1) Is the magnitude of an earthquake related to the depth below the surface at which the quake occurs? Let x be the magnitude of an earthquake (on the Richter scale), and let y be the depth (in kilometers) of the quake below the surface at the epicenter.
x 2.9 4.7 3.3 4.5 2.6 3.2 3.4
y 4.6 10.3 11.2 10.0 7.9 3.9 5.5
(b) Use a calculator to verify that Σx = 24.6, Σx2 = 90.20, Σy = 53.4, Σy2 = 460.56 and Σxy = 195.43.
Compute r. (Round to 3 decimal places.)
2) 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, and let y represent the player's 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.
x 0.251 0.251 0.286 0.263 0.268 0.339 0.299
y 1.2 3.7 5.5 3.8 3.5 7.3 5.0
b) Use a calculator to verify that Σx = 1.957, Σx2 = 0.553, Σy = 30.0, Σy2 = 150.36 and Σxy = 8.710. Compute r. (Round to 3 decimal places.)