Given the least squares regression line = -2.48 + 1.63x, and a coefficient of determination of 0.81, the coefficient of correlation is:
A) -0.85
B) 0.85
C) -0.90
D) 0.90
E) -0.81

Question

Given the least squares regression line  = -2.48 + 1.63x, and a coefficient of determination of 0.81, the coefficient of correlation is:
A) -0.85 
B) 0.85 
C) -0.90 
D) 0.90 
E) -0.81

Quizplus · Accepted Answer

The coefficient of determination (R-squared) is the square of the coefficient of correlation (r).

R-squared = 0.81

r^2 = 0.81

Taking the square root of both sides, we get:

|r| = sqrt(0.81)

|r| = 0.9

Since the regression line has a positive slope, the coefficient of correlation is also positive. Therefore, the answer is D) 0.90.

Given the Least Squares Regression Line = -2