In simple linear regression,the coefficient of correlation r and the least squares estimate $b _ { 1 }$ of the population slope $\beta _ { 1 }$ :
A) must have the same numerical value.
B) must have opposite signs.
C) must have the same sign.
D) may have opposite signs or the same sign.

Question

Quizplus · Accepted Answer

The coefficient of correlation $r$ and the least squares estimate $b_1$ of the population slope $\beta_1$ must have the same sign. This is because both $r$ and $b_1$ reflect the direction of the linear relationship between the two variables. If the relationship is positive, both will be positive; if the relationship is negative, both will be negative.

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