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	0.247	0.249	0.286	0.263	0.268	0.339	0.299
y	1.0	3.5	5.5	3.8	3.5	7.3	5.0

(b) Use a calculator to verify that Σx = 1.951, Σx² = 0.550, Σy = 29.6, Σy² = 148.48 and Σxy = 8.599.

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 increase 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 decrease as x increases.

Answer 1

(a)

	x	y	x^2	y^2	xy
	0.247	1	0.061009	1	0.247
	0.249	3.5	0.062001	12.25	0.8715
	0.286	5.5	0.081796	30.25	1.573
	0.263	3.8	0.069169	14.44	0.9994
	0.268	3.5	0.071824	12.25	0.938
	0.339	7.3	0.114921	53.29	2.4747
	0.299	5	0.089401	25	1.495
sum	1.951	29.6	0.550121	148.48	8.5986

Correlation coefficient r is given by

= 0.906

The value of r lies between -1 to 1

If value of r is positive , there is positive correlation between x and y , that is as x increases y increases.

If value of r is negative , there is negative correlation between x and y , that is as x increases y decreases.

Here r is positive , thus y increases as x increases

Thus ,

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