(b) Verify the given sums Ex, Ey, Ex, Ey, Exy, and the value of the sample correlation coefficient r. (Round your value for r to three decimal places.) Ex -92 Ey -617 Ex -2336 Ey - 82455 Exy - 13634 (c) Find x, and y. Then find the equation of the least-squares line ý -a+ bx. (Round your answers for x and y to two decimal places. Round your answers for a and b to three decimal places.) x- 15.333 y=102 833 ý- 33.681 4.510 (d) Graph the least-squares line. Be sure to plot the point (x, y) as a point on the line. y 200 200 150 150 100 100 50 50 10 20 30 40 10 20 30 40 y y 200 200 150 150 100 100 50 50 10 20 30 40 10 20 30 40 (e) Find the value of the coefficient of determination. What percentage of the variation in y can be explained by the corresponding variation in x and the least-squares line? What percentage is unexplained? (Round your answer for to three decimal places. Round your answers for the percentage one decimal place.) explained unexplained (1) The calves you want to buy are 24 weeks old. What does the least-squares line predict for a healthy weight? (Round your answer to two decimal places.) Okg

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?

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?

(b) For the (x, y) data set of part (a), compute the equation of the sample least-squares line ŷ = a + bx. (Use 4 decimal places.) a   b   If the number of hits was 9.1 (× 105) one day, what do you predict for the number of hits the next day? (Use 1 decimal place.) (× 105) hits (c) Compute the sample correlation coefficient r and the coefficient of determination r2. (Use 4 decimal places.) r   r2   Test ρ > 0 at the 1% level of significance. (Use 2 decimal places.) t   critical t