A regression model is constructed with the goal of predicting the number of moto

Question

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:

a)At a level of significance of 0.05, the result of the F test for this model is that the null hypothesis isis 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.

ANOVA DF SS MS F Probability Regression 4 169.139 42.28475 16.3791393... < 0.001 Residual 45 116.173 2.58162222... Total 49 285.312 Regression analysis R2 0.59282119... s 1.60674274... Regression coefficients Estimate Standard Error t Probability Intercept 13.04 2.914 4.47494852... < 0.001 Population
of city 2.060 0.1152 17.88194444... < 0.001 No. of vehicles
per capita 1.795 0.1025 17.51219512... < 0.001 No. of traffic offenses 0.276 0.2866 0.96301465... 0.3406868... Average annual
temp. 0.386 0.3903 0.98898283... 0.32795967...

Explanation / Answer

a) Null hypothesis is rejected as calculated p-value is 0.001 which is less than 0.05.

b) I would first remove: no. of traffic offenses as the assocoated p-value is higher than all other variables also the coefficients is lesser.

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