Answer: 40.27

## Explanation This is a seasonal dummy model with quarterly data. The model includes: - $\beta_0$: Intercept term - $\gamma_j$: Seasonal coefficients for quarters (with s-1 = 3 dummies, meaning quarter 4 is the base/reference quarter) - $D_{jt}$: Dummy variables for quarters 1, 2, and 3 **Step 1: Forecast for Q2 2020** For Q2, the dummy variables are: - $D_{1t} = 0$ (not Q1) - $D_{2t} = 1$ (Q2) - $D_{3t} = 0$ (not Q3) Forecast: $E(\hat{Y}_{Q_2}) = \beta_0 + \gamma_1 \times 0 + \gamma_2 \times 1 + \gamma_3 \times 0$ $= -10.42 + 0 \times 6.25 + 1 \times 50.52 + 0 \times 10.25$ $= -10.42 + 50.52 = 40.10$ **Step 2: Forecast for Q3 2020** For Q3, the dummy variables are: - $D_{1t} = 0$ (not Q1) - $D_{2t} = 0$ (not Q2) - $D_{3t} = 1$ (Q3) Forecast: $E(\hat{Y}_{Q_3}) = \beta_0 + \gamma_1 \times 0 + \gamma_2 \times 0 + \gamma_3 \times 1$ $= -10.42 + 0 \times 6.25 + 0 \times 50.52 + 1 \times 10.25$ $= -10.42 + 10.25 = -0.17$ **Step 3: Calculate the difference** $Q_2 - Q_3 = 40.10 - (-0.17) = 40.10 + 0.17 = 40.27$ Therefore, the difference between the forecasted growth rates for Q2 and Q3 2020 is **40.27**, which corresponds to option C.

Author: Nikitesh Somanthe