a) Is there enough evidence at the 5% significance level to infer that the model is useful in predicting length of life? {Hint: Test using Ho - B-B-0 and Me: At least one A is not equal to zero) ANS: Partial solution: Ho: B; - By - B - 0 H: At least one B is not equal to zero Rejection region: F> F0.3.2.84 Test statistic F? which means? b) Is there enough evidence at the 1% significance level to infer that the average number of hours of exercise per the age at death are linearly related? ANS: H: B. - 0 vs. H: 8,0 Rejection region: 1>10.005,36 = 2.724 Test statistict=? which means ? c) What is the coefficient of determination? What does this statistic tell you? ANS: d) What is the adjusted coefficient of determination in this situation? What does this statistic tell you? ANS: e) Interpret the coefficient b2. ANS: Interpret the coefficient bs. NS: 7) An actuary wanted to develop a model to predict how long individuals will live. After consulting a number of physicians, she collected the age at death (), the average number of hours of exercise per week (x), the cholesterol level (x2), and the number of points that the individual's blood pressure exceeded the recommended value (x3). A random sample of 40 individuals was selected. The computer output of the multiple regression model is shown below. (15 marks) THE REGRESSION EQUATION IS y = 55.8 + 1.79x -0.02 1x2 -0.061x3 Predictor Constant X1 X2 Coef 55.8 1.79 -0.021 -0.016 StDev 11.8 0.44 0.011 0.014 T 4.729 4.068 -1.909 -1.143 X3 R-Sq = 22.5% S = 9.47 Adj RP =18.3% ANALYSIS OF VARIANCE SS F 3.477 MS 312 89.722 df 3 36 39 Source of Variation Regression Error Total 936 3230 4166 a) Is there enough evidence at the 5% significance level to infer that the model is useful in predicting length of life? {Hint: Test using Ho - B-B-0 and Me: At least one A is not equal to zero) ANS: Partial solution: Ho: B; - By - B - 0 H: At least one B is not equal to zero Rejection region: F> F0.3.2.84 Test statistic F? which means? b) Is there enough evidence at the 1% significance level to infer that the average number of hours of exercise per the age at death are linearly related? ANS: H: B. - 0 vs. H: 8,0 Rejection region: 1>10.005,36 = 2.724 Test statistict=? which means ? c) What is the coefficient of determination? What does this statistic tell you? ANS: d) What is the adjusted coefficient of determination in this situation? What does this statistic tell you? ANS: e) Interpret the coefficient b2. ANS: Interpret the coefficient bs. NS: 7) An actuary wanted to develop a model to predict how long individuals will live. After consulting a number of physicians, she collected the age at death (), the average number of hours of exercise per week (x), the cholesterol level (x2), and the number of points that the individual's blood pressure exceeded the recommended value (x3). A random sample of 40 individuals was selected. The computer output of the multiple regression model is shown below. (15 marks) THE REGRESSION EQUATION IS y = 55.8 + 1.79x -0.02 1x2 -0.061x3 Predictor Constant X1 X2 Coef 55.8 1.79 -0.021 -0.016 StDev 11.8 0.44 0.011 0.014 T 4.729 4.068 -1.909 -1.143 X3 R-Sq = 22.5% S = 9.47 Adj RP =18.3% ANALYSIS OF VARIANCE SS F 3.477 MS 312 89.722 df 3 36 39 Source of Variation Regression Error Total 936 3230 4166
