To calculate the simple exponential smoothing forecast for the 3rd week using a smoothing constant (\(\alpha\)) of 0.3, we can use the formula:
\[ F_t = \alpha \cdot Y_{t-1} + (1 - \alpha) \cdot F_{t-1} \]
where:
- \(F_t\) is the forecast for time period \(t\),
- \(Y_{t-1}\) is the actual data point from the previous period,
- \(F_{t-1}\) is the forecast from the previous period.
Since we need to compute the forecast for the 3rd week, we first need to establish an initial forecast for the first week. A common approach is to set the initial forecast equal to the first actual value or an average of the initial values.
Steps to Calculate Forecasts:
-
Set Initial Forecast:
- For Week 1, we can set \(F_1 = Y_1 = 4.00\)
-
Calculate Forecast for Week 2: \[ F_2 = \alpha \cdot Y_{1} + (1 - \alpha) \cdot F_{1} \] \[ F_2 = 0.3 \cdot 4 + 0.7 \cdot 4 = 4.00 \]
-
Calculate Forecast for Week 3: \[ F_3 = \alpha \cdot Y_{2} + (1 - \alpha) \cdot F_{2} \] \[ F_3 = 0.3 \cdot 4 + 0.7 \cdot 4 = 4.00 \]
Conclusion:
The forecast for Week 3 (\(F_3\)) is 4.00.
Hence, the simple exponential smoothing forecast for the 3rd week is 4.00.