Question

In the multiple linear regression model with estimation by ordinary least squares, is it really necessary to perform the normality analysis of the residues? What if the errors are not normal? How to proceed with the tests if the errors have a t-Student distribution with 5 degrees of freedom? (Do not confuse model errors with waste!)

Answer 1

In regression analysis in order to obtain the least square estimates of the parameters, the assumption of normality of residuals is not required. The Gauss-Markov theorem does not state about the normality assumption to obtain BLUE (Best Linear Unbiased Estimator).

However, we need the normality assumption to test the significance of the variables and to construct the confidence interval estimates of the parameters.

If the errors are non-normal and follow t-distribution, then we can still carry out the testing of hypotheses if the sample size is large enough. However, since the sample-size is very small here (as the degrees of freedom is 5), we can't carry it hypothesis testing of significance of variables.