Model Summary - Wald Statistic

The Wald statistic is used to test the linear hypotheses about the regression coefficients, and it is based on large sample sizes, like the large-sample normality of parameter estimates.

Testing for Single Parameter βk

To test the null hypothesis that the single parameter estimate equals 0, the Wald statistic is given by:

The Wald statistic is asymptotically distributed as with 1 degree of freedom. The estimated standard error of the i^th estimated coefficient, , is the square root of the i^th diagonal element of the estimated covariance matrix , that is, .

Testing for several βk

When β is k-dimensional, and asymptotic is normal, the hypothesis test is given by the following quadratic form:

This statistic is asymptotically distributed as with degrees of freedom equal to the number of parameters estimated for a given effect and can be used to test the hypothesis that all parameters estimated for a given effect are equal to 0.