Answer to Question #121720 in Statistics and Probability for Joseph Se

Question #121720

1. Suppose the correlation coefficient between an explanatory variable (the size of a person’s home, measured in square feet) and a response variable (the amount they spend on alcohol per year, measured in US Dollars) is 0.34. If we change the units used to measure their home size from square feet to square meters, which of the following will be true? Assume 1 square foot is roughly 0.09 square meters.

A. The new correlation should be approximately R = 0.34/0.09 = 3.78
B. The new correlation should besame: R=0.34
C. The new correlation should be approximately R=0.34 x (0.09)^2 = 0.003
D. The new correlation should be R= 0.34 x 0.09 = 0.03

Expert's answer

Answer: option B. The new correlation should be the same .

Explanation : correlation coefficient is unitless and so stays the same when the units of the involved variables change .