Answer: 14,400

The model is given as: $$y_t = 0.2 \times \text{Time}_t + 10.5 + 3.0 \times D_{2t} + 5.4 \times D_{3t} + 0.7 \times D_{4t}$$ Since $y_{(T+1)}$ refers to June 2019, September 2020 corresponds to $y_{(T+16)}$ (16 periods later). September falls under the fourth quarter dummy $D_{4t}$ (since $D_4$ = 1 for Q4, and 0 otherwise). Plugging into the model: $$y_{(T+16)} = 0.2 \times 16 + 10.5 + 0.7 \times 1$$ $$= 3.2 + 10.5 + 0.7$$ $$= 14.4$$ Thus, the model predicts 14,400 housing starts in September 2020.

Author: Nikitesh Somanthe