Suppose that the least-squares regression line for predicting y from x is y = 100 + 1.3x. Which of the following is a possible value for the correlation between x and y?
A) 1.3
B) -1.3
C) 0
D) -0.5
E) 0.5

Question

Quizplus · Accepted Answer

The correlation coefficient (r) is equal to the slope of the least-squares regression line (b) multiplied by the standard deviation of y (sy) divided by the standard deviation of x (sx). Therefore, r = b(sy/sx) = 1.3(sy/sx). Since the slope is positive, the correlation coefficient must also be positive. Therefore, the only possible value from the given choices is 0.5.

Suppose That the Least-Squares Regression Line for Predicting Y from X