warning: non-integer x = 51.199980
#> Warning: non-integer x = 57.099980
#> Warning: non-integer x = 76.799990
#> Warning: non-integer x = 83.099980
#> Warning: non-integer x = 91.599980
#> Warning: non-integer x = 100.500000
#> Warning: non-integer x = 105.299990
#> Warning: non-integer x = 27.099990
#> Warning: non-integer x = 30.299990
#> Warning: non-integer x = 38.199980
#> Warning: non-integer x = 43.199980
#> Warning: non-integer x = 52.500000
#> Warning: non-integer x = 67.299990
#> Warning: non-integer x = 74.199950
#> Warning: non-integer x = 81.199950
#> Warning: non-integer x = 87.500000
#> Warning: non-integer x = 94.399960
#> Warning: non-integer x = 101.399960
#> Warning: non-integer x = 26.799990
#> Warning: non-integer x = 31.099990
#> Warning: non-integer x = 37.799990
#> Warning: non-integer x = 44.599980
#> Warning: non-integer x = 50.500000
#> Warning: non-integer x = 58.299990
#> Warning: non-integer x = 68.299990
#> Warning: non-integer x = 75.099980
#> Warning: non-integer x = 84.399960
#> Warning: non-integer x = 87.299990
#> Warning: non-integer x = 96.399960
#> Warning: non-integer x = 104.399960
#> Warning: non-integer x = 24.500000
#> Warning: non-integer x = 31.599990
#> Warning: non-integer x = 37.399990
#> Warning: non-integer x = 46.399990
#> Warning: non-integer x = 53.599980
#> Warning: non-integer x = 61.199980
#> Warning: non-integer x = 70.099980
#> Warning: non-integer x = 77.500000
#> Warning: non-integer x = 86.199950
#> Warning: non-integer x = 89.199950
#> Warning: non-integer x = 96.899960
#> Warning: non-integer x = 104.500000
#> Warning: non-integer x = 23.099990
#> Warning: non-integer x = 30.099990
#> Warning: non-integer x = 40.699980
#> Warning: non-integer x = 46.599980
#> Warning: non-integer x = 52.099980
#> Warning: non-integer x = 60.500000
#> Warning: non-integer x = 73.500000
#> Warning: non-integer x = 77.299990
#> Warning: non-integer x = 86.899960
#> Warning: non-integer x = 96.399960
#> Warning: non-integer x = 21.500000
#> Warning: non-integer x = 24.599990
#> Warning: non-integer x = 28.500000
#> Warning: non-integer x = 39.099980
#> Warning: non-integer x = 45.299990
#> Warning: non-integer x = 59.599980
#> Warning: non-integer x = 69.500000
#> Warning: non-integer x = 75.199950
#> Warning: non-integer x = 84.899960
#> Warning: non-integer x = 93.399960
#> Warning: non-integer x = 99.299990
#> Warning: non-integer x = 24.099990
#> Warning: non-integer x = 28.099990
#> Warning: non-integer x = 32.500000
#> Warning: non-integer x = 40.599980
#> Warning: non-integer x = 53.799990
#> Warning: non-integer x = 61.199980
#> Warning: non-integer x = 71.899960
#> Warning: non-integer x = 79.500000
#> Warning: non-integer x = 87.399960
#> Warning: non-integer x = 93.299990
#> Warning: non-integer x = 101.599980
#> Warning: non-integer x = 34.199980
#> Warning: non-integer x = 42.099980
#> Warning: non-integer x = 50.099980
#> Warning: non-integer x = 57.599980
#> Warning: non-integer x = 62.299990
#> Warning: non-integer x = 76.099980
#> Warning: non-integer x = 81.500000
#> Warning: non-integer x = 84.299990
#> Warning: non-integer x = 97.899960
#> Warning: non-integer x = 108.599980
#> Warning: non-integer x = 25.099990
#> Warning: non-integer x = 23.200000
#> Warning: non-integer x = 28.899990
#> Warning: non-integer x = 36.799990
#> Warning: non-integer x = 44.199980
#> Warning: non-integer x = 52.799990
#> Warning: non-integer x = 62.199980
#> Warning: non-integer x = 69.399960
#> Warning: non-integer x = 78.099980
#> Warning: non-integer x = 88.799990
#> Warning: non-integer x = 102.399960
#> Warning: non-integer x = 106.799990
#> Warning: non-integer x = 32.199980
#> Warning: non-integer x = 36.399990
#> Warning: non-integer x = 41.799990
#> Warning: non-integer x = 48.199980
#> Warning: non-integer x = 55.899990
#> Warning: non-integer x = 60.099980
#> Warning: non-integer x = 68.500000
#> Warning: non-integer x = 77.799990
#> Warning: non-integer x = 86.399960
#> Warning: non-integer x = 96.699950
#> Warning: non-integer x = 111.099980
#> Warning: non-integer x = 115.399960
#> Warning: non-integer x = 24.700000
#> Warning: non-integer x = 28.899990
#> Warning: non-integer x = 34.599980
#> Warning: non-integer x = 42.199980
#> Warning: non-integer x = 48.199980
#> Warning: non-integer x = 54.399990
#> Warning: non-integer x = 62.500000
#> Warning: non-integer x = 69.799990
#> Warning: non-integer x = 78.599980
#> Warning: non-integer x = 96.399960
#> Warning: non-integer x = 103.199950
#> Warning: non-integer x = 24.200000
#> Warning: non-integer x = 29.200000
#> Warning: non-integer x = 36.199980
#> Warning: non-integer x = 43.099980
#> Warning: non-integer x = 49.199980
#> Warning: non-integer x = 70.899960
#> Warning: non-integer x = 87.199950
#> Warning: non-integer x = 94.699950
#> Warning: non-integer x = 100.599980
#> Warning: non-integer x = 24.500000
#> Warning: non-integer x = 28.399990
#> Warning: non-integer x = 41.899990
#> Warning: non-integer x = 55.599980
#> Warning: non-integer x = 64.099980
