To calculate the simple exponential smoothing forecast for the 3rd week using the data provided and a smoothing constant (α) of 0.3, we will first need to establish our initial forecast for week 1.
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Initial Forecast (F1) for Week 1:
- We can use the actual value of the first week as the initial forecast:
- \( F_1 = 8.00 \)
- We can use the actual value of the first week as the initial forecast:
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Forecast for Week 2 (F2):
- Using the formula for exponential smoothing: \[ F_t = \alpha \times A_{t-1} + (1 - \alpha) \times F_{t-1} \]
- Where \( A_{t-1} \) is the actual value from the previous week, \( F_{t-1} \) is the forecast for the previous week, and \( \alpha = 0.3 \).
- Therefore, \[ F_2 = 0.3 \times A_1 + 0.7 \times F_1 \]
- Substituting the values: \[ F_2 = 0.3 \times 8.00 + 0.7 \times 8.00 = 8.00 \]
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Forecast for Week 3 (F3):
- Now we calculate the forecast for week 3: \[ F_3 = 0.3 \times A_2 + 0.7 \times F_2 \]
- Where \( A_2 = 2.00 \): \[ F_3 = 0.3 \times 2.00 + 0.7 \times 8.00 \]
- Calculating this: \[ F_3 = 0.6 + 5.6 = 6.2 \]
Thus, the simple exponential smoothing forecast for the 3rd week is:
6.2