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.