Question

Consider a linear model to explain monthly beer consumption:

E(u | income, price, education)=0,

Var(u | income, price, education)= .

Can we use the regression results above to make inference on coefficients? Explain.

Answer 1

The above conditions are neccessary but not sufficient conditions to make inference on the coefficients.

To make correct inference on the coefficients we need correct standard error and p value. If Multicolinearity i.e cov(Xi,Xj)= k ( a non zero number and i is not equal to j) a then it appears, then it will inflate the standard error and the gives the incorrect p value. Even if the E(u)=0 and V(u|Xi)= constant.This problem will affect the model and the inference of the coefficients wil be incorrect.

If autocorrelation i.e cov(ui,uj)= k ( a non zero number and i is not equal to j) appears then it will inflate the standard error and the gives the incorrect p value. Even if the E(u)=0 and V(u|Xi)= constant.This problem will affect the model and the inference of the coefficients wil be incorrect.