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.