Chapter 10, Problem 10.15AC

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

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?

Problem 1: I have uploaded data (PCE-PDI.xls) for the US total personal consumption expenditures and total disposable income from 1971:1 to 2009:7. Divide the entire sample into two subsamples: 1971:01 to 1985:12 and 1986:01 to 2009:07. Here consumption expenditure (PCE) is the dependent variable and disposable income (PDI) is the independent variable. Let variable Y denotes consumption expenditure and variable X denotes disposable income. (a)   Estimate a two-variable regression model for both subsamples and report the estimated results.