The exercise involving data in this and subsequent sections were designed to be solved using Excel.
The following estimated regression equation was developed for a model involving two independent variables.
y=40.7+ 8.63x1+ 2.71x2
After x2 was dropped from the model, the least-squares method was used to obtain an estimated regression equation involving only x1 as an independent variable. y=42.0+9.01x1
a. In the two independent variable cases, the coefficient x1 represents the expected change in (Select your answer: y, x1, x2) corresponding to a one-unit increase in (Select your answer: y, x1, x2) when (Select your answer: y, x1, x2) is held constant.
In the single independent variable case, the coefficient x1 represents the expected change in (Select your answer: y, x1, x2) corresponding to a one-unit increase in (Select your answer: y, x1, x2).
b. Could multicollinearity explain why the coefficient of x1 differs in the two models? Assume that x1 and x2 are correlated.

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cchilabert cchilabert · Answer 1 · 2020-04-05T04:23:00+02:00

Answer:

Step-by-step explanation:

Hello!

You have two regression models:

The multiple regression model that was estimated is y=40.7+ 8.63x1+ 2.71x2

The Simple regression model that was estimated is y=42.0+9.01x1

a.

MRmodel the 8.63 represents the modification in the estimated mean of Y when X₁ increases one unit and X₂ remains constant.

SRmodel the 9.01 represents the modification in the estimated average of Y when X₁ increases one unit.

b.

Yes, since both variables X₁ and X₂ are correlated, the effect that X₁ has over Y is directly affected by the precence of X₂

I hope you have a nice day!