#> Warning: non-integer x = 71.199950
#> Warning: non-integer x = 80.500000
#> Warning: non-integer x = 90.199950
#> Warning: non-integer x = 98.899960
#> Warning: non-integer x = 103.799990
#> Warning: non-integer x = 26.599990
#> Warning: non-integer x = 33.099980
#> Warning: non-integer x = 38.399990
#> Warning: non-integer x = 46.599980
#> Warning: non-integer x = 52.299990
#> Warning: non-integer x = 61.500000
#> Warning: non-integer x = 69.299990
#> Warning: non-integer x = 74.199950
#> Warning: non-integer x = 80.199950
#> Warning: non-integer x = 87.199950
#> Warning: non-integer x = 94.799990
#> Warning: non-integer x = 26.799990
#> Warning: non-integer x = 33.599980
#> Warning: non-integer x = 42.099980
#> Warning: non-integer x = 47.899990
#> Warning: non-integer x = 56.199980
#> Warning: non-integer x = 63.399990
#> Warning: non-integer x = 71.799990
#> Warning: non-integer x = 87.599980
#> Warning: non-integer x = 94.899960
#> Warning: non-integer x = 30.599990
#> Warning: non-integer x = 37.599980
#> Warning: non-integer x = 42.799990
#> Warning: non-integer x = 47.399990
#> Warning: non-integer x = 56.599980
#> Warning: non-integer x = 62.399990
#> Warning: non-integer x = 71.799990
#> Warning: non-integer x = 86.799990
#> Warning: non-integer x = 94.199950
#> Warning: non-integer x = 101.899960
#> Warning: non-integer x = 112.500000
#> Warning: non-integer x = 21.899990
#> Warning: non-integer x = 26.799990
#> Warning: non-integer x = 34.699980
#> Warning: non-integer x = 41.299990
#> Warning: non-integer x = 48.699980
#> Warning: non-integer x = 57.899990
#> Warning: non-integer x = 65.399960
#> Warning: non-integer x = 71.299990
#> Warning: non-integer x = 80.599980
#> Warning: non-integer x = 88.399960
#> Warning: non-integer x = 96.299990
#> Warning: non-integer x = 103.500000
#> Warning: non-integer x = 26.799990
#> Warning: non-integer x = 39.099980
#> Warning: non-integer x = 46.399990
#> Warning: non-integer x = 61.599980
#> Warning: non-integer x = 68.799990
#> Warning: non-integer x = 72.199950
#> Warning: non-integer x = 77.199950
#> Warning: non-integer x = 83.799990
#> Warning: non-integer x = 90.799990
#> Warning: non-integer x = 24.200000
#> Warning: non-integer x = 25.399990
#> Warning: non-integer x = 30.700000
#> Warning: non-integer x = 35.599980
#> Warning: non-integer x = 42.799990
#> Warning: non-integer x = 49.500000
#> Warning: non-integer x = 57.199980
#> Warning: non-integer x = 65.599980
#> Warning: non-integer x = 72.399960
#> Warning: non-integer x = 81.199950
#> Warning: non-integer x = 85.199950
#> Warning: non-integer x = 90.199950
#> Warning: non-integer x = 25.200000
#> Warning: non-integer x = 29.799990
#> Warning: non-integer x = 35.699980
#> Warning: non-integer x = 55.899990
#> Warning: non-integer x = 63.500000
#> Warning: non-integer x = 79.500000
#> Warning: non-integer x = 83.599980
#> Warning: non-integer x = 89.399960
#> Warning: non-integer x = 98.500000
#> Warning: non-integer x = 23.500000
#> Warning: non-integer x = 25.899990
#> Warning: non-integer x = 32.199980
#> Warning: non-integer x = 32.399990
#> Warning: non-integer x = 29.799990
#> Warning: non-integer x = 32.799990
#> Warning: non-integer x = 56.899990
#> Warning: non-integer x = 64.799990
#> Warning: non-integer x = 72.099980
#> Warning: non-integer x = 81.399960
#> Warning: non-integer x = 26.599990
#> Warning: non-integer x = 38.199980
#> Warning: non-integer x = 46.399990
#> Warning: non-integer x = 53.199980
#> Warning: non-integer x = 59.599980
#> Warning: non-integer x = 66.199950
#> Warning: non-integer x = 72.599980
#> Warning: non-integer x = 80.099980
#> Warning: non-integer x = 97.699950
#> Warning: non-integer x = 35.399990
#> Warning: non-integer x = 42.299990
#> Warning: non-integer x = 49.500000
#> Warning: non-integer x = 58.699980
#> Warning: non-integer x = 66.599980
#> Warning: non-integer x = 71.399960
#> Warning: non-integer x = 78.799990
#> Warning: non-integer x = 85.500000
#> Warning: non-integer x = 91.299990
#> Warning: non-integer x = 97.799990
#> Warning: non-integer x = 29.299990
#> Warning: non-integer x = 45.399990
#> Warning: non-integer x = 51.799990
#> Warning: non-integer x = 58.799990
#> Warning: non-integer x = 62.599980
#> Warning: non-integer x = 71.599980
#> Warning: non-integer x = 76.699950
#> Warning: non-integer x = 81.699950
#> Warning: non-integer x = 86.399960
#> Warning: non-integer x = 92.099980
#> Warning: non-integer x = 25.299990
#> Warning: non-integer x = 31.599990
#> Warning: non-integer x = 35.199980
#> Warning: non-integer x = 37.299990
#> Warning: non-integer x = 40.799990
#> Warning: non-integer x = 47.699980
#> Warning: non-integer x = 64.599980
#> Warning: non-integer x = 71.199950
#> Warning: non-integer x = 80.500000
#> Warning: non-integer x = 85.899960
#> Warning: non-integer x = 22.099990
#> Warning: non-integer x = 26.299990
#> Warning: non-integer x = 33.299990
#> Warning: non-integer x = 39.599980
#> Warning: non-integer x = 41.399990
#> Warning: non-integer x = 46.299990
