Suppose the correlation coefficient between a predictor variable (a person’s hei

Question

Suppose the correlation coefficient between a predictor variable (a person’s height, measured in centimeters) and a response variable (a person’s weight, measured in kilograms) is 0.72.

Suppose that we change the units used to measure height from centimeters to inches and the units used to measure weight from kilograms to pounds, and then we recompute the correlation coefficient. Which of the following would be true?

Select one:

a. The new correlation coefficient should be the same: R = 0.72.

b. The new correlation coefficient should be R = 0.72 × (2.54/2.2) 0.83.

c. The new correlation coefficient should be R = 0.72 × (2.2/2.54) 0.62.

d. The new correlation coefficient should be something other than the options given here.

Explanation / Answer

ANSWER: (a)

(The new correlation coefficient should be the same: R = 0.72.)

EXPLANATION:

Correlation coefficient is independent of change of origin and scale. It is one of the property of correlation coefficient.

Therefore from the above property correlation coefficient is remains unchanged

Hence the new correlation coefficient should be the same: R = 0.72.

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