A regression model is constructed with the goal of predicting the number of motor vehicle accidents in a city per year based upon the population of the city, the number of recorded traffic offenses per year, the number of vehicles per capita in the city, and the average annual temperature in the town. A random sample of 50 cities was studied for this purpose.
Here is an analysis output on the regression model:
ANOVA
DF
SS
MS
F
Probability
Regression
4
180.029
45.00725
16.98742923...
< 0.001
Residual
45
119.225
2.64944444...
Total
49
299.254
Regression analysis
R2
0.60159263...
s
1.62771141...
Regression coefficients
Estimate
Standard Error
t
Probability
Intercept
19.82
3.145
6.30206677...
< 0.001
Population of city
2.567
0.0551
46.58802178...
< 0.001
No. of vehicles per capita
1.024
0.1622
6.31319359...
< 0.001
No. of traffic offenses
0.297
0.2735
1.08592322...
0.28329605...
Average annual temp.
0.178
0.5943
0.29951203...
0.76592846...
a) At a level of significance of 0.05, the result of the F test for this model is that the null hypothesis is rejected.
b) Suppose you are going to construct a new model by removing the most insignificant variable. You would first remove:
A. population of city
B. no. of vehicles per capita
C. no. of traffic offenses
D. average annual temp.