Math Problem Statement
Sales of tablet computers at Marika Gonzalez's electronics store in Washington, D.C., over the past 10 weeks are shown in the table below:
Week
1
2
3
4
5
6
7
8
9
10
Demand
21
20
28
37
24
29
37
20
25
28
Part 2 a) The forecast for weeks 2 through 10 using exponential smoothing with alpha = 0.60 and a week 1 initial forecast of 21.0 are (round your responses to two decimal places):
Solution
The forecast for weeks 2 through 10 using exponential smoothing with and an initial forecast of 21.0 is as follows:
- Week 2: 21.00
- Week 3: 20.40
- Week 4: 24.96
- Week 5: 32.18
- Week 6: 27.27
- Week 7: 28.31
- Week 8: 33.52
- Week 9: 25.41
- Week 10: 25.16
Would you like more details or explanations on any part of the calculation?
Here are 5 related questions to expand the discussion:
- How does the value of affect the forecasts in exponential smoothing?
- What would the forecasts look like if were set to 0.30?
- How does exponential smoothing compare to moving averages for forecasting?
- Can you derive the Mean Squared Error (MSE) of these forecasts?
- How can you adjust forecasts if there is a sudden trend change in demand?
Tip: A higher value gives more weight to recent demand, making the forecast more responsive to recent changes.
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Math Problem Analysis
Mathematical Concepts
Exponential Smoothing
Forecasting
Time Series Analysis
Formulas
Exponential Smoothing Formula: F_t = α * D_{t-1} + (1 - α) * F_{t-1}
Theorems
-
Suitable Grade Level
College/University Level (Statistics or Business)
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