Question

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	0.253	0.245	0.286	0.263	0.268	0.339	0.299
y	1.4	3.7	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 = 1.953, Σx² = 0.551, Σy = 30.2, Σy² = 150.88 and Σxy = 8.741.

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.

Answer 1

	X	Y	X * Y	X2	Y2
	0.253	1.4	0.3542	0.064009	1.96
	0.245	3.7	0.9065	0.060025	13.69
	0.286	5.5	1.573	0.081796	30.25
	0.263	3.8	0.9994	0.069169	14.44
	0.268	3.5	0.938	0.071824	12.25
	0.339	7.3	2.4747	0.114921	53.29
	0.299	5	1.495	0.089401	25
Total	1.953	30.2	8.7408	0.551145	150.88

r = 0.878

Given our value of r, y should tend to increase as x increases.