Question:
An electric car manufacturer underestimated the January sales of car by 20 units, while the actual sales was 120 units.
If the manufacturer uses exponential smoothing with a smoothing constant of $\alpha = 0.2$, then the sales forecast for the month of February of the same year is ________________ units (in integer).
An electric car manufacturer underestimated the January sales of car by 20 units, while the actual sales was 120 units.
If the manufacturer uses exponential smoothing with a smoothing constant of $\alpha = 0.2$, then the sales forecast for the month of February of the same year is ________________ units (in integer).
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Exponential smoothing corrects forecast errors slowly when $\alpha$ is small and quickly when $\alpha$ is large.
Updated On: Dec 1, 2025
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Correct Answer: 104
Solution and Explanation
Exponential smoothing uses the formula:
\[ F_{t+1} = F_t + \alpha (A_t - F_t) \] The manufacturer underestimated sales by 20 units. Therefore, forecast for January was:
\[ F_{Jan} = 120 - 20 = 100 \] Actual January sales:
\[ A_{Jan} = 120 \] Now compute forecast for February:
\[ F_{Feb} = 100 + 0.2(120 - 100) \] \[ F_{Feb} = 100 + 4 = 104 \] Thus, the forecasted sales for February is:
\[ \boxed{104} \]
\[ F_{t+1} = F_t + \alpha (A_t - F_t) \] The manufacturer underestimated sales by 20 units. Therefore, forecast for January was:
\[ F_{Jan} = 120 - 20 = 100 \] Actual January sales:
\[ A_{Jan} = 120 \] Now compute forecast for February:
\[ F_{Feb} = 100 + 0.2(120 - 100) \] \[ F_{Feb} = 100 + 4 = 104 \] Thus, the forecasted sales for February is:
\[ \boxed{104} \]
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