Qualitative and Dummy Variables in Regression Modeling

• Handle qualitative independent variables with a quantitative proxy or use a dummy variable.
• When using a dummy independent variables (such as assigning a number to the degree of consumer confidence), define a collectively exhaustive set of “j” categories, then j-1 (“j minus one”) will give you the number of dummy variables for inclusion in your model.
• Models with dummy independents can easily be misspecified.

Model types with qualitative dependent variables

• Probit models – based on a normal distribution and attempt to estimate the probability that the dependent variable will equal 1.
• Logit models – based on the logistic distribution and like Probit models, they attempt to estimate the probability that the dependent variable will equal 1.
• Discriminant Analysis – creates a score and if the score crosses a threshold then the dependent variable is assigned a 1.

Looking at the big picture, you want your multiple regression model to:

1. Have a good theoretical basis and;
2. Pass the most stringent statistical tests (refer back to the sub-section “Assumption Violations”).