Customer's Age (Death) Excel was used to run a simple linear regression analysis. Excel output and diagnostic plots follow for your reference in answering the remaining questions. 15 Father's Age (Death) Residual Plot Residuals -10 -15 10 10 5 0 40 50 80 90 100 Father's Age (Death) 100 90 80 Normal Probability Plot 70 50 40 30 20 10 0 0 20 40 60 80 100 120 Sample Percentile SUMMARY OUTPUT Regression Statistics Multiple R 0.69406672 R Square Adjusted R Square Standard Error Observations 0.481728612 0.476440129 3.936905277 100 ANOVA Regression Residual Total df SS MS F 1 1411.826131 1411.82613 91.09012 Significance F 1.18186E-15 98 99 1518.923869 2930.75 15.4992232 Coefficients Standard Error Intercept Father's Age (Death) 29.28584902 0.627659604 4.539696555 t Stat P-value 6.45105872 4.23E-09 0.065764048 9.54411453 1.18E-15 Lower 95% Upper 95% 20.27696896 38.29472909 0.497152992 0.758166217 Lower 95.0% Upper 95.0% 20.27696896 0.497152992 38.29472909 0.758166217

Olympic Pole Vault The graph in Figure 7 indicates that in recent years the winning Olympic men’s pole vault height has fallen below the value predicted by the regression line in Example 2. This might have occurred because when the pole vault was a new event there was much room for improvement in vaulters’ performances, whereas now even the best training can produce only incremental advances. Let’s see whether concentrating on more recent results gives a better predictor of future records. (a) Use the data in Table 2 (page 176) to complete the table of winning pole vault heights shown in the margin. (Note that we are using x=0 to correspond to the year 1972, where this restricted data set begins.) (b) Find the regression line for the data in part ‚(a). (c) Plot the data and the regression line on the same axes. Does the regression line seem to provide a good model for the data? (d) What does the regression line predict as the winning pole vault height for the 2012 Olympics? Compare this predicted value to the actual 2012 winning height of 5.97 m, as described on page 177. Has this new regression line provided a better prediction than the line in Example 2?