Effect coding is a coding scheme used when an analysis of variance (ANOVA) is performed with multiple linear regression (MLR). With effect coding, the experimental effect is analyzed as a set of (nonorthogonal) contrasts that opposes all but one experimental condition to one given experimental condition (usually the last one). With effect coding, the intercept is equal to the grand mean, and the slope for a contrast expresses the difference between a group and the grand mean.
In linear multiple regression analysis, the goal is to predict, knowing the measurements collected on N subjects, a dependent variable Y from a set of J independent variables denoted
We denote by X the N × (J + 1) augmented matrix collecting the data for the independent variables ...
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