A linear regression model is developed that has a slope of -2.5 and an intercept of 10.The sample coefficient of determination is 0.50.Which of the following statements is TRUE?
A)The sample correlation coefficient must be 0.250.
B)The sample correlation coefficient must be -0.707.
C)The sample correlation coefficient must be -0.250.
D)The sample correlation coefficient must be 1.00.

Question

Quizplus · Accepted Answer

The coefficient of determination (R-squared) is the square of the sample correlation coefficient (r), therefore:

R^2 = r^2

0.50 = r^2
r = ±0.707

Since the slope is negative, the correlation coefficient must also be negative, therefore:

r = -0.707

Therefore, the answer is B.

A Linear Regression Model Is Developed That Has a Slope