General Linear Model

A common set of statistical ∗assumptions upon which are based ∗regression, ∗correlation, and ∗analysis of variance—in [Page 132]short, the full range of methods used to study the ∗linear relations between one continuous dependent variable and one or more independent variables, whether continuous or categorical. The model is “general” in that the kind of independent variable is not specified.

The basic idea is that the relation between a dependent variable and the independent variables can be expressed as a linear equation containing a ∗term for the weighted sum of the values of the independent variables—plus a term for everything that we do not know about, which is called an ∗error term. The method used to decide how much weight to give to the independent variable(s) is the ∗least squares criterion. Compare ∗polynomial regression analysis.

You can get a good practical “feel” for the general linear model by spending a few hours calculating by hand standard deviations, Pearson correlations, regression equations, t-tests, and F tests. You will quickly discover that many of the steps in these calculations are generally the same.