#> Warning: non-integer x = 52.399990
#> Warning: non-integer x = 59.399990
#> Warning: non-integer x = 66.699950
#> Warning: non-integer x = 73.899960
#> Warning: non-integer x = 76.799990
#> Warning: non-integer x = 23.700000
#> Warning: non-integer x = 28.799990
#> Warning: non-integer x = 35.099980
#> Warning: non-integer x = 49.099980
#> Warning: non-integer x = 58.799990
#> Warning: non-integer x = 65.399960
#> Warning: non-integer x = 68.500000
#> Warning: non-integer x = 90.699950
#> Warning: non-integer x = 28.899990
#> Warning: non-integer x = 35.799990
#> Warning: non-integer x = 47.500000
#> Warning: non-integer x = 56.399990
#> Warning: non-integer x = 63.699980
#> Warning: non-integer x = 70.299990
#> Warning: non-integer x = 89.199950
#> Warning: non-integer x = 96.299990
#> Warning: non-integer x = 99.799990
#> Warning: non-integer x = 30.099990
#> Warning: non-integer x = 37.099980
#> Warning: non-integer x = 53.599980
#> Warning: non-integer x = 61.099980
#> Warning: non-integer x = 78.199950
#> Warning: non-integer x = 87.099980
#> Warning: non-integer x = 94.399960
#> Warning: non-integer x = 102.500000
#> Warning: non-integer x = 107.500000
#> Warning: non-integer x = 35.399990
#> Warning: non-integer x = 48.599980
#> Warning: non-integer x = 56.399990
#> Warning: non-integer x = 75.500000
#> Warning: non-integer x = 77.799990
#> Warning: non-integer x = 85.799990
#> Warning: non-integer x = 101.399960
#> Warning: non-integer x = 27.299990
#> Warning: non-integer x = 31.200000
#> Warning: non-integer x = 43.899990
#> Warning: non-integer x = 49.799990
#> Warning: non-integer x = 57.199980
#> Warning: non-integer x = 65.199950
#> Warning: non-integer x = 73.199950
#> Warning: non-integer x = 78.799990
#> Warning: non-integer x = 87.399960
#> Warning: non-integer x = 100.500000
#> Warning: non-integer x = 25.700000
#> Warning: non-integer x = 28.700000
#> Warning: non-integer x = 33.399990
#> Warning: non-integer x = 46.699980
#> Warning: non-integer x = 56.599980
#> Warning: non-integer x = 65.199950
#> Warning: non-integer x = 73.199950
#> Warning: non-integer x = 81.699950
#> Warning: non-integer x = 90.299990
#> Warning: non-integer x = 103.500000
#> Warning: non-integer x = 26.500000
#> Warning: non-integer x = 27.599990
#> Warning: non-integer x = 36.500000
#> Warning: non-integer x = 40.299990
#> Warning: non-integer x = 49.099980
#> Warning: non-integer x = 55.399990
#> Warning: non-integer x = 59.599980
#> Warning: non-integer x = 76.599980
#> Warning: non-integer x = 86.500000
#> Warning: non-integer x = 91.599980
#> Warning: non-integer x = 98.599980
#> Warning: non-integer x = 28.299990
#> Warning: non-integer x = 30.099990
#> Warning: non-integer x = 38.299990
#> Warning: non-integer x = 44.500000
#> Warning: non-integer x = 51.599980
#> Warning: non-integer x = 57.599980
#> Warning: non-integer x = 82.299990
#> Warning: non-integer x = 99.699950
#> Warning: non-integer x = 106.699950
#> Warning: non-integer x = 27.599990
#> Warning: non-integer x = 30.599990
#> Warning: non-integer x = 38.699980
#> Warning: non-integer x = 47.199980
#> Warning: non-integer x = 54.099980
#> Warning: non-integer x = 61.500000
#> Warning: non-integer x = 68.500000
#> Warning: non-integer x = 75.199950
#> Warning: non-integer x = 81.699950
#> Warning: non-integer x = 90.199950
#> Warning: non-integer x = 98.399960
#> Warning: non-integer x = 105.399960
#> Warning: non-integer x = 31.500000
#> Warning: non-integer x = 34.799990
#> Warning: non-integer x = 40.699980
#> Warning: non-integer x = 47.699980
#> Warning: non-integer x = 55.899990
#> Warning: non-integer x = 62.199980
#> Warning: non-integer x = 70.699950
#> Warning: non-integer x = 86.199950
#> Warning: non-integer x = 94.699950
#> Warning: non-integer x = 109.199950
#> Warning: non-integer x = 27.099990
#> Warning: non-integer x = 42.500000
#> Warning: non-integer x = 50.099980
#> Warning: non-integer x = 56.500000
#> Warning: non-integer x = 72.500000
#> Warning: non-integer x = 80.500000
#> Warning: non-integer x = 108.399960
#> Warning: non-integer x = 31.799990
#> Warning: non-integer x = 44.799990
#> Warning: non-integer x = 50.899990
#> Warning: non-integer x = 57.399990
#> Warning: non-integer x = 62.500000
#> Warning: non-integer x = 71.699950
#> Warning: non-integer x = 78.199950
#> Warning: non-integer x = 85.799990
#> Warning: non-integer x = 91.799990
#> Warning: non-integer x = 100.199950
#> Warning: non-integer x = 27.700000
#> Warning: non-integer x = 33.599980
#> Warning: non-integer x = 46.699980
#> Warning: non-integer x = 54.799990
#> Warning: non-integer x = 69.799990
#> Warning: non-integer x = 83.599980
#> Warning: non-integer x = 88.199950
#> Warning: non-integer x = 96.799990
#> Warning: non-integer x = 102.299990
#> Warning: non-integer x = 23.599990
#> Warning: non-integer x = 36.299990
#> Warning: non-integer x = 42.399990
#> Warning: non-integer x = 50.500000
#> Warning: non-integer x = 57.599980
#> Warning: non-integer x = 66.599980
#> Warning: non-integer x = 74.199950
