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Answer: A trading-day variation variable for modeling trading volume throughout the year.
Perfect multicollinearity occurs when there is an exact linear relationship between independent variables. In option IV (a dummy variable for each season, plus an intercept), this creates the **dummy variable trap**. **Explanation:** - When you include dummy variables for all seasons (e.g., Q1, Q2, Q3, Q4) AND an intercept, the sum of all seasonal dummies equals 1 in every observation. - This means one dummy variable is perfectly predictable from the others plus the intercept: Q4 = 1 - Q1 - Q2 - Q3 - This creates perfect multicollinearity because the variables are linearly dependent. **Why other options don't cause perfect multicollinearity:** - **I:** Only one seasonal dummy doesn't create multicollinearity - **II:** Easter dummy variable alone doesn't cause perfect multicollinearity - **III:** Trading-day variation variable alone doesn't cause perfect multicollinearity The correct answer is IV only, which corresponds to option C in the multiple choice format.
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Which of the following scenarios would produce a forecasting model that exhibits perfect multicollinearity? A model that includes:
A
Only one seasonal dummy that is equal to 1.
B
A holiday variation variable that accounts for an "Easter dummy variable."
C
A trading-day variation variable for modeling trading volume throughout the year.
D
A dummy variable for each season, plus an intercept.
E
II only.
F
I and III.