To calculate the simple exponential smoothing forecast for the 4th week using an alpha (\(\alpha\)) of 0.3, we can use the formula:
\[ F_t = \alpha \times Y_{t-1} + (1 - \alpha) \times F_{t-1} \]
Where:
- \(F_t\) is the forecast for the current period.
- \(Y_{t-1}\) is the actual value from the previous period.
- \(F_{t-1}\) is the forecast for the previous period.
To start, we need an initial forecast for Week 1. A common practice is to use the actual value of Week 1 as the initial forecast:
- Set \(F_1 = Y_1 = 6.00\).
Now, we will compute the forecasts for Week 2 and Week 3.
Forecast for Week 2:
\[
F_2 = \alpha \times Y_1 + (1 - \alpha) \times F_1
\]
\[
F_2 = 0.3 \times 6.00 + 0.7 \times 6.00
\]
\[
F_2 = 1.8 + 4.2 = 6.00
\]
Forecast for Week 3:
\[
F_3 = \alpha \times Y_2 + (1 - \alpha) \times F_2
\]
\[
F_3 = 0.3 \times 4.00 + 0.7 \times 6.00
\]
\[
F_3 = 1.2 + 4.2 = 5.40
\]
Forecast for Week 4:
\[
F_4 = \alpha \times Y_3 + (1 - \alpha) \times F_3
\]
\[
F_4 = 0.3 \times 2.00 + 0.7 \times 5.40
\]
\[
F_4 = 0.6 + 3.78 = 4.38
\]
The simple exponential smoothing forecast for the 4th week, where \(\alpha = 0.3\), is 4.38.