#> Warning: non-integer x = 89.299990
#> Warning: non-integer x = 26.899990
#> Warning: non-integer x = 32.299990
#> Warning: non-integer x = 38.599980
#> Warning: non-integer x = 57.799990
#> Warning: non-integer x = 58.599980
#> Warning: non-integer x = 65.899960
#> Warning: non-integer x = 71.199950
#> Warning: non-integer x = 79.399960
#> Warning: non-integer x = 91.699950
#> Warning: non-integer x = 22.599990
#> Warning: non-integer x = 28.500000
#> Warning: non-integer x = 32.699980
#> Warning: non-integer x = 39.899990
#> Warning: non-integer x = 47.599980
#> Warning: non-integer x = 53.799990
#> Warning: non-integer x = 67.199950
#> Warning: non-integer x = 74.099980
#> Warning: non-integer x = 89.399960
#> Warning: non-integer x = 93.500000
#> Warning: non-integer x = 19.399990
#> Warning: non-integer x = 21.399990
#> Warning: non-integer x = 25.299990
#> Warning: non-integer x = 31.899990
#> Warning: non-integer x = 37.599980
#> Warning: non-integer x = 43.699980
#> Warning: non-integer x = 48.899990
#> Warning: non-integer x = 53.699980
#> Warning: non-integer x = 59.299990
#> Warning: non-integer x = 64.899960
#> Warning: non-integer x = 65.799990
#> Warning: non-integer x = 27.299990
#> Warning: non-integer x = 32.399990
#> Warning: non-integer x = 38.299990
#> Warning: non-integer x = 45.799990
#> Warning: non-integer x = 53.799990
#> Warning: non-integer x = 68.699950
#> Warning: non-integer x = 75.799990
#> Warning: non-integer x = 80.799990
#> Warning: non-integer x = 86.799990
#> Warning: non-integer x = 91.399960
#> Warning: non-integer x = 99.799990
#> Warning: non-integer x = 26.200000
#> Warning: non-integer x = 31.099990
#> Warning: non-integer x = 34.599980
#> Warning: non-integer x = 41.199980
#> Warning: non-integer x = 49.199980
#> Warning: non-integer x = 55.599980
#> Warning: non-integer x = 62.599980
#> Warning: non-integer x = 72.099980
#> Warning: non-integer x = 77.500000
#> Warning: non-integer x = 83.799990
#> Warning: non-integer x = 93.399960
#> Warning: non-integer x = 98.399960
#> Warning: non-integer x = 24.899990
#> Warning: non-integer x = 29.700000
#> Warning: non-integer x = 33.799990
#> Warning: non-integer x = 38.799990
#> Warning: non-integer x = 48.299990
#> Warning: non-integer x = 52.899990
#> Warning: non-integer x = 70.399960
#> Warning: non-integer x = 76.799990
#> Warning: non-integer x = 83.299990
#> Warning: non-integer x = 102.699950
#> Warning: non-integer x = 24.599990
#> Warning: non-integer x = 34.599980
#> Warning: non-integer x = 41.500000
#> Warning: non-integer x = 49.699980
#> Warning: non-integer x = 56.500000
#> Warning: non-integer x = 66.899960
#> Warning: non-integer x = 75.799990
#> Warning: non-integer x = 84.599980
#> Warning: non-integer x = 98.799990
#> Warning: non-integer x = 107.199950
#> Warning: non-integer x = 32.699980
#> Warning: non-integer x = 38.299990
#> Warning: non-integer x = 45.500000
#> Warning: non-integer x = 48.599980
#> Warning: non-integer x = 62.599980
#> Warning: non-integer x = 70.199950
#> Warning: non-integer x = 73.799990
#> Warning: non-integer x = 80.299990
#> Warning: non-integer x = 85.500000
#> Warning: non-integer x = 93.099980
#> Warning: non-integer x = 35.199980
#> Warning: non-integer x = 41.500000
#> Warning: non-integer x = 47.699980
#> Warning: non-integer x = 53.799990
#> Warning: non-integer x = 61.599980
#> Warning: non-integer x = 79.099980
#> Warning: non-integer x = 85.699950
#> Warning: non-integer x = 92.500000
#> Warning: non-integer x = 101.099980
#> Warning: non-integer x = 34.500000
#> Warning: non-integer x = 40.399990
#> Warning: non-integer x = 53.500000
#> Warning: non-integer x = 60.199980
#> Warning: non-integer x = 68.599980
#> Warning: non-integer x = 73.399960
#> Warning: non-integer x = 78.500000
#> Warning: non-integer x = 90.599980
#> Warning: non-integer x = 97.199950
#> Warning: non-integer x = 31.200000
#> Warning: non-integer x = 38.799990
#> Warning: non-integer x = 44.699980
#> Warning: non-integer x = 53.599980
#> Warning: non-integer x = 59.199980
#> Warning: non-integer x = 67.099980
#> Warning: non-integer x = 76.399960
#> Warning: non-integer x = 83.799990
#> Warning: non-integer x = 71.599980
#> Warning: non-integer x = 97.399960
#> Warning: non-integer x = 107.099980
#> Warning: non-integer x = 24.299990
#> Warning: non-integer x = 28.399990
#> Warning: non-integer x = 40.299990
#> Warning: non-integer x = 46.199980
#> Warning: non-integer x = 51.899990
#> Warning: non-integer x = 58.099980
#> Warning: non-integer x = 62.599980
#> Warning: non-integer x = 68.199950
#> Warning: non-integer x = 78.399960
#> Warning: non-integer x = 87.500000
#> Warning: non-integer x = 90.399960
#> Warning: non-integer x = 24.599990
#> Warning: non-integer x = 25.799990
#> Warning: non-integer x = 28.599990
#> Warning: non-integer x = 30.399990
#> Warning: non-integer x = 36.099980
#> Warning: non-integer x = 36.099980
#> Warning: non-integer x = 49.299990
#> Warning: non-integer x = 57.899990
#> Warning: non-integer x = 75.699950
#> Warning: non-integer x = 81.399960
