George Caloz & Frères, located in Grenchen, Switzerland, makes luxury custom watches in small lots. One of the company’s products, a platinum diving watch, goes through an etching process. The company has recorded etching costs as follows over the last six weeks:

George Caloz & Frères, located in Grenchen, Switzerland, makes luxury custom watches in small lots. One of the company’s products, a platinum diving watch, goes through an etching process. The company has recorded etching costs as follows over the last six weeks:

Week	Units			Total Etching Cost
1		9			$	25
2		6			$	20
3		11			$	30
4		5			$	21
5		7			$	21
6		14			$	32
		52			$	149

For planning purposes, management would like to know the variable etching cost per unit and the total fixed etching cost per week.

Required:

1. Prepare a scattergraph plot. (Plot etching costs on the vertical axis and units on the horizontal axis.)

2-a. Using the least-squares regression method, estimate the variable etching cost per unit and the total fixed etching cost per week.

2-b. Express these estimates in the form Y = a + bX.

Explanation

2-a. & 2-b.

Note that the R² is approximately 0.93, which means that 93% of the variation in etching costs is explained by the number of units etched. This is a very high R² which indicates a very good fit.

The regression equation, in the form Y = a + bX, is as follows (where a is rounded to nearest dollar and b is rounded to the nearest cent):

Y = $12.19 + $1.46X

3. If the company processes eighteen units next week, what would be the expected total etching cost?
 

3.

Total expected etching cost if 18 units are processed:

Variable cost: 18 units × $1.46 per unit	$	26.28
Fixed cost		12.19
Total expected cost	$	38.47

 
Thanks