To calculate the simple exponential smoothing forecast for the 4th week with a smoothing constant (α) of 0.4, we can follow these steps:
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The initial forecast for week 1 can be set as the actual value of week 1: \[ F_1 = Y_1 = 6.00 \]
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For subsequent weeks, the forecast can be calculated using the formula: \[ F_t = \alpha Y_{t-1} + (1 - \alpha) F_{t-1} \] where:
- \( F_t \) is the forecast for the current week
- \( Y_{t-1} \) is the actual value from the previous week
- \( F_{t-1} \) is the forecast from the previous week
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Now, we can calculate the forecasts step by step:
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For Week 2: \[ F_2 = 0.4 \times Y_1 + (1 - 0.4) \times F_1 \] \[ F_2 = 0.4 \times 6.00 + 0.6 \times 6.00 = 6.00 \]
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For Week 3: \[ F_3 = 0.4 \times Y_2 + (1 - 0.4) \times F_2 \] \[ F_3 = 0.4 \times 4.00 + 0.6 \times 6.00 \] \[ F_3 = 1.60 + 3.60 = 5.20 \]
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For Week 4: \[ F_4 = 0.4 \times Y_3 + (1 - 0.4) \times F_3 \] \[ F_4 = 0.4 \times 7.00 + 0.6 \times 5.20 \] \[ F_4 = 2.80 + 3.12 = 5.92 \]
Finally, rounding to 1 decimal place, the forecast for the 4th week is: \[ \text{Forecast for week 4} = 5.9 \]
So, the answer is: 5.9