In a simple linear regression problem, the least squares line is = -3.75 + 1.25x, and the coefficient of determination is 0.81. The coefficient of correlation must be -0.90.

Question

In a simple linear regression problem, the least squares line is  = -3.75 + 1.25x, and the coefficient of determination is 0.81. The coefficient of correlation must be -0.90.

Quizplus · Accepted Answer

The coefficient of correlation (√r²) is equal to the absolute value of the slope of the least squares line multiplied by the ratio of the standard deviation of y to the standard deviation of x. 
r = (-3.75) * (1/s) 
where s is the ratio of the standard deviation of y to the standard deviation of x. 
Therefore, r can't be -0.90 with the given slope of 1.25, intercept of -3.75, and coefficient of determination of 0.81.

In a Simple Linear Regression Problem, the Least Squares Line