Chapter 3, Exercise Solutions, Principles of Econometrics, 3e40Exercise 3.5 (continued) (d) To test the hypothesis that the slope of the relationship is one, we proceed as we did in part (c), using 1 instead of 5. Thus, our hypotheses are H0: β2= 1 versus H1: β2≠1. The rejection region is | t| > 2.101. The value of the test statistic is 3.8802125.70.1121t−==Since 25.72.101,ctt=>=we reject the null hypothesis. We conclude that the amount of life insurance does not increase at the same rate as income increases. (e) Life insurance companies are interested in household characteristics that influence the amount of life insurance cover that is purchased by different households. One likely important determinant of life insurance cover is household income. To see if income is important, and to quantify its effect on insurance, we set up the model 12iiiINSURANCEINCOMEe= β + β+where iINSURANCEis life insurance cover by the i-th household, iINCOMEis household income, β1and β2are unknown parameters that describe the relationship, and eiis a random uncorrelated error that is assumed to have zero mean and constant variance
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