MATH 376 -- Mathematical Statistics
Another Multiple Regression Example
April 23, 2012

 
> Problem74 <- read.table("/home/fac/little/public_html/ProbStat1112/MultReg2R.dat",header=T)
> Problem74
   x1 x2 x3 x4    y
1  -1 -1 -1 -1 24.4
2  -1 -1 -1  1 22.2
3  -1 -1  1 -1 25.9
4  -1 -1  1  1 24.5
5  -1  1 -1 -1 25.2
6  -1  1 -1  1 19.4
7  -1  1  1 -1 28.4
8  -1  1  1  1 24.1
9   1 -1 -1 -1 23.5
10  1 -1 -1  1 22.1
11  1 -1  1 -1 16.5
12  1 -1  1  1 19.6
13  1  1 -1 -1 19.3
14  1  1 -1  1 14.2
15  1  1  1 -1 16.0
16  1  1  1  1 12.7

> x1 <- Problem74[,1]
> x1
 [1] -1 -1 -1 -1 -1 -1 -1 -1  1  1  1  1  1  1  1  1
> x2 <- Problem74[,2]
> x3 <- Problem74[,3]
> x4 <- Problem74[,4]
> y <- Problem74[,5]

> summary(lm(y ~ x1 + x2 + x3 + x4))

Call:
lm(formula = y ~ x1 + x2 + x3 + x4)

Residuals:
    Min      1Q  Median      3Q     Max 
-3.8125 -2.2500 -0.1125  2.0000  4.2375 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)  21.1250     0.7493  28.193 1.31e-11 ***
x1           -3.1375     0.7493  -4.187  0.00152 ** 
x2           -1.2125     0.7493  -1.618  0.13391    
x3           -0.1625     0.7493  -0.217  0.83228    
x4           -1.2750     0.7493  -1.702  0.11689    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

Residual standard error: 2.997 on 11 degrees of freedom
Multiple R-squared: 0.6774,     Adjusted R-squared:  0.56 
F-statistic: 5.774 on 4 and 11 DF,  p-value: 0.009383 

% Comment: Fitting the linear model could also be done without
% assigning the separate names for the columns: 

> lm(Problem74[,5] ~ Problem74[,1] + Problem74[,2] + Problem74[,3] + Problem74[,4])