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) sVar(X) 0 B) $\bar { X }$ = 0 C) sCov(X, Y) 0 D) sCov(X, Y)

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) sVar(X) > 0
B) $\bar { X }$ = 0
C) sCov(X, Y) > 0
D) sCov(X, Y) < 0

Quizplus · Accepted Answer

The intercept is equal to the point where the regression line intersects the y-axis, or where X=0. If X is centered at 0 (meaning the mean of X is 0), then the intercept will equal the sample average of Y. Therefore, if $\bar{X}$ = 0 (choice B), the intercept will equal the sample average of the outcome variable Y. The other choices are not relevant to the calculation of the intercept.

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