## Normality tests

Let us now consider the fundamental problem of testing disturbance normality in the context of the linear regression model:

Y = Xp + u, (23.12)

where Y = (y1, …, yn)’ is a vector of observations on the dependent variable, X is the matrix of n observations on k regressors, P is a vector of unknown coefficients and u = (u1, …, un)’ is an n-dimensional vector of iid disturbances. The problem consists in testing:

H0 : f(u) = ф (u; 0, о), о > 0, (23.13)

where f(u) is the probability density function (pdf) of ui, and ф (u; p, о) is the normal pdf with mean p and standard deviation о. In this context, normality tests are typically based on the least squares residual vector

й = y – xp = Mxu, (23.14)

where p = (XX)-1 X’y and Mx = In – X(XX)-1X’...

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