Question

For problem 14.72 assume that the first seven homes are in Norfolk and the next eight are in Virginia Beach. After adding this variable by hand to the model as a dummy variable: 1 for Norfolk and 0 for VA Bch.

1. Assess multicollinearity for the model.

2. Interpret the coefficient for the dummy variable.

3. Determine the significance of the dummy variable to the model.

House
Assessed Value ($000)
Size of House (Thousands of Square Feet)
Age (Years)
1 184.4 2.00 3.42
2 177.4 1.71 11.50
3 175.7 1.45 8.33
4 185.9 1.76 0.00
5 179.1 1.93 7.42
6 170.4 1.20 32.00
7 175.8 1.55 16.00
8 185.9 1.93 2.00
9 178.5 1.59 1.75
10 179.2 1.50 2.75
11 186.7 1.90 0.00
12 179.3 1.39 0.00
13 174.5 1.54 12.58
14 183.8 1.89 2.75
15 176.8 1.59 7.17

Answer 1

Here I attach the R code used:

accessvalue=c(184.4,177.4,175.7,185.9,179.1,170.4,175.8,185.9,178.5,179.2,186.7,179.3,174.5,183.8,176.8)
sizeofhouse=c(2.00,1.71,1.45,1.76,1.93,1.20,1.55,1.93,1.59,1.50,1.90,1.39,1.54,1.89,1.59)
age=c(3.42,11.50,8.33,0.00,7.42,32.00,16.00,2.00,1.75,2.75,0.00,0.00,12.58,2.75,7.17)
dummy=c(1,1,1,1,1,1,1,0,0,0,0,0,0,0,0)
fit=lm(accessvalue~sizeofhouse+age+dummy)
summary(fit)
anova(fit)
library(car)
vif(fit)

1.

The VIF value indicate that there is no multicollinearity in the data( since, vif is less than 5).

2.

The coefficient of the dummy variable is 0.08661

3.

The dummy variable is not significant to the model. since the p value is 0.95202.