Answer: 30

## Explanation The model is given as: $$ y_t = 0.2 \times \text{Time}_t + 10.5 + 3.0 \times D_{2t} + 2.1 \times D_{3t} + 2.8 \times D_{4t} $$ Since we have three dummies and an intercept, quarterly seasonality is reflected by the intercept (10.5) plus the three seasonal dummy variables ($D_2$, $D_3$, and $D_4$). If $y_{(T+1)} = \text{May 2019}$, then: - April 2020 = $y_{(T+12)}$ - July 2020 = $y_{(T+15)}$ Note that April falls under $D_{(2t)}$ (Spring season), while July falls under $D_{(3t)}$ (Summer season). **Calculation for April 2020 ($y_{(T+12)}$):** - Time component: $0.2 \times 12 = 2.4$ - Intercept: $10.5$ - Spring dummy: $3.0 \times 1 = 3.0$ - Total: $2.4 + 10.5 + 3.0 = 15.9$ **Calculation for July 2020 ($y_{(T+15)}$):** - Time component: $0.2 \times 15 = 3.0$ - Intercept: $10.5$ - Summer dummy: $2.1 \times 1 = 2.1$ - Total: $3.0 + 10.5 + 2.1 = 15.6$ **Difference:** $$ y_{(T+12)} - y_{(T+15)} = 15.9 - 15.6 = 0.3 $$ Since the number of guests is given in hundreds, the actual difference is: $$0.3 \times 100 = 30 \text{ guests}$$ Thus, the model predicts 1,590 guests in April and 1,560 guests in July, representing a difference of 30 guests.

Author: Tanishq Prabhu