The ANOVA table provides information on the full regression model, each of the main effects (and interactions), and residual sum of squares. The first row of the table provides the variation of the outcome (Y) variable, without considering the other variables or the regression. This is calculated as the sum of the square of the difference between each Y value (yi) and the mean of all the Y values (y̅). This is reported as the total sum of squares in the bottom row of the ANOVA table.
Mathematically, SStotal = Σ[(yi - y̅)2]
Then it computes the sum of the square of the discrepancy (difference) between the actual Y values (values of the outcome variable in the input data table, yi) and the Y values predicted by the regression model (ŷ). This is the sum of squares of the residuals.
Again, mathematically, SSresidual = Σ[(yi - ŷ)2]
The difference between these two SS values is the sum of squares of the regression.
SStotal - SSresidual = SSreg
The ANOVA table computes a F ratio, which is used to compute a P value. This P value tests the null hypothesis that the regression model is entirely useless so the predictions of the regression model are no better than just predicting that each Y value equals the mean of all Y values. It is only worth looking at the other regression results when this P value is small.
Immediately below the information for the regression, each of the main effects and interaction terms contained within the model will be listed along with their type III sum of squares, degrees of freedom, mean square (equal to the sum of squares divided by the degrees of freedom), the F statistic (equal to the MS for the term divided by the MS of the residual), and the P value determined from this F statistic.
P values reported in the ANOVA table provide information on that term’s overall effect on the model. For parameters of continuous variables, these P values are the same as the ones shown in the Parameter Estimates section of the results table. In both cases, the P value is determined using the null hypothesis that the effect of the term is zero. For the P value in the ANOVA table, this means comparing if the model with the specific term is the same as the model without the specific term. For the P value in the Parameter Estimates section, this means comparing if the beta coefficient is equal to zero.
The interpretation is different for categorical variables with two or more levels (or interactions including those parameters). For these terms, a single P value is given in the ANOVA table, while individual P values are calculated for each level (or interaction) of the categorical variable (except for the reference level). The P value in the ANOVA table still tests the null hypothesis that the model with and without this term are the same. This P value cannot be used to determine which specific levels or interactions are significant. Moreover, the P values in the Parameter Estimates section for these variables each represent a comparison between that specific level (or interaction) and the variables reference level. No information is given comparing one level to another (only one level to the reference).
