Explanation

An indicator variable (also known as a dummy variable or binary variable) in simple linear regression is a categorical variable that takes only two values: 0 or 1.

Key Points:

1. Definition: Indicator variables are used to represent categorical data in regression models. They take the value 1 when a certain condition is true and 0 when it is false.

2. Purpose: They allow the inclusion of qualitative variables (like gender, yes/no responses, presence/absence) in regression analysis.

3. Why not the other options:

   • Option B (between 0 and 1): This describes continuous variables that can take any value between 0 and 1, not indicator variables.
   • Option C (in the range -1 to 1): This describes correlation coefficients or standardized variables, not indicator variables.

4. Example: In a regression model predicting salary, an indicator variable for gender might be coded as:

   • 1 for male
   • 0 for female

5. Interpretation: The coefficient of an indicator variable represents the average difference in the dependent variable between the group coded as 1 and the reference group coded as 0.

Correct Answer: A - Indicator variables take values of either 0 or 1.