bailsofhay — Nov 25, 2013, 5:57 PM
data=read.table("http://www.stat.lsu.edu/exstweb/statlab/datasets/KNNLData/CH06PR05.txt")
names(data)=c("y","x1","x2")
### Part a ###
fit=lm(y~x1+x2+I(x1*x2), data=data)
fit
Call:
lm(formula = y ~ x1 + x2 + I(x1 * x2), data = data)
Coefficients:
(Intercept) x1 x2 I(x1 * x2)
27.15 5.92 7.87 -0.50
### Part b ###
# Alternatives: Ho: B3 = 0, Ha: B3 is not equal to 0.
# Decision Rule: If F* < or equal to F critical, conclude Ho, if F* > F critical, Conclude Ha.
fitred=lm(y~x1+x2, data=data)
fitred
Call:
lm(formula = y ~ x1 + x2, data = data)
Coefficients:
(Intercept) x1 x2
37.65 4.42 4.37
anova.fit=anova(fitred,fit)
anova.fit
Analysis of Variance Table
Model 1: y ~ x1 + x2
Model 2: y ~ x1 + x2 + I(x1 * x2)
Res.Df RSS Df Sum of Sq F Pr(>F)
1 13 94.3
2 12 74.3 1 20 3.23 0.097 .
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
top=anova.fit[2,4]
SSEf=anova.fit[2,2]
dft=anova.fit[2,3]
dff=anova.fit[2,1]
# F* is:
Fs=(top/dft)/(SSEf/dff)
Fs
[1] 3.23
# F critical is:
Fc=qf(.95,1,12)
Fc
[1] 4.747
# Conclude Ho since F* << F Critical.