Chapter 12, Problem 12.44AC

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?

The manager of the purchasing department of a large saving and loan organization would like to develop a model to predict the amount of time​ (measured in​ hours) it takes to record a loan application. Data are collected from a sample of 30​ days, and the number of applications recorded and completion time in hours is recorded. Attached below is the regression output. What can be said about the​ 90% confidence interval for the mean change in the amount of time needed as a result of recording one additional loan​ application?           Question content area bottom Part 1   A. The​ 90% confidence interval is narrower than​ [0.0109, 0.0143].   B. The​ 90% confidence interval is wider than​ [0.1492, 0.6555].   C. The​ 90% confidence interval is wider than​ [0.0109, 0.0143].

The table below lists measured amounts of redshift and the distances (billions of light-years) to randomly selected astronomical objects. Find the (a) explained variation, (b) unexplained variation, and (c) indicated prediction interval. There is sufficient evidence to support a claim of a linear correlation, so it is reasonable to use the regression equation when making predictions. For the prediction interval, use a 90% confidence level with a redshift of 0.0126. Redshift Distance 0.0237 0.34 a. Find the explained variation. 0.448262 (Round to six decimal places as needed.) b. Find the unexplained variation. (Round to six decimal places as needed.) 0.0541 0.75 0.0723 0.98 C 0.0397 0.57 0.0444 0.62 0.0103 0.13 D