Question 7. The estimated goodness of fit of the regression is R2 = 0.5. According to the regression output, we can infer that: (a) The correlation between Log of Wage yi and its fitted values yˆi is −0.5 (b) The correlation between Log of Wage yi and its fitted values yˆi is 0.5 (c) The correlation between Log of Wage yi and its fitted values yˆi is + √0.5  (d) The correlation between Log of Wage yi and its fitted values yˆi is − 0.5 (e) The correlation between Log of Wage yi and its fitted values yˆi is 0.5^2

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?

Can the average rate of change of a function be constant?

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

If your graphing calculator is capable of computing a least-squares sinusoidal regression model, use it to find a second model for the data. Graph this new equation along with your first model. How do they compare?

What is the y -intercept on the graph of the logistic model given in the previous exercise?

Sales of a video game released in the year 2000 took off at first, but then steadily slowed as time moved on. Table 4 shows the number of games sold, in thousands, from the years 20002010. a. Let x represent time in years starting with x=1 for the year 2000. Let y represent the number of games sold in thousands. Use logarithmic regression to fit a model to these data. b. If games continue to sell at this rate, how many games will sell in 2015? Round to the nearest thousand.