In the simple linear regression, the intercept will equal the sample average of the outcome (Y) variable if which of the following is true? A) sCov(X,Y) = 0 B) sVar(X) 0 C) sCov(X,Y) 0

Question

In the simple linear regression, the intercept will equal the sample average of the outcome (Y) variable if which of the following is true?
A) sCov(X,Y) = 0
B) sVar(X) > 0
C) sCov(X,Y) < 0
D) sVar(Y) > 0

Quizplus · Accepted Answer

The intercept in a simple linear regression model equals the sample average of the outcome variable (Y) when the sample covariance between X and Y (sCov(X,Y)) is zero. This is because the regression line would pass through the mean of Y when there is no linear relationship between X and Y, making the slope coefficient zero and leaving the intercept as the mean of Y.

In the Simple Linear Regression, the Intercept Will Equal the Sample