the following regression equation was developed for a model

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

yhat = 40.7 + 8.63x1 + 2.71x2

After x2 was dropped from the model, the least swuares method was used to obtain an estimated regression equation involving only x1 as an independent variable.

yhat= 42.0 + 9.01x1

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?

Solution

Coefficient of x1 in first equation is 8.63 and in second equation its 9.01

As both the coeffiecient are positive we conclude that x1 contributes positively towards the estimation of dependent variable.

X1 in equation 1 is less than equation 2 which mean as x2 is removed x1 contributes more in estimation of y . Which imply there exist dependency between the two variables i.e multicollinearity exist. Because multicollinearity is a phenomenon in which two or more predictor variables in a multiple regression model are highly correlated, meaning that one can be linearly predicted from the others with a non-trivial degree of accuracy. i.e in second equation x2 is getting predicted by x1 and hence its coefficient is increasing.