Explanation

When modeling quarterly seasonality with an intercept term, the correct number of dummy variables to use is 3.

Key Concepts:

• Dummy Variable Trap: When using dummy variables for categorical data with k categories, we use k-1 dummy variables to avoid perfect multicollinearity.
• Quarterly Data: There are 4 quarters in a year.
• Intercept Term: The intercept represents the baseline level for the omitted category.

Why 3 Dummy Variables?

• With 4 quarters, we need 4-1 = 3 dummy variables
• The intercept captures the baseline for the omitted quarter
• Each dummy variable represents the deviation from the baseline for its respective quarter

Example:

If we omit Q4 as the baseline:

• D1 = 1 for Q1, 0 otherwise
• D2 = 1 for Q2, 0 otherwise
• D3 = 1 for Q3, 0 otherwise
• Q4 is captured by the intercept when all dummies = 0

Using 4 dummy variables would create perfect multicollinearity with the intercept, making the model unidentifiable.