GRM Whole Model - Testing the Whole Model

Given the Model SS and the Error SS, you can perform a test that all the regression coefficients for the X variables (b1 through bk, excluding the b0 coefficient for the intercept) are zero. This test is equivalent to a comparison of the fit of the regression surface defined by the predicted values (computed from the whole model regression equation) to the fit of the regression surface defined solely by the dependent variable mean (computed from the reduced regression equation containing only the intercept). Assuming that X¢ X is full-rank, the whole model hypothesis mean square

MSH = (Model SS)/k

where k is the number of columns of X (excluding the intercept column), is an estimate of the variance of the predicted values. The error mean square

s2 = MSE = (Error SS) / (n - k - 1)

where n is the number of observations, is an unbiased estimate of the residual or error variance. The test statistic is

F = MSH / MSE

where F has (k, n - k - 1) degrees of freedom.

If X¢ X is not full rank, r + 1 is substituted for k, where r is the rank or the number of non-redundant columns of X¢ X.

If the whole model test is not significant the analysis is complete; the whole model is concluded to fit the data no better than the reduced model using the dependent variable mean alone. It is futile to seek a submodel that adequately fits the data when the whole model is inadequate.

Note: in the case of non-intercept models, some multiple regression programs will compute the full model test based on the proportion of variance around 0 (zero) accounted for by the predictors; for more information (see Kvålseth, 1985; OKunade, Chang, and Evans, 1993). STATISTICA GRM will actually compute both values (i.e., based on the residual variance around 0, and around the respective dependent variable means; see also the Between effects options (described in terms of GLM) on the Summary tab of the Results dialog).

Topics on Building the Whole Model