Question

# In baseball, is there a linear correlation between batting average and home run percentage? Let x...

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 0.257 0.286 0.263 0.268 0.339 0.299 y 1.3 3 5.5 3.8 3.5 7.3 5

(a) Make a scatter diagram of the data.

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(b) Use a calculator to verify that Σx = 1.963, Σx2 = 0.556, Σy = 29.4, Σy2 = 145.92 and Σxy = 8.577.

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

a)

The points form a near to straight line and increase the value of x increases the corresponding value of y and vice versa. Hence, these two variables have a positive association.

b)

As x increases, the value of r implies that y should tend to increase.

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