Least-Squares Regression

Serenity Living manufactures gas fireplaces for home use. Each unit produced goes through a complex quality control process. The company has observed quality control costs as follows over the past six weeks:

Total
Units Quality Control
Week Produced Costs

1 24 $540
2 15 $400
3 30 $620
4 12 $380
5 18 $480
6 27 $580

For planning purposes, the company's management wants to know the amount of variable quality control costs per unit and the total fixed quality control costs per week.

Required:

1. Using the least-squares regression method, estimate the variable and fixed elements of the quality control cost.

2. Express the cost data in (1) above in the form Y = a + bX.

3. If the company produces 20 gas fireplaces next week, what would be the expected total quality control costs?

4. Evaluate the economic plausibility of using units produced to predict total quality control costs.