Given the least squares regression line = -4.63 + 1.38x, and a coefficient of determination of 0.9025, the correlation coefficient must be:
A) -0.95
B) +0.95
C) +1.38
D) -0.81
E) 0.81

Question

Given the least squares regression line  = -4.63 + 1.38x, and a coefficient of determination of 0.9025, the correlation coefficient must be:
A) -0.95 
B) +0.95 
C) +1.38 
D) -0.81 
E) 0.81

Quizplus · Accepted Answer

The coefficient of determination (R-squared) is equal to the square of the Pearson correlation coefficient (r). 
R^2 = r^2

So, taking the square root of R^2 gives us the absolute value of r: 
|r| = sqrt(R^2) 
|r| = sqrt(0.9025) 
|r| = 0.95

Since the regression line has a positive slope (1.38x), we know that the correlation is positive if r is positive and negative if r is negative. Therefore, the answer is B, +0.95.

Given the Least Squares Regression Line = -4