A time series regression equation measuring the number of surfboards sold by a surfboard manufacturing company in Australia is given below: Y = 35 + 4Q₁ + 0.5Q₃ + 8Q₄ + 3t With t in quarters and the origin is December 2010 and Q₁ is the indicator variable for March, Q₃ is the indicator variable for September and Q₄ is the indicator variable for December. Which of the following statements is correct? A)There is a mistake with this regression model because all the coefficients of the indicator variables are positive. B)There is no indicator variable for the June quarter in this model because there is no seasonal effect in June due to winter in Australia. C)There is a mistake with this model because the indicator variable for the June quarter has been left out. D)There is no indicator variable for the June quarter in this model because we need one less indicator variable than number of categories to use indicator variables with regression for a time series.

Question

Quizplus · Accepted Answer

In regression analysis with categorical variables, one category is typically left out as the baseline, and indicator variables are created for the other categories. This approach, known as the "dummy variable trap," avoids multicollinearity by ensuring that the indicator variables are not perfectly multicollinear. In this case, with four quarters in a year, three indicator variables are used, one for each quarter except the baseline (June), to avoid perfect multicollinearity and allow the model to estimate the effect of the other quarters relative to the baseline.

A Time Series Regression Equation Measuring the Number of Surfboards