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Analysis and Interpretation of Multiple Linear Regression Models

Advanced statistical modeling techniques and their applications

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    Analysis and Interpretation of Multiple Linear Regression Models PROBLEM 1 IHI Insurance have conducted a multiple linear regression analysis to predict the value of the number of annual claims incurred by a motor insurance policyholder (y)based on the age of the policyholder in years (x 1 ) and the value of the car insured in thousands of dollars (x 2 ). The analysis was based on a random sample of 500 policyholders. The ages in the sample ranged from 16 to 70 and the values of the cars in the sample ranged from $1,100 to $52,000. The multiple linear regression equation corresponding to IHI's analysis is: y ^ i = 13 + ( - 0.5)x 1i + (0.1)x 2i . Select whether the following statements regarding the multiple linear regression equation are true or false: True False a) Holding x 1 constant, a one thousand dollar increase in x 2 will result in a decrease of 0.5 in the predicted value of y. b) A 22 year old policyholder with a car worth $20,000 is predicted to make 4 claims. c) Holding x 2 constant, a one year increase in x 1 will result in an increase of 0.1 in the predicted value of Y.

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    PROBLEM 2 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 4 161.359 40.33975 10.72878373... < 0.001 Residual 45 169.198 3.75995556... Total 49 330.557 Regression analysis R 2 0.48814274... s 1.93906048... Regression coefficients Estimate Standard Error t Probability Intercept 19.70 2.852 6.90743338... < 0.001 Population of city 2.496 0.1337 18.66866118... < 0.001 No. of vehicles per capita 1.473 0.2480 5.93951613... < 0.001 No. of traffic offenses 0.293 0.4064 0.72096457... 0.47466038... Average annual temp. 0.403 0.4530 0.88962472... 0.37839879... 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:

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