Analysis and Interpretation of Multiple Linear Regression Models

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Analysis and Interpretation of Multiple Linear Regression ModelsPROBLEM 1IHI Insurance have conducted a multiple linear regression analysis to predict the value of the number ofannual claims incurred by a motor insurancepolicyholder(y)based on the age of the policyholder inyears(x1)and thevalue of the car insured in thousands of dollars(x2). The analysis was based on a randomsample of 500 policyholders. The ages in the sample ranged from 16 to 70 and the values of the cars in thesample ranged from $1,100 to $52,000. The multiple linear regression equation corresponding to IHI'sanalysis is:y^i= 13 + (-0.5)x1i+ (0.1)x2i.Select whether the following statements regarding the multiple linear regressionequation are true or false:TrueFalsea)Holding x1constant, a one thousand dollar increase in x2will result in adecrease 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 4claims.c)Holding x2constant, a one year increase in x1will result in an increase of0.1 in the predicted value of Y.

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PROBLEM 2A regression model is constructed with the goal of predicting the number of motor vehicleaccidents in a cityper year based upon the population of the city, the number of recorded traffic offenses per year, the numberof vehicles per capita in the city and the average annual temperature in the town. A random sample of 50cities were studied for this purpose.Here is an analysis output on the regression model:ANOVADFSSMSFProbabilityRegression4161.35940.3397510.72878373...< 0.001Residual45169.1983.75995556...Total49330.557Regression analysisR20.48814274...s1.93906048...Regression coefficientsEstimateStandard ErrortProbabilityIntercept19.702.8526.90743338...< 0.001Populationof city2.4960.133718.66866118...< 0.001No. of vehiclesper capita1.4730.24805.93951613...< 0.001No. of traffic offenses0.2930.40640.72096457...0.47466038...Average annualtemp.0.4030.45300.88962472...0.37839879...a)At a level of significance of 0.05, the result of the F test for this model is that the nullhypothesisisrejected.b)Suppose you are going to construct a new model by removing the most insignificant variable. You wouldfirst remove:

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