In baseball, is there a linear correlation between batting average and home run percentage? Let x represent the batting average of a professional baseball player. Let y represent the home run percentage (number of home runs per 100 times at bat). A random sample of n = 7 professional baseball players gave the following information:

ˆ‘x = 1.957; ˆ‘y = 30.1; ˆ‘x2 ‰ˆ 0.553; ˆ‘y2 = 150.15; ˆ‘xy ‰ˆ 8.753
(a) Verify that Se ‰ˆ 0.647.
(b) Verify that r ‰ˆ 0.948. Test that p is positive. Use α = 0.01.
(c) Verify that b ‰ˆ 55.166. Test that β is positive. Use α = 0.01.
(d) Verify that Å· ‰ˆ ˆ’11.123 + 55.166x. Find a 90% confidence interval for the predicted home run percentage for a player with a batting average of 0.310.

x 0.243 0.259 0.286 0.263 0.268 0.39 0.299 y 1.4 3.6 5.5 3.8 3.5 7.3 5.0