#> Warning: non-integer x = 88.699950
#> Warning: non-integer x = 21.200000
#> Warning: non-integer x = 25.799990
#> Warning: non-integer x = 29.399990
#> Warning: non-integer x = 36.799990
#> Warning: non-integer x = 43.199980
#> Warning: non-integer x = 51.099980
#> Warning: non-integer x = 59.299990
#> Warning: non-integer x = 72.799990
#> Warning: non-integer x = 78.599980
#> Warning: non-integer x = 93.799990
#> Warning: non-integer x = 95.199950
#> Warning: non-integer x = 29.399990
#> Warning: non-integer x = 34.599980
#> Warning: non-integer x = 40.599980
#> Warning: non-integer x = 46.599980
#> Warning: non-integer x = 62.500000
#> Warning: non-integer x = 78.299990
#> Warning: non-integer x = 83.199950
#> Warning: non-integer x = 34.699980
#> Warning: non-integer x = 42.799990
#> Warning: non-integer x = 48.399990
#> Warning: non-integer x = 53.299990
#> Warning: non-integer x = 71.099980
#> Warning: non-integer x = 77.399960
#> Warning: non-integer x = 94.500000
#> Warning: non-integer x = 104.599980
#> Warning: non-integer x = 29.599990
#> Warning: non-integer x = 34.199980
#> Warning: non-integer x = 63.500000
#> Warning: non-integer x = 72.699950
#> Warning: non-integer x = 78.699950
#> Warning: non-integer x = 84.899960
#> Warning: non-integer x = 96.399960
#> Warning: non-integer x = 100.199950
#> Warning: non-integer x = 22.399990
#> Warning: non-integer x = 25.200000
#> Warning: non-integer x = 36.500000
#> Warning: non-integer x = 43.299990
#> Warning: non-integer x = 58.099980
#> Warning: non-integer x = 70.699950
#> Warning: non-integer x = 78.099980
#> Warning: non-integer x = 83.500000
#> Warning: non-integer x = 26.599990
#> Warning: non-integer x = 28.200000
#> Warning: non-integer x = 38.399990
#> Warning: non-integer x = 45.799990
#> Warning: non-integer x = 54.899990
#> Warning: non-integer x = 60.099980
#> Warning: non-integer x = 56.899990
#> Warning: non-integer x = 64.899960
#> Warning: non-integer x = 81.899960
#> Warning: non-integer x = 90.899960
#> Warning: non-integer x = 28.200000
#> Warning: non-integer x = 35.299990
#> Warning: non-integer x = 42.699980
#> Warning: non-integer x = 48.199980
#> Warning: non-integer x = 53.199980
#> Warning: non-integer x = 64.799990
#> Warning: non-integer x = 71.500000
#> Warning: non-integer x = 76.099980
#> Warning: non-integer x = 86.099980
#> Warning: non-integer x = 92.500000
#> Warning: non-integer x = 27.099990
#> Warning: non-integer x = 34.699980
#> Warning: non-integer x = 40.699980
#> Warning: non-integer x = 47.599980
#> Warning: non-integer x = 56.500000
#> Warning: non-integer x = 72.299990
#> Warning: non-integer x = 95.099980
#> Warning: non-integer x = 105.699950
#> Warning: non-integer x = 37.799990
#> Warning: non-integer x = 43.299990
#> Warning: non-integer x = 51.500000
#> Warning: non-integer x = 63.699980
#> Warning: non-integer x = 70.500000
#> Warning: non-integer x = 80.399960
#> Warning: non-integer x = 106.099980
#> Warning: non-integer x = 29.500000
#> Warning: non-integer x = 31.399990
#> Warning: non-integer x = 39.399990
#> Warning: non-integer x = 44.799990
#> Warning: non-integer x = 50.299990
#> Warning: non-integer x = 65.599980
#> Warning: non-integer x = 72.399960
#> Warning: non-integer x = 80.199950
#> Warning: non-integer x = 90.399960
#> Warning: non-integer x = 99.099980
#> Warning: non-integer x = 22.799990
#> Warning: non-integer x = 33.899990
#> Warning: non-integer x = 37.699980
#> Warning: non-integer x = 41.399990
#> Warning: non-integer x = 48.199980
#> Warning: non-integer x = 53.699980
#> Warning: non-integer x = 62.599980
#> Warning: non-integer x = 70.399960
#> Warning: non-integer x = 78.500000
#> Warning: non-integer x = 85.899960
#> Warning: non-integer x = 22.299990
#> Warning: non-integer x = 24.700000
#> Warning: non-integer x = 30.399990
#> Warning: non-integer x = 36.899990
#> Warning: non-integer x = 44.099980
#> Warning: non-integer x = 52.799990
#> Warning: non-integer x = 60.299990
#> Warning: non-integer x = 67.799990
#> Warning: non-integer x = 75.399960
#> Warning: non-integer x = 87.599980
#> Warning: non-integer x = 101.399960
#> Warning: non-integer x = 23.799990
#> Warning: non-integer x = 37.099980
#> Warning: non-integer x = 43.199980
#> Warning: non-integer x = 50.399990
#> Warning: non-integer x = 60.199980
#> Warning: non-integer x = 82.399960
#> Warning: non-integer x = 91.199950
#> Warning: non-integer x = 101.799990
#> Warning: non-integer x = 109.599980
#> Warning: non-integer x = 25.799990
#> Warning: non-integer x = 29.200000
#> Warning: non-integer x = 35.799990
#> Warning: non-integer x = 41.099980
#> Warning: non-integer x = 55.199980
#> Warning: non-integer x = 62.199980
#> Warning: non-integer x = 69.799990
#> Warning: non-integer x = 76.399960
#> Warning: non-integer x = 83.199950
#> Warning: non-integer x = 93.199950
#> Warning: non-integer x = 32.899990
#> Warning: non-integer x = 46.199980
#> Warning: non-integer x = 53.500000
#> Warning: non-integer x = 58.599980
#> Warning: non-integer x = 68.199950
