- Know what an indicator variable is
- Find and describe an appropriate multiple linear regression model equation with categorical predictors
Recall that the data set contains information about high school student achievement scores on math, science, reading, writing, and social studies tests. The data set contains information about [latex]200[/latex] high school students and [latex]10[/latex] variables for each student. Descriptions of the variables are as follows:
| Variable name | Definition |
| id | Identification number of the student |
| female | Gender of the student (0 = male, 1 = female) |
| race | Ethnic background of the student (1 = Hispanic, 2 = Asian, 3 = Black, 4 = White) |
| ses | Socio-economic status of the student (1 = low, 2 = medium, 3 = high) |
| schtyp | School type (1 = public, 2 = private) |
| prog | Program type (1 = general, 2 = academic preparatory, 3 = vocational/technical) |
| read | Score from test of reading |
| write | Score from test of writing |
| math | Score from test of math |
| science | Score from test of science |
| socst | Score from test of social studies |
For the variable prog, we will need to create two indicator variables to add the explanatory variable into the model.
One indicator variable for prog could be defined as academic preparatory, and the other indicator variable for prog could be defined as vocational/technical.
These two indicator variables would be defined using the following:
- If prog = academic preparatory, the indicator variable for academic_preparatory = [latex]1[/latex]. Otherwise, if prog = vocation/technical or general, the indicator variable for academic_preparatory = [latex]0[/latex].
- If prog = vocational/technical, the indicator variable for vocational_technical = [latex]1[/latex]. Otherwise, if prog = academic preparatory or general, the indicator variable for vocational_technical = [latex]0[/latex].
We do not need three indicator variables because prog = general is captured when academic_preparatory = 0 and vocational_technical = 0.