1) Consider the following time series data. Week 1 3 Value 18 16 2 13 Year 1 2 3 4 4 11 a) Construct a time series plot. What type of pattern exist in the data? b) Develop a three-week moving average for this time series. Compute MSE and forecast for week 7. c) Use a = 0.2 to compute the exponential smoothing values for the time series. Compute MSE and forecast for week 7. d) Compare the three-week moving average forecast with the exponential smoothing forecast using a = 0.2. which appears to provide better forecast based on MSE? Explain. e) Use trial and error to find a value of the exponential smoothing coefficient a that results in a smaller MSE than what you calculated for a = 0.2. 5 17 2) The president of small manufacturing firm is concerned about the continual increase in manufacturing costs over the past several years. The following figures provide a time series of the cost per unit for the firm's leading product over the past eight years. Cost/Unit ($) Cost/Unit ($) 26.60 20.00 24.50 30.00 31.00 36.00 28.20 27.50 6 14 Year 5 6 7 8 a) Construct a time series plot. What type of pattern exists in the data? b) Use regression analysis to find the parameters for the line that minimizes MSE for this time series. c) What is the average cost increase that the firm has been realizing per year? d) Compute an estimate of the cost/unit for next year.
1) Consider the following time series data. Week 1 3 Value 18 16 2 13 Year 1 2 3 4 4 11 a) Construct a time series plot. What type of pattern exist in the data? b) Develop a three-week moving average for this time series. Compute MSE and forecast for week 7. c) Use a = 0.2 to compute the exponential smoothing values for the time series. Compute MSE and forecast for week 7. d) Compare the three-week moving average forecast with the exponential smoothing forecast using a = 0.2. which appears to provide better forecast based on MSE? Explain. e) Use trial and error to find a value of the exponential smoothing coefficient a that results in a smaller MSE than what you calculated for a = 0.2. 5 17 2) The president of small manufacturing firm is concerned about the continual increase in manufacturing costs over the past several years. The following figures provide a time series of the cost per unit for the firm's leading product over the past eight years. Cost/Unit ($) Cost/Unit ($) 26.60 20.00 24.50 30.00 31.00 36.00 28.20 27.50 6 14 Year 5 6 7 8 a) Construct a time series plot. What type of pattern exists in the data? b) Use regression analysis to find the parameters for the line that minimizes MSE for this time series. c) What is the average cost increase that the firm has been realizing per year? d) Compute an estimate of the cost/unit for next year.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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How do I construct a time series plot and determine type of pattern in data?
Transcribed Image Text:## Time Series and Cost Analysis
### Problem 1: Time Series Data Analysis
#### Given Data:
- **Weeks**: 1, 2, 3, 4, 5, 6
- **Values**: 18, 13, 16, 11, 17, 14
#### Tasks:
a) **Construct a Time Series Plot**: Identify any patterns such as trends, seasonal effects, or randomness.
b) **Three-Week Moving Average**:
- Calculate the moving average for the series.
- Compute Mean Squared Error (MSE) and forecast for week 7.
c) **Exponential Smoothing with α = 0.2**:
- Compute smoothed values.
- Calculate MSE and forecast for week 7.
d) **Comparison of Forecasts**:
- Compare the accuracy of three-week moving average versus exponential smoothing.
- Determine which method gives a better forecast based on MSE.
e) **Optimize α for Exponential Smoothing**:
- Use trial and error to find a value of α that reduces the MSE compared to α = 0.2.
### Problem 2: Manufacturing Cost Analysis
#### Cost Data:
| Year | Cost/Unit ($) |
|------|---------------|
| 1 | 20.00 |
| 2 | 24.50 |
| 3 | 28.20 |
| 4 | 27.50 |
| 5 | 26.60 |
| 6 | 30.00 |
| 7 | 31.00 |
| 8 | 36.00 |
#### Tasks:
a) **Construct a Time Series Plot**: Identify patterns such as upward or downward trends in cost/unit over time.
b) **Regression Analysis**:
- Find parameters for the trend line minimizing MSE.
c) **Average Cost Increase**:
- Calculate the average annual increase in cost.
d) **Estimate Future Costs**:
- Predict the cost per unit for the next year based on the trend.
This analysis involves constructing plots and conducting statistical calculations to understand trends and make forecasts.
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