#> Warning: non-integer x = 80.799990
#> Warning: non-integer x = 84.500000
#> Warning: non-integer x = 24.799990
#> Warning: non-integer x = 35.799990
#> Warning: non-integer x = 42.299990
#> Warning: non-integer x = 50.899990
#> Warning: non-integer x = 57.799990
#> Warning: non-integer x = 64.799990
#> Warning: non-integer x = 71.799990
#> Warning: non-integer x = 83.799990
#> Warning: non-integer x = 92.099980
#> Warning: non-integer x = 26.200000
#> Warning: non-integer x = 30.399990
#> Warning: non-integer x = 37.399990
#> Warning: non-integer x = 49.500000
#> Warning: non-integer x = 55.099980
#> Warning: non-integer x = 64.199950
#> Warning: non-integer x = 75.599980
#> Warning: non-integer x = 83.299990
#> Warning: non-integer x = 87.399960
#> Warning: non-integer x = 94.699950
#> Warning: non-integer x = 98.399960
#> Warning: non-integer x = 32.500000
#> Warning: non-integer x = 38.799990
#> Warning: non-integer x = 47.799990
#> Warning: non-integer x = 54.500000
#> Warning: non-integer x = 70.099980
#> Warning: non-integer x = 76.599980
#> Warning: non-integer x = 86.199950
#> Warning: non-integer x = 95.799990
#> Warning: non-integer x = 101.399960
#> Warning: non-integer x = 112.299990
#> Warning: non-integer x = 32.399990
#> Warning: non-integer x = 38.199980
#> Warning: non-integer x = 44.699980
#> Warning: non-integer x = 53.199980
#> Warning: non-integer x = 62.399990
#> Warning: non-integer x = 70.500000
#> Warning: non-integer x = 72.799990
#> Warning: non-integer x = 86.599980
#> Warning: non-integer x = 93.299990
#> Warning: non-integer x = 104.199950
#> Warning: non-integer x = 27.399990
#> Warning: non-integer x = 32.199980
#> Warning: non-integer x = 37.899990
#> Warning: non-integer x = 45.899990
#> Warning: non-integer x = 51.199980
#> Warning: non-integer x = 57.099980
#> Warning: non-integer x = 76.799990
#> Warning: non-integer x = 83.099980
#> Warning: non-integer x = 91.599980
#> Warning: non-integer x = 100.500000
#> Warning: non-integer x = 105.299990
#> Warning: non-integer x = 27.099990
#> Warning: non-integer x = 30.299990
#> Warning: non-integer x = 38.199980
#> Warning: non-integer x = 43.199980
#> Warning: non-integer x = 52.500000
#> Warning: non-integer x = 67.299990
#> Warning: non-integer x = 74.199950
#> Warning: non-integer x = 81.199950
#> Warning: non-integer x = 87.500000
#> Warning: non-integer x = 94.399960
#> Warning: non-integer x = 101.399960
#> Warning: non-integer x = 26.799990
#> Warning: non-integer x = 31.099990
#> Warning: non-integer x = 37.799990
#> Warning: non-integer x = 44.599980
#> Warning: non-integer x = 50.500000
#> Warning: non-integer x = 58.299990
#> Warning: non-integer x = 68.299990
#> Warning: non-integer x = 75.099980
#> Warning: non-integer x = 84.399960
#> Warning: non-integer x = 87.299990
#> Warning: non-integer x = 96.399960
#> Warning: non-integer x = 104.399960
#> Warning: non-integer x = 24.500000
#> Warning: non-integer x = 31.599990
#> Warning: non-integer x = 37.399990
#> Warning: non-integer x = 46.399990
#> Warning: non-integer x = 53.599980
#> Warning: non-integer x = 61.199980
#> Warning: non-integer x = 70.099980
#> Warning: non-integer x = 77.500000
#> Warning: non-integer x = 86.199950
#> Warning: non-integer x = 89.199950
#> Warning: non-integer x = 96.899960
#> Warning: non-integer x = 104.500000
#> Warning: non-integer x = 23.099990
#> Warning: non-integer x = 30.099990
#> Warning: non-integer x = 40.699980
#> Warning: non-integer x = 46.599980
#> Warning: non-integer x = 52.099980
#> Warning: non-integer x = 60.500000
#> Warning: non-integer x = 73.500000
#> Warning: non-integer x = 77.299990
#> Warning: non-integer x = 86.899960
#> Warning: non-integer x = 96.399960
#> Warning: non-integer x = 21.500000
#> Warning: non-integer x = 24.599990
#> Warning: non-integer x = 28.500000
#> Warning: non-integer x = 39.099980
#> Warning: non-integer x = 45.299990
#> Warning: non-integer x = 59.599980
#> Warning: non-integer x = 69.500000
#> Warning: non-integer x = 75.199950
#> Warning: non-integer x = 84.899960
#> Warning: non-integer x = 93.399960
#> Warning: non-integer x = 99.299990
#> Warning: non-integer x = 24.099990
#> Warning: non-integer x = 28.099990
#> Warning: non-integer x = 32.500000
#> Warning: non-integer x = 40.599980
#> Warning: non-integer x = 53.799990
#> Warning: non-integer x = 61.199980
#> Warning: non-integer x = 71.899960
#> Warning: non-integer x = 79.500000
#> Warning: non-integer x = 87.399960
#> Warning: non-integer x = 93.299990
#> Warning: non-integer x = 101.599980
#> Warning: non-integer x = 34.199980
#> Warning: non-integer x = 42.099980
#> Warning: non-integer x = 50.099980
#> Warning: non-integer x = 57.599980
#> Warning: non-integer x = 62.299990
#> Warning: non-integer x = 76.099980
#> Warning: non-integer x = 81.500000
#> Warning: non-integer x = 84.299990
#> Warning: non-integer x = 97.899960
#> Warning: non-integer x = 108.599980
#> Warning: non-integer x = 25.099990
#> Warning: non-integer x = 23.200000
#> Warning: non-integer x = 28.899990
