Question

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

y​=40.7+8.63x1​+2.71x2​

After was dropped from the model, the least squares method was used to obtain an estimated regression equation involving only as an independent variable.

y=42.0+9.01x1​

Required:
a. Give an interpretation of the coefficient of x1 in both models.
b. Could multicollinearity explain why the coefficient of x1 differs in the two models? If so, how?

Answer 1

Kindly check explanation

Explanation:

Given :

Regression equation for 2 independent variables :

y=40.7+8.63x1+2.71x2 (model 1)

Regression model for only x1 variable :

y=42.0+9.01x1 (model 2)

The Coefficient of x1 = 8.63 is the change in the estimated predicted value of the dependent variable due to a unit increase in the independent variable (x1) when the other independent variable (x2) is held constant

For Model 2:

The Coefficient of x1 = 9.01 is the change in the estimated predicted value of the dependent variable due to a unit increase in the independent variable (x1)

2.)

Yes, for model 1, we have a multiple regression model (more than 1 independent variable). Multicolinearlity sets in when the independent variables in a multiple regression model are highly correlated. Hence, the Coefficient of each independent variable varies highly when modeled separately compared to when used together to generate a single model. Hence.The reason for the difference.