QuestionQuestion

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 3.2 4.0 3.3 4.5 2.6 3.2 3.4
y 4.7 9.7 11.2 10.0 7.9 3.9 5.5
(a) Make a scatter diagram of the data. Then visualize the line you think best fits the data.
(b) Use a calculator to verify that Σx = 24.2, Σx2 = 85.94, Σy = 52.9, Σy2 = 449.49 and Σxy = 187.52 Compute r. (Round to 3 decimal places.)

As x increases, does the value of r imply that y should tend to increase or decrease? Explain your answer.
Given our value of r, y should tend to decrease as x increases.
Given our value of r, we can not draw any conclusions for the behavior of y as x increases.   
Given our value of r, y should tend to increase as x increases.
Given our value of r, y should tend to remain constant as x increases.

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 0.237 0.259 0.286 0.263 0.268 0.339 0.299
y 1.2 3.1 5.5 3.8 3.5 7.3 5.0
(a) Make a scatter diagram of the data.

Then visualize the line you think best fits the data.
(b) Use a calculator to verify that Σx = 1.951, Σx2 = 0.550, Σy = 29.4, Σy2 = 146.28 and Σxy = 8.567.

Compute r. (Round to 3 decimal places.)

As x increases, does the value of r imply that y should tend to increase or decrease? Explain your answer.
Given our value of r, y should tend to decrease as x increases.
Given our value of r, we can not draw any conclusions for the behavior of y as x increases.   
Given our value of r, y should tend to remain constant as x increases.
Given our value of r, y should tend to increase as x increases.

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