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)
>
>
> pairs(supervisor.table, pch=23, bg='orange', cex.labels=6, cex=2)
>
> # Fit multiple regression model
>
>
>
>
> supervisor.lm <- lm(Y ~ X1 + X2 + X3 + X4 + X5 + X6)
> print(summary(supervisor.lm))
Call:
lm(formula = Y ~ X1 + X2 + X3 + X4 + X5 + X6)
Residuals:
Min 1Q Median 3Q Max
-10.9418 -4.3555 0.3158 5.5425 11.5990
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 10.78708 11.58926 0.931 0.361634
X1 0.61319 0.16098 3.809 0.000903 ***
X2 -0.07305 0.13572 -0.538 0.595594
X3 0.32033 0.16852 1.901 0.069925 .
X4 0.08173 0.22148 0.369 0.715480
X5 0.03838 0.14700 0.261 0.796334
X6 -0.21706 0.17821 -1.218 0.235577
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 7.068 on 23 degrees of freedom
Multiple R-squared: 0.7326, Adjusted R-squared: 0.6628
F-statistic: 10.5 on 6 and 23 DF, p-value: 1.240e-05
>
> # Confidence intervals for the coefficients
>
> print(confint(supervisor.lm))
2.5 % 97.5 %
(Intercept) -13.18712881 34.7612816
X1 0.28016866 0.9462066
X2 -0.35381806 0.2077178
X3 -0.02827872 0.6689430
X4 -0.37642935 0.5398936
X5 -0.26570179 0.3424647
X6 -0.58571106 0.1515977
>
> # Confidence intervals for the regression function
>
> print(predict(supervisor.lm, list(X1=60, X2=50, X3=55, X4=65, X5=75, X6=40), interval='confidence'))
fit lwr upr
1 61.05302 57.3486 64.75744
> print(predict(supervisor.lm, list(X1=60, X2=50, X3=55, X4=65, X5=75, X6=40), interval='prediction'))
fit lwr upr
1 61.05302 45.96979 76.13626
>
> # Adjusted R^2
>
> SST <- sum((Y - mean(Y))^2)
> MST <- SST / (length(Y) - 1)
> SSE <- sum(resid(supervisor.lm)^2)
> MSE <- SSE / supervisor.lm$df.residual
>
>
> R2 <- 1 - SSE/SST
> R2.adj <- 1 - MSE / MST
>
> print(data.frame(R2,R2.adj))
R2 R2.adj
1 0.732602 0.662846
>
>
>
> proc.time()
user system elapsed
0.792 0.040 1.092
R script