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.

Question

Mathematics

Leland Mathews

27 November, 16:10

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.

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Answers (1)

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Korbin Solis · Answer 1

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

Step-by-step explanation:

The correlation coefficient is a statistical measure that calculates the strength of the relationship between the relative movements of two variables.

It is a relative dimensionless measure, so it does not depend on the units of measurement of the variables involved.

If the variables are correlated in centimeters and kilograms, they will also be correlated in inches and pounds, and with the same relative magnitude.

So the answer is

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