Summary Method for LTS objects

summary method for class "lts".

# S3 method for class 'lts'
summary(object, correlation = FALSE, ...)

# S3 method for class 'summary.lts'
print(x, digits = max(3, getOption("digits") - 3),
     signif.stars = getOption("show.signif.stars"), ...)

Arguments

object: an object of class "lts", usually, a result of a call to ltsReg.
correlation: logical; if TRUE, the correlation matrix of the estimated parameters is returned and printed.
x: an object of class "summary.lts", usually, a result of a call to summary.lts.
digits: the number of significant digits to use when printing.
signif.stars: logical indicating if “significance stars” should be printer, see printCoefmat.
...: further arguments passed to or from other methods.

Details

These functions compute and print summary statistics for weighted least square estimates with weights based on LTS estimates. Therefore the statistics are similar to those for LS but all terms are multiplied by the corresponding weight.

Correlations are printed to two decimal places: to see the actual correlations print summary(object)$correlation directly.

Value

The function summary.lts computes and returns a list of summary statistics of the fitted linear model given in object, using the components of this object (list elements).

residuals: the residuals - a vector like the response y containing the residuals from the weighted least squares regression.
coefficients: a $p \times 4$ matrix with columns for the estimated coefficient, its standard error, t-statistic and corresponding (two-sided) p-value.
sigma: the estimated scale of the reweighted residuals $$\hat\sigma^2 = \frac{1}{n-p}\sum_i{R_i^2},$$ where $R_i$ is the $i$-th residual, residuals[i].
df: degrees of freedom, a 3-vector $(p, n-p, p*)$, the last being the number of non-aliased coefficients.
fstatistic: (for models including non-intercept terms) a 3-vector with the value of the F-statistic with its numerator and denominator degrees of freedom.
r.squared: $R^2$, the “fraction of variance explained by the model”, $$R^2 = 1 - \frac{\sum_i{R_i^2}}{\sum_i(y_i- y^*)^2},$$ where $y^*$ is the mean of $y_i$ if there is an intercept and zero otherwise.
adj.r.squared: the above $R^2$ statistic “adjusted”, penalizing for higher $p$.
cov.unscaled: a $p \times p$ matrix of (unscaled) covariances of the $\hat\beta_j$, $j=1, \dots, p$.
correlation: the correlation matrix corresponding to the above cov.unscaled, if correlation = TRUE is specified.

Examples

data(Animals2)
ltsA <- ltsReg(log(brain) ~ log(body), data = Animals2)
(slts <- summary(ltsA))
#> 
#> Call:
#> ltsReg.formula(formula = log(brain) ~ log(body), data = Animals2)
#> 
#> Residuals (from reweighted LS):
#>     Min      1Q  Median      3Q     Max 
#> -1.6565 -0.4141  0.0000  0.5004  1.6781 
#> 
#> Coefficients:
#>           Estimate Std. Error t value Pr(>|t|)    
#> Intercept  2.08980    0.09039   23.12   <2e-16 ***
#> log(body)  0.74049    0.02690   27.53   <2e-16 ***
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#> 
#> Residual standard error: 0.6517 on 59 degrees of freedom
#> Multiple R-Squared: 0.9278,	Adjusted R-squared: 0.9265 
#> F-statistic: 757.9 on 1 and 59 DF,  p-value: < 2.2e-16 
#> 
## non-default options for printing the summary:
print(slts, digits = 5, signif.stars = FALSE)
#> 
#> Call:
#> ltsReg.formula(formula = log(brain) ~ log(body), data = Animals2)
#> 
#> Residuals (from reweighted LS):
#>      Min       1Q   Median       3Q      Max 
#> -1.65648 -0.41410  0.00000  0.50036  1.67812 
#> 
#> Coefficients:
#>           Estimate Std. Error t value  Pr(>|t|)
#> Intercept 2.089803   0.090391  23.119 < 2.2e-16
#> log(body) 0.740490   0.026898  27.529 < 2.2e-16
#> 
#> Residual standard error: 0.65173 on 59 degrees of freedom
#> Multiple R-Squared: 0.92777,	Adjusted R-squared: 0.92655 
#> F-statistic: 757.87 on 1 and 59 DF,  p-value: < 2.22e-16 
#>

Arguments

Details

Value

See also

Examples