Answer: 14

## Explanation The model is given as: $$y_t = 0.2 \times \text{Time}_t + 10.5 + 3.0 \times D_{2t} + 5.4 \times D_{3t} + 0.7 \times D_{4t}$$ ### Step 1: Determine the Time Period - The model starts in May 2019 - $y_{(T+1)}$ refers to June 2019 - We need to find September 2020 From June 2019 to September 2020: - June 2019 to May 2020 = 12 months - June 2020 to September 2020 = 4 months - Total = 16 months So September 2020 = $y_{(T+16)}$ ### Step 2: Identify the Seasonal Component From the seasonal table: - September falls under Fall season - Fall season uses dummy variable $D_{4t}$ Therefore, for September 2020: - $D_{2t} = 0$ (not Spring) - $D_{3t} = 0$ (not Summer) - $D_{4t} = 1$ (Fall season) ### Step 3: Calculate the Prediction $$y_{(T+16)} = 0.2 \times 16 + 10.5 + 3.0 \times 0 + 5.4 \times 0 + 0.7 \times 1$$ $$y_{(T+16)} = 3.2 + 10.5 + 0 + 0 + 0.7$$ $$y_{(T+16)} = 14.4$$ Since housing starts are given in thousands, the model predicts approximately **14** housing starts in September 2020. ### Key Points: - The intercept (10.5) represents the baseline for Winter season - Seasonal dummies add to this baseline for their respective seasons - The trend component (0.2 × Time) captures the linear growth over time

Author: Tanishq Prabhu