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. Year Cost/Unit ($) Year Cost/Unit ($) 1 20.00 5 2 24.50 6 3 28.20 7 4 27.50 8 26.60 30.00 31.00 36.00 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.

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How do I construct a time series plot and determine pattern of data? What formula do I use for regression analysis to find the parameters for the line that minimizes MSE for this time series?
### Manufacturing Cost Analysis

The president of a 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 per Unit Data

| Year | Cost/Unit ($) | Year | Cost/Unit ($) |
|------|---------------|------|---------------|
| 1    | 20.00         | 5    | 26.60         |
| 2    | 24.50         | 6    | 30.00         |
| 3    | 28.20         | 7    | 31.00         |
| 4    | 27.50         | 8    | 36.00         |

#### Analysis Tasks

a) **Construct a time series plot:** 
   - What type of pattern exists in the data?

b) **Use regression analysis:** 
   - Find the parameters for the line that minimizes the Mean Squared Error (MSE) for this time series.

c) **Determine the average cost increase:**
   - What is the average cost increase that the firm has been realizing per year?

d) **Estimate future costs:**
   - Compute an estimate of the cost per unit for next year. 

The data presented shows a general upward trend in cost per unit over the years, indicating a rise in manufacturing expenses. Further analysis may reveal specific patterns or influencing factors.
Transcribed Image Text:### Manufacturing Cost Analysis The president of a 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 per Unit Data | Year | Cost/Unit ($) | Year | Cost/Unit ($) | |------|---------------|------|---------------| | 1 | 20.00 | 5 | 26.60 | | 2 | 24.50 | 6 | 30.00 | | 3 | 28.20 | 7 | 31.00 | | 4 | 27.50 | 8 | 36.00 | #### Analysis Tasks a) **Construct a time series plot:** - What type of pattern exists in the data? b) **Use regression analysis:** - Find the parameters for the line that minimizes the Mean Squared Error (MSE) for this time series. c) **Determine the average cost increase:** - What is the average cost increase that the firm has been realizing per year? d) **Estimate future costs:** - Compute an estimate of the cost per unit for next year. The data presented shows a general upward trend in cost per unit over the years, indicating a rise in manufacturing expenses. Further analysis may reveal specific patterns or influencing factors.
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