In a simple linear regression analysis,the correlation coefficient (a)and the slope (b)___________ have the same sign.
A)Always
B)Sometimes
C)Never

Question

Quizplus · Accepted Answer

The slope (b) of a simple linear regression indicates the direction and magnitude of the relationship between two variables, while the correlation coefficient (a) measures the strength and direction of the linear association between the two variables. Since both the slope and the correlation coefficient use the same basic formula and involve the same basic calculations, they will always have the same sign. Specifically, when the correlation coefficient is positive, the slope will be positive, indicating a positive relationship between the two variables. When the correlation coefficient is negative, the slope will be negative, indicating a negative relationship between the two variables. Therefore, the answer is always.

In a Simple Linear Regression Analysis,the Correlation Coefficient (A)and the Slope