Question

In a multiple regression problem involving two independent variables, if b1 is computed to be +2.0, it means that

A. the relationship between X1 and Y is significant.

B. the estimated average of Y increases by 2 units for each increase of 1 unit of X1, holding X2 constant.

C. the estimated average of Y is 2 when X1 equals zero.

D. the estimated average of Y increases by 2 units for each increase of 1 unit of X1, without regard to X2.

Answer 1

D. the estimated average of Y increases by 2 units for each increase of 1 unit of X1, without regard to X2.

Explanation:

Hello!

Given any linear or multiple regression, βi represents the modification on the population mean of Y when Xi increases one unit. And its estimator bi is defined as the modification on the estimated mean of Y when Xi increases one unit.

So if you have an estimated multiple regression model Yi= b₀ + b₁X₁ + b₂X₂ + ... + bkXk

Where k is the number of regressive variables.

b₁ is the modification of the estimated average of Y when X₁ increases one unit and the rest of the independent variables remain constant.

In other words, the estimated mean of Y increases 2 for each unit increase of X₁.

I hope it helps!