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?

Kindly check explanation

Step-by-step 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.