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 sample coefficient of determination is defined as the proportion of the total variation in the dependent variable that is explained by the regression model. It is represented by the symbol R^2 and can take values between 0 and 1.

In this case, R^2 = 0.50, which means that 50% of the total variation in the dependent variable is explained by the regression model.

The sample correlation coefficient (r) is the square root of R^2, with a sign that depends on the slope of the regression line. Since the slope is negative, the sign of r must also be negative.

Therefore, r = -sqrt(0.50) = -0.707.

The correct answer is B.

A Linear Regression Model Is Developed That Has a Slope