What does 's' denote in describing a General Linear Model (GLM) and a note on Generalized Linear Models in SPSS?

The GLM terminology is described [http://www.fil.ion.ucl.ac.uk/~mgray/ here] in relation to using SPM.

Examples of GLMs include linear regressions and analysis of variance and are of form.

Y = XB + error
or, in words,
Response = Prediction + residual

s is, therefore, the residual standard deviation which, for example, corresponds to the square root of the mean square error term in an analysis of variance.

Note: The use of Mean Square Error is equivalent to the 'Deviance' Scale Parameter Method using the default linear model (for a continuous response) under the 'Estimation' tab in the Generalized Linear Model (under 'analyze' in SPSS). The default setting for the Scale Parameter method in the 'Generalized Linear Model' is actually 'Log-likelihood' which yields a statistic which has a critical value following a chi-square distribution. This statistic is not usually used directly for regression/anova models with continuous responses but is incorporated as a denominator in a F ratio. It is, however, used directly for categorical responses which is why we tend to quote chi-square values, rather than F values, when assessing the influence of predictor variables on group responses.

Scaled Pearson = $$\sum_text{i} \frac{(\mbox{i-th residual}^text{2})}{\mbox{i-th predicted value}}$$

Pearson Chi-square = deviance = $$\sum_text{i} (\mbox{i-th residual}^text{2})$$