#> Warning: non-integer x = 36.799990
#> Warning: non-integer x = 44.199980
#> Warning: non-integer x = 52.799990
#> Warning: non-integer x = 62.199980
#> Warning: non-integer x = 69.399960
#> Warning: non-integer x = 78.099980
#> Warning: non-integer x = 88.799990
#> Warning: non-integer x = 102.399960
#> Warning: non-integer x = 106.799990
#> Warning: non-integer x = 32.199980
#> Warning: non-integer x = 36.399990
#> Warning: non-integer x = 41.799990
#> Warning: non-integer x = 48.199980
#> Warning: non-integer x = 55.899990
#> Warning: non-integer x = 60.099980
#> Warning: non-integer x = 68.500000
#> Warning: non-integer x = 77.799990
#> Warning: non-integer x = 86.399960
#> Warning: non-integer x = 96.699950
#> Warning: non-integer x = 111.099980
#> Warning: non-integer x = 115.399960
#> Warning: non-integer x = 24.700000
#> Warning: non-integer x = 28.899990
#> Warning: non-integer x = 34.599980
#> Warning: non-integer x = 42.199980
#> Warning: non-integer x = 48.199980
#> Warning: non-integer x = 54.399990
#> Warning: non-integer x = 62.500000
#> Warning: non-integer x = 69.799990
#> Warning: non-integer x = 78.599980
#> Warning: non-integer x = 96.399960
#> Warning: non-integer x = 103.199950
#> Warning: non-integer x = 24.200000
#> Warning: non-integer x = 29.200000
#> Warning: non-integer x = 36.199980
#> Warning: non-integer x = 43.099980
#> Warning: non-integer x = 49.199980
#> Warning: non-integer x = 70.899960
#> Warning: non-integer x = 87.199950
#> Warning: non-integer x = 94.699950
#> Warning: non-integer x = 100.599980
#> Warning: non-integer x = 24.500000
#> Warning: non-integer x = 28.399990
#> Warning: non-integer x = 41.899990
#> Warning: non-integer x = 55.599980
#> Warning: non-integer x = 64.099980
#> Warning: non-integer x = 71.199950
#> Warning: non-integer x = 80.500000
#> Warning: non-integer x = 90.199950
#> Warning: non-integer x = 98.899960
#> Warning: non-integer x = 103.799990
#> Warning: non-integer x = 26.599990
#> Warning: non-integer x = 33.099980
#> Warning: non-integer x = 38.399990
#> Warning: non-integer x = 46.599980
#> Warning: non-integer x = 52.299990
#> Warning: non-integer x = 61.500000
#> Warning: non-integer x = 69.299990
#> Warning: non-integer x = 74.199950
#> Warning: non-integer x = 80.199950
#> Warning: non-integer x = 87.199950
#> Warning: non-integer x = 94.799990
#> Warning: non-integer x = 26.799990
#> Warning: non-integer x = 33.599980
#> Warning: non-integer x = 42.099980
#> Warning: non-integer x = 47.899990
#> Warning: non-integer x = 56.199980
#> Warning: non-integer x = 63.399990
#> Warning: non-integer x = 71.799990
#> Warning: non-integer x = 87.599980
#> Warning: non-integer x = 94.899960
#> Warning: non-integer x = 30.599990
#> Warning: non-integer x = 37.599980
#> Warning: non-integer x = 42.799990
#> Warning: non-integer x = 47.399990
#> Warning: non-integer x = 56.599980
#> Warning: non-integer x = 62.399990
#> Warning: non-integer x = 71.799990
#> Warning: non-integer x = 86.799990
#> Warning: non-integer x = 94.199950
#> Warning: non-integer x = 101.899960
#> Warning: non-integer x = 112.500000
#> Warning: non-integer x = 21.899990
#> Warning: non-integer x = 26.799990
#> Warning: non-integer x = 34.699980
#> Warning: non-integer x = 41.299990
#> Warning: non-integer x = 48.699980
#> Warning: non-integer x = 57.899990
#> Warning: non-integer x = 65.399960
#> Warning: non-integer x = 71.299990
#> Warning: non-integer x = 80.599980
#> Warning: non-integer x = 88.399960
#> Warning: non-integer x = 96.299990
#> Warning: non-integer x = 103.500000
#> Warning: non-integer x = 26.799990
#> Warning: non-integer x = 39.099980
#> Warning: non-integer x = 46.399990
#> Warning: non-integer x = 61.599980
#> Warning: non-integer x = 68.799990
#> Warning: non-integer x = 72.199950
#> Warning: non-integer x = 77.199950
#> Warning: non-integer x = 83.799990
#> Warning: non-integer x = 90.799990
#> Warning: non-integer x = 24.200000
#> Warning: non-integer x = 25.399990
#> Warning: non-integer x = 30.700000
#> Warning: non-integer x = 35.599980
#> Warning: non-integer x = 42.799990
#> Warning: non-integer x = 49.500000
#> Warning: non-integer x = 57.199980
#> Warning: non-integer x = 65.599980
#> Warning: non-integer x = 72.399960
#> Warning: non-integer x = 81.199950
#> Warning: non-integer x = 85.199950
#> Warning: non-integer x = 90.199950
#> Warning: non-integer x = 25.200000
#> Warning: non-integer x = 29.799990
#> Warning: non-integer x = 35.699980
#> Warning: non-integer x = 55.899990
#> Warning: non-integer x = 63.500000
#> Warning: non-integer x = 79.500000
#> Warning: non-integer x = 83.599980
#> Warning: non-integer x = 89.399960
#> Warning: non-integer x = 98.500000
#> Warning: non-integer x = 23.500000
#> Warning: non-integer x = 25.899990
#> Warning: non-integer x = 32.199980
#> Warning: non-integer x = 32.399990
#> Warning: non-integer x = 29.799990
#> Warning: non-integer x = 32.799990
#> Warning: non-integer x = 56.899990
#> Warning: non-integer x = 64.799990
#> Warning: non-integer x = 72.099980
