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
19
23
29
38
25
29
35
22
25
29
Part 2 a) The forecast for weeks 2 through 10 using exponential smoothing with alpha = 0.60 and a week 1 initial forecast of 19.0 are (round your responses to two decimal places): Week 1 2 3 4 5 6 7 8 9 10 Demand 19 23 29 38 25 29 35 22 25 29 Forecast 19.0 19.00 21.40 25.96 33.18 28.27 28.71 32.48 26.19 25.48
Part 3 b) For the forecast developed using exponential smoothing (alpha = 0.60 and initial forecast 19.0), the MAD = 5.40 sales (round your response to two decimal places). Part 4 c) For the forecast developed using exponential smoothing (alpha = 0.60 and initial forecast 19.0), the tracking signal = enter your response here (round your response to two decimal places).
Solution
Let's walk through the process of finding the Tracking Signal step-by-step.
Formula for Tracking Signal:
Step 1: Compute the Forecast Errors
The forecast error for each week is:
Here’s the data from the question:
Week | Demand (Actual) | Forecast | Forecast Error |
---|---|---|---|
1 | 19 | 19.00 | 0.00 |
2 | 23 | 19.00 | 4.00 |
3 | 29 | 21.40 | 7.60 |
4 | 38 | 25.96 | 12.04 |
5 | 25 | 33.18 | -8.18 |
6 | 29 | 28.27 | 0.73 |
7 | 35 | 28.71 | 6.29 |
8 | 22 | 32.48 | -10.48 |
9 | 25 | 26.19 | -1.19 |
10 | 29 | 25.48 | 3.52 |
Step 2: Compute the Cumulative Forecast Error (CFE)
Adding all the forecast errors:
Step 3: Use the Given MAD
The Mean Absolute Deviation (MAD) is provided as:
Step 4: Calculate the Tracking Signal
Final Answer:
The Tracking Signal is:
Would you like further explanations or help with any part of this calculation?
Here are 5 related questions:
- How does changing the value of alpha affect the exponential smoothing forecast?
- What is the significance of a tracking signal outside the range [-4, 4]?
- How can you adjust your forecasting model if the tracking signal indicates bias?
- How do MAD and MSE compare in measuring forecast accuracy?
- What other forecasting techniques could be used instead of exponential smoothing?
Tip: A positive tracking signal suggests the forecast underestimates demand, while a negative signal indicates overestimation.
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Math Problem Analysis
Mathematical Concepts
Forecasting
Exponential Smoothing
Tracking Signal
Mean Absolute Deviation (MAD)
Formulas
Forecast_t = Alpha * Demand_(t-1) + (1 - Alpha) * Forecast_(t-1)
Tracking Signal = Cumulative Forecast Error (CFE) / MAD
Forecast Error = Actual Demand - Forecast
Theorems
-
Suitable Grade Level
Undergraduate Business/Statistics
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