Final answer:
Naomi used a smoothing constant of 0.333 for her exponential smoothing forecast, placing approximately 33.3% of the weight on the most recent actual sales value.
Step-by-step explanation:
The student's question involves determining the smoothing constant α used in exponential smoothing for forecasting sales. Exponential smoothing is a rule of thumb technique for smoothing time series data, particularly for recursively applying a type of infinite impulse response filter with exponential decay. It's widely used in business and economics for forecasting purposes. In this case, Naomi's forecast for last month was 42 and actual sales were 51, and her forecast for this month is 45.
To find the smoothing constant α used by Naomi, we need to use the formula for exponential smoothing:
Ft+1 = αAt + (1 - α)Ft
Where:
- Ft+1 is the forecast for the next period
- α is the smoothing constant (which we are trying to find)
- At is the actual sales in the current period
- Ft is the forecast for the current period
Given that the forecast for this month (Ft+1) is 45, the actual sales from last month (At) were 51, and the forecast for last month (Ft) was 42, we can rearrange the formula to solve for α:
45 = α(51) + (1 - α)(42)
Simplifying, we get:
45 = 42 + 9α
3 = 9α
α = 3/9
α = 0.333
Therefore, the smoothing constant α that Naomi used is 0.333. This means that approximately 33.3% of the weight was placed on the most recent actual value when making the forecast.