Managing your Money A particularsavings and loan corporation is interested indetermining

Chapter 13, Problem 36

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Managing your Money A particularsavings and loan corporation is interested indetermining how well the amount of money in familysavings accounts can be predicted using the three independentvariablesannual income, number in the familyunit, and area in which the family lives. Supposethat there are two specific areas of interest to the corporation.The following data were collected, wherey Amount in all savings accountsx1 Annual incomex2 Number in family unitx3 0 if in Area 1; 1 if notBoth y and x1 were recorded in units of $1000.y x1 x2 x30.5 19.2 3 00.3 23.8 6 01.3 28.6 5 00.2 15.4 4 05.4 30.5 3 11.3 20.3 2 112.8 34.7 2 11.5 25.2 4 10.5 18.6 3 115.2 45.8 2 1 The following computer printout resulted when thedata were analyzed.a. Interpret R2 and comment on the fit of the model.b. Test for a significant regression of y on x1, x2, andx3 at the 5% level of significance.c. Test the hypothesis H0 : b3 0 againstHa : b3 0 using a .05. Comment on theresults of your test.d. What can be said about the utility of x3 as a predictorvariable in this problem?Regression Analysis: y versus x1, x2, x3The regression equation isy = -3.11 + 0.503 x1 - 1.61 x2 - 1.15 x3Predictor Coef SE Coef T PConstant -3.112 3.600 -0.86 0.421x1 0.50314 0.07670 6.56 0.001x2 -1.6126 0.6579 -2.45 0.050x3 -1.155 1.791 -0.64 0.543S = 1.89646 R-Sq = 92.2% R-Sq(adj) = 88.4%Analysis of VarianceSource DF SS MS F PRegression 3 256.621 85.540 23.78 0.001Residual Error 6 21.579 3.597Total 9 278.200Source DF Seq SSx1 1 229.113x2 1 26.012x3 1 1.496