R version 2.9.2 (2009-08-24)
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ISBN 3-900051-07-0
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>
> heights.table <- read.table('http://www-stat.stanford.edu/~jtaylo/courses/stats191/data/heights.table', header=T, sep=',')
> attach(heights.table)
>
>
>
> wife.lm <- lm(WIFE ~ HUSBAND)
>
> # Compute coefficients by hand to make sure they agree
>
> beta.1.hat <- cov(HUSBAND, WIFE) / var(HUSBAND)
> beta.0.hat <- mean(WIFE) - beta.1.hat * mean(HUSBAND)
> print(c(beta.1.hat, beta.0.hat))
[1] 0.6959256 42.5487122
>
> # Estimate sigma squared -- df.resid are degrees of freedom
>
> sigma.hat <- sqrt(sum(resid(wife.lm)^2) / wife.lm$df.resid)
> print(sigma.hat)
[1] 5.951824
>
>
> print(summary(wife.lm))
Call:
lm(formula = WIFE ~ HUSBAND)
Residuals:
Min 1Q Median 3Q Max
-19.4235 -3.9438 0.8399 4.0123 11.1439
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 42.54871 10.77592 3.949 0.000153 ***
HUSBAND 0.69593 0.06176 11.268 < 2e-16 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 5.952 on 93 degrees of freedom
Multiple R-squared: 0.5772, Adjusted R-squared: 0.5727
F-statistic: 127 on 1 and 93 DF, p-value: < 2.2e-16
> # find where beta.0.hat, beta.1.hat and
> # sigma.hat appear
>
> SSE = sum(resid(wife.lm)^2)
> SSR = sum((predict(wife.lm) - mean(WIFE))^2)
> SST = sum((WIFE-mean(WIFE)^2))
> print(c(SST, SSE+SSR))
[1] -2532677.642 7792.358
>
> F = (SSR / 1) / (SSE / 93)
> df.num = 1
> df.den = 93
> p.value = 1 - pf(F, df.num, df.den)
> print(data.frame(df.num, df.den, F, p.value))
df.num df.den F p.value
1 1 93 126.9727 0
>
>
>
> proc.time()
user system elapsed
0.552 0.052 0.729
R script