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 were studied for this purpose.
Here is an analysis output on the regression model:
ANOVA
DF SS MS F Probability
Regression 4 161.318 40.3295 16.47955524... < 0.001
Residual 45 110.126 2.44724444... Total 49 271.444 Regression analysis
R2 0.59429569...
s 1.56436711...
Regression coefficients
Estimate Standard Error t Probability
Intercept 13.66 3.560 3.83707865... < 0.001
Population
of city 2.020 0.1555 12.9903537... < 0.001
No. of vehicles
per capita 1.928 0.2031 9.49286066... < 0.001
No. of traffic offenses 0.763 0.4651 1.64050742... 0.10787224...
Average annual
temp. 0.223 0.3730 0.59785523... 0.5529336...
a)At a level of significance of 0.05, the result of the F test for this model is that the null hypothesis (is/is not) rejected.
b)Suppose you are going to construct a new model by removing the most insignificant variable. You would first remove:
population of city
no. of vehicles per capita
no. of traffic offenses
average annual temp.