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Build a multiple regression containing qualitative explanatory variables and explain what its output means

CFA® Level II · Quantitative Methods · Extensions of Multiple Regression · L2.QM.4.b

The idea

A qualitative factor enters a regression through dummy variables coded 0 or 1. With n categories use n − 1 dummies, otherwise they sum to the intercept and create perfect collinearity: the dummy variable trap. An intercept dummy shifts the line up or down for the category, so its coefficient is the difference in the expected dependent variable against the omitted base group. A slope dummy, the dummy multiplied by a continuous variable, lets that variable's effect differ by category. With both, the category's intercept is b0 plus the dummy coefficient and its slope is the base slope plus the interaction coefficient. A t-test on each tells whether the difference is significant.

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