#> Warning: non-integer x = 81.399960
#> Warning: non-integer x = 26.599990
#> Warning: non-integer x = 38.199980
#> Warning: non-integer x = 46.399990
#> Warning: non-integer x = 53.199980
#> Warning: non-integer x = 59.599980
#> Warning: non-integer x = 66.199950
#> Warning: non-integer x = 72.599980
#> Warning: non-integer x = 80.099980
#> Warning: non-integer x = 97.699950
#> Warning: non-integer x = 35.399990
#> Warning: non-integer x = 42.299990
#> Warning: non-integer x = 49.500000
#> Warning: non-integer x = 58.699980
#> Warning: non-integer x = 66.599980
#> Warning: non-integer x = 71.399960
#> Warning: non-integer x = 78.799990
#> Warning: non-integer x = 85.500000
#> Warning: non-integer x = 91.299990
#> Warning: non-integer x = 97.799990
#> Warning: non-integer x = 29.299990
#> Warning: non-integer x = 45.399990
#> Warning: non-integer x = 51.799990
#> Warning: non-integer x = 58.799990
#> Warning: non-integer x = 62.599980
#> Warning: non-integer x = 71.599980
#> Warning: non-integer x = 76.699950
#> Warning: non-integer x = 81.699950
#> Warning: non-integer x = 86.399960
#> Warning: non-integer x = 92.099980
#> Warning: non-integer x = 25.299990
#> Warning: non-integer x = 31.599990
#> Warning: non-integer x = 35.199980
#> Warning: non-integer x = 37.299990
#> Warning: non-integer x = 40.799990
#> Warning: non-integer x = 47.699980
#> Warning: non-integer x = 64.599980
#> Warning: non-integer x = 71.199950
#> Warning: non-integer x = 80.500000
#> Warning: non-integer x = 85.899960
#> Warning: non-integer x = 22.099990
#> Warning: non-integer x = 26.299990
#> Warning: non-integer x = 33.299990
#> Warning: non-integer x = 39.599980
#> Warning: non-integer x = 41.399990
#> Warning: non-integer x = 46.299990
#> Warning: non-integer x = 52.399990
#> Warning: non-integer x = 59.399990
#> Warning: non-integer x = 66.699950
#> Warning: non-integer x = 73.899960
#> Warning: non-integer x = 76.799990
#> Warning: non-integer x = 23.700000
#> Warning: non-integer x = 28.799990
#> Warning: non-integer x = 35.099980
#> Warning: non-integer x = 49.099980
#> Warning: non-integer x = 58.799990
#> Warning: non-integer x = 65.399960
#> Warning: non-integer x = 68.500000
#> Warning: non-integer x = 90.699950
#> Warning: non-integer x = 28.899990
#> Warning: non-integer x = 35.799990
#> Warning: non-integer x = 47.500000
#> Warning: non-integer x = 56.399990
#> Warning: non-integer x = 63.699980
#> Warning: non-integer x = 70.299990
#> Warning: non-integer x = 89.199950
#> Warning: non-integer x = 96.299990
#> Warning: non-integer x = 99.799990
#> Warning: non-integer x = 30.099990
#> Warning: non-integer x = 37.099980
#> Warning: non-integer x = 53.599980
#> Warning: non-integer x = 61.099980
#> Warning: non-integer x = 78.199950
#> Warning: non-integer x = 87.099980
#> Warning: non-integer x = 94.399960
#> Warning: non-integer x = 102.500000
#> Warning: non-integer x = 107.500000
#> Warning: non-integer x = 35.399990
#> Warning: non-integer x = 48.599980
#> Warning: non-integer x = 56.399990
#> Warning: non-integer x = 75.500000
#> Warning: non-integer x = 77.799990
#> Warning: non-integer x = 85.799990
#> Warning: non-integer x = 101.399960
#> Warning: non-integer x = 27.299990
#> Warning: non-integer x = 31.200000
#> Warning: non-integer x = 43.899990
#> Warning: non-integer x = 49.799990
#> Warning: non-integer x = 57.199980
#> Warning: non-integer x = 65.199950
#> Warning: non-integer x = 73.199950
#> Warning: non-integer x = 78.799990
#> Warning: non-integer x = 87.399960
#> Warning: non-integer x = 100.500000
#> Warning: non-integer x = 25.700000
#> Warning: non-integer x = 28.700000
#> Warning: non-integer x = 33.399990
#> Warning: non-integer x = 46.699980
#> Warning: non-integer x = 56.599980
#> Warning: non-integer x = 65.199950
#> Warning: non-integer x = 73.199950
#> Warning: non-integer x = 81.699950
#> Warning: non-integer x = 90.299990
#> Warning: non-integer x = 103.500000
#> Analysis of 'Wald statistic' Table
#> Model: poisson, link: identity
#> Response: Weight
#> Terms added sequentially (first to last)
#> 
#>           Df   X2 P(>|Chi|)    
#> Cu         2    1      0.48    
#> Time       1 7093    <2e-16 ***
#> I(Time^2)  1  109    <2e-16 ***
#> I(Time^3)  1  105    <2e-16 ***
#> Cu:Time    2    2      0.42    
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

# Notice the difference here: Clusters of observations must
# appear as chunks in data. 

set.seed(1)
chick1 <- ChickWeight
chick2 <- chick1[sample(nrow(chick1)),]
chick3 <- chick2[order(chick2$Chick),]

fit1 <- geeglm(weight~Time, id=Chick, data=chick1)
fit2 <- geeglm(weight~Time, id=Chick, data=chick2)
fit3 <- geeglm(weight~Time, id=Chick, data=chick3)

vcov(fit1)
#>             (Intercept)    Time
#> (Intercept)      4.2035 -0.9245
#> Time            -0.9245  0.2751
vcov(fit2)
#>             (Intercept)     Time
#> (Intercept)      3.2852 -0.45463
#> Time            -0.4546  0.07912
vcov(fit3)
#>             (Intercept)    Time
#> (Intercept)      4.2035 -0.9245
#> Time            -0.9245  0.2751