2. 2. Two variables, x and y, were measured for a random sample of 25 subjects, and two separate regression models were fit to the data. Least squares estimation of the parameters in Model A yielded the following equation and residual plot. log y 0.251+0.281 x Residuals Versus x (response is log y) log y 0.264+ 0.230 log x Residuals Versus log r (response is log y) Residual 0.015 F 0.075 f 0.010+ 0.050- 0.005+ 0.000 Residual 0.025- 0.000- -0.005+ -0.025 -0.010+ -0.050- -0.015+ 0.0 0.2 0.4 0.6 0.8 1.0 -1.4 -1.2 -1.0 -0.8 -0.6 -0.4 -0.2 -0.0 log x Least squares estimation of the parameters in Model B yielded the following equation and residual plot. Which of the following conclusions is correct? a) Model A is appropriate, since the relationship between x and y is linear. b) Model B is appropriate, since the relationship between x and y is linear. c) Model A is appropriate, since the relationship between log x and log y is linear. d) Model A is appropriate, since the relationship between log x and y is linear. e) Model B is appropriate, since the relationship between x and log y is linear. turay

Find the equation of the regression line for the following data set. x 1 2 3 y 0 3 4

The following fictitious table shows kryptonite price, in dollar per gram, t years after 2006. t= Years since 2006 0 1 2 3 4 5 6 7 8 9 10 K= Price 56 51 50 55 58 52 45 43 44 48 51 Make a quartic model of these data. Round the regression parameters to two decimal places.

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?