In simple linear regression, the coefficient of correlation r and the least squares estimate $\hat { \beta } _ { 1 }$ of the population slope $\beta _ { 1 }$ :
A)Must be the same size and sign.
B)May have a different size and different sign.
C)May be the same size but have different sign.
D)May be different sizes but will have the same sign.

Question

Quizplus · Accepted Answer

The coefficient of correlation $r$ and the least squares estimate $\hat { \beta } _ { 1 }$ of the population slope $\beta _ { 1 }$ can have different magnitudes because $r$ is a standardized measure of linear association ranging between -1 and 1, while $\hat { \beta } _ { 1 }$ can take any real value depending on the scale of the variables. However, their signs must be the same since both indicate the direction of the relationship between the variables.

In Simple Linear Regression, the Coefficient of Correlation R and the Least