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	0.263	0.286	0.263	0.268	0.339	0.299
y	1.1	3.3	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 = 1.971, Σx² = 0.560, Σy = 29.5, Σy² = 147.33 and Σxy = 8.626.

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 remain constant 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 decrease as x increases.Given our value of r, we can not draw any conclusions for the behavior of y as x increases.

Answer 1

Solution:

First input given data in excel,

and follow the steps:

select data ----> Insert ------>Charts ------> Scatter Chart

b) Following are the steps to find correlation.

Given values are correct. Σx = 1.971, Σx² = 0.560, Σy = 29.5, Σy² = 147.33, Σxy = 8.626 and n = 7

Formula for correlation:

Just put the above values in above formula, we get

r = 0.915

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

Done