GLM Introductory Overview - Simple Regression
Simple regression designs involve a single continuous predictor variable. If there were 3 cases with values on a predictor variable P of, say, 7, 4, and 9, and the design is for the first-order effect of P, the X matrix would be
and using P for X1 the regression equation would be
Y = b0 + b1P
If the simple regression design is for a higher-order effect of P, say the quadratic effect, the values in the X1 column of the design matrix would be raised to the 2nd power, that is, squared
and using P2 for X1 the regression equation would be
Y = b0 + b1P2
The sigma-restricted and overparameterized coding methods do not apply to simple regression designs and any other design containing only continuous predictors (since there are no categorical predictors to code). Regardless of which coding method is chosen, values on the continuous predictor variables are raised to the desired power and used as the values for the X variables. No recoding is performed. It is therefore sufficient, in describing regression designs, to simply describe the regression equation without explicitly describing the design matrix X.
Between-subject designs
Within-subject (repeated measures) designs
Multivariate designs