Question

The following estimated regression equation was developed for a model involving two independent variables.

y hat = 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 hat = 42.0 + 9.01x1

a. In the two independent variable case, the coefficient x1 represents the expected change in - Select your answer -yx1x2Item 1corresponding to a one unit increase in - Select your answer -yx1x2Item 2 when - Select your answer -yx1x2Item 3 is held constant.

In the single independent variable case, the coefficient x1 represents the expected change in - Select your answer -yx1x2Item 4corresponding to a one unit increase in - Select your answer -yx1x2Item 5 .

b. Could multicollinearity explain why the coefficient of x1 differs in the two models? Assume that x1 and x2 are correlated.
- Select your answer -Yes, because a change in x1 would be accompanied by a change in x2Yes, because a change in x1 would not be accompanied by a change in x2

Answer 1

Explanation:

Hello!

Given the estimated regression equations

^Y= 40.7 + 8.63X₁ + 2.71X₂

and after the second independent variable was removed from the model:

^Y= 42.0 + 9.01X₁

a.

For the first regression equation:

The coefficient 8.63 represents the change of the sample mean of Y when X₁ increases one unit and X₂ remains constant.

For the second regression equation:

The coefficient 9.01 represents the change of the sample mean of Y when X₁ increases one unit.

b.

If the two independent variables X₁ and X₂ are correlated, this means that the observed values of X₁ change when analyzed altogether with X₂.

And when analyzed alone, the values of X₁ will be different, that's why the estimated coefficients for X₁ was different when calculated for the multiple regression and the simple regression.

Correct Answer: Yes, because a change in X₁ would be accompanied by a change in X₂

I hope this helps!