8.1 GENERAL CONCEPT OF INDICATOR VARIABLES
The variables employed in regression analysis are often quantitative variables, that is, the variables have a well-defined scale of measurement. Variables such as temperature, distance, pressure, and income are quantitative variables. In some situations it is necessary to use qualitative or categorical variables as predictor variables in regression. Examples of qualitative or categorical variables are operators, employment status (employed or unemployed), shifts (day, evening, or night), and sex (male or female). In general, a qualitative variable has no natural scale of measurement. We must assign a set of levels to a qualitative variable to account for the effect that the variable may have on the response. This is done through the use of indicator variables. Sometimes indicator variables are called dummy variables.
Suppose that a mechanical engineer wishes to relate the effective life of a cutting tool (y) used on a lathe to the lathe speed in revolutions per minute (x1) and the type of cutting tool used. The second regressor variable, tool type, is qualitative and has two levels (e.g., tool types A and B). We use an indicator variable that takes on the values 0 and 1 to identify the classes of the regressor variable “tool type.” Let
The choice of 0 and 1 to identify the levels of a qualitative variable is ...