Answer: A dummy variable for each season plus a dummy for the intercept

## Explanation Multicollinearity occurs when there is a perfect linear relationship between independent variables in a regression model. In the context of dummy variables for seasonal effects: 1. **The Dummy Variable Trap**: When using dummy variables to represent categorical variables (like seasons), we need to avoid including all categories plus an intercept term. If we include a dummy variable for each season (e.g., 4 seasons) AND also include an intercept term, we create perfect multicollinearity. 2. **Why option D causes multicollinearity**: - If we have a dummy variable for each season (say 4 seasons: Spring, Summer, Fall, Winter) - AND we also include an intercept term - Then the sum of all seasonal dummy variables equals 1 for every observation - This creates a perfect linear relationship: Intercept = 1 - (Dummy_Spring + Dummy_Summer + Dummy_Fall + Dummy_Winter) - This is the classic dummy variable trap 3. **Correct approach**: To avoid multicollinearity when using dummy variables: - Use n-1 dummy variables for n categories - OR include all n dummy variables but exclude the intercept term - For 4 seasons, we would use 3 dummy variables plus an intercept, or 4 dummy variables without an intercept 4. **Why other options don't necessarily indicate multicollinearity**: - **A**: One seasonal dummy variable doesn't necessarily cause multicollinearity - **B**: Two seasonal dummy variables (each equal to 1) might not cause multicollinearity depending on the intercept - **C**: Two seasonal dummy variables with one equal to 1 and one equal to 0 might not cause multicollinearity **Key takeaway**: The combination of having a dummy variable for each category PLUS an intercept term always creates perfect multicollinearity, which is why option D definitely indicates the existence of multicollinearity.

Author: Nikitesh Somanthe