Aircraft Data

Aircraft Data, deals with 23 single-engine aircraft built over the years 1947-1979, from Office of Naval Research. The dependent variable is cost (in units of $100,000) and the explanatory variables are aspect ratio, lift-to-drag ratio, weight of plane (in pounds) and maximal thrust.

data(aircraft, package="robustbase")

Format

A data frame with 23 observations on the following 5 variables.

X1

Aspect Ratio

X2

Lift-to-Drag Ratio

X3

Weight

X4

Thrust

Y

Cost

Source

P. J. Rousseeuw and A. M. Leroy (1987) Robust Regression and Outlier Detection; Wiley, page 154, table 22.

Examples

data(aircraft)
summary( lm.airc <-        lm(Y ~ ., data = aircraft))
#> 
#> Call:
#> lm(formula = Y ~ ., data = aircraft)
#> 
#> Residuals:
#>     Min      1Q  Median      3Q     Max 
#> -14.891  -3.955  -1.233   5.753  17.594 
#> 
#> Coefficients:
#>               Estimate Std. Error t value Pr(>|t|)    
#> (Intercept) -3.7913892 10.1157023  -0.375  0.71219    
#> X1          -3.8529189  1.7630016  -2.185  0.04232 *  
#> X2           2.4882665  1.1867538   2.097  0.05042 .  
#> X3           0.0034988  0.0004790   7.305 8.72e-07 ***
#> X4          -0.0019537  0.0004986  -3.918  0.00101 ** 
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#> 
#> Residual standard error: 8.406 on 18 degrees of freedom
#> Multiple R-squared:  0.8836,	Adjusted R-squared:  0.8578 
#> F-statistic: 34.17 on 4 and 18 DF,  p-value: 3.501e-08
#> 
summary(rlm.airc <- MASS::rlm(Y ~ ., data = aircraft))
#> 
#> Call: rlm(formula = Y ~ ., data = aircraft)
#> Residuals:
#>      Min       1Q   Median       3Q      Max 
#> -13.0636  -3.6520  -0.6103   4.7975  26.9243 
#> 
#> Coefficients:
#>             Value   Std. Error t value
#> (Intercept) -1.2850  8.6035    -0.1494
#> X1          -3.4214  1.4994    -2.2818
#> X2           2.2160  1.0093     2.1955
#> X3           0.0029  0.0004     7.2207
#> X4          -0.0016  0.0004    -3.6940
#> 
#> Residual standard error: 6.946 on 18 degrees of freedom

aircraft.x <- data.matrix(aircraft[,1:4])
c_air <- covMcd(aircraft.x)
c_air
#> Minimum Covariance Determinant (MCD) estimator approximation.
#> Method: Fast MCD(alpha=0.5 ==> h=14); nsamp = 500; (n,k)mini = (300,5)
#> Call:
#> covMcd(x = aircraft.x)
#> Log(Det.):  30.28 
#> 
#> Robust Estimate of Location:
#>        X1         X2         X3         X4  
#>     4.188      1.944  14404.688  11165.000  
#> Robust Estimate of Covariance:
#>             X1         X2        X3        X4
#> X1      3.0537    -0.1493     -6756     -9478
#> X2     -0.1493     0.3612      1839      1581
#> X3  -6756.3061  1839.4958  31615868  33454095
#> X4  -9478.3250  1580.7394  33454095  47868871