Imagine a family member looks over your shoulder as you look at the variance equation Σki=1(xi − μ)2P(X = xi) and asks why the P(X = xi) term is there. What would you say?

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?

Econometrics  1. A sample of 60 women found that they run an average a of 5km a week with a variance of 64. Another sample of 80 men found that they ran an average of 3km a week with a variance of 81. Test that there is no difference in the distance run by men and women.

A set of n = 25 pairs of X and Y values has a correlation of r = -0.50 with SSX = 38 and SSY = 14.      Find the standard error of estimate for the regression equation.      What percentage of the variance in Y is accounted for by X?