R version 2.9.2 (2009-08-24)
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ISBN 3-900051-07-0
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>
> # Read in new data
>
> supervisor.table <- read.table('http://www-stat.stanford.edu/~jtaylo/courses/stats191/data/supervisor.table', header=T)
> attach(supervisor.table)
>
> # original regression model
>
> supervisor.lm <- lm(Y ~ X1 + X2 + X3 + X4 + X5 + X6)
> reduced.lm <- lm(Y ~ X1 + X4 + X5 + X6)
>
> # A function to do "nested" F-tests
>
> f.test.lm <- function(R.lm, F.lm) {
+ SSE.R <- sum(resid(R.lm)^2)
+ SSE.F <- sum(resid(F.lm)^2)
+ df.num <- R.lm$df - F.lm$df
+ df.den <- F.lm$df
+ F <- ((SSE.R - SSE.F) / df.num) / (SSE.F / df.den)
+ p.value <- 1 - pf(F, df.num, df.den)
+ return(data.frame(F, df.num, df.den, p.value))
+ }
>
> print(f.test.lm(reduced.lm, supervisor.lm))
F df.num df.den p.value
1 1.846191 2 23 0.1804745
>
> # R has another way to do this
>
> print(anova(reduced.lm, supervisor.lm))
Analysis of Variance Table
Model 1: Y ~ X1 + X4 + X5 + X6
Model 2: Y ~ X1 + X2 + X3 + X4 + X5 + X6
Res.Df RSS Df Sum of Sq F Pr(>F)
1 25 1333.46
2 23 1149.00 2 184.46 1.8462 0.1805
>
> # the models should be "nested"
> # that is, modelR should be a special case of modelF
> # R can recognize this for you (at least sometimes)
>
> print(anova(lm(Y ~ X1 + X3), lm(Y ~ X2 + X4)))
Analysis of Variance Table
Model 1: Y ~ X1 + X3
Model 2: Y ~ X2 + X4
Res.Df RSS Df Sum of Sq F Pr(>F)
1 27 1254.7
2 27 2657.7 0 -1403.0
>
>
>
>
> proc.time()
user system elapsed
0.588 0.028 0.623
R script