Question

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 Etching Cost

1 10 $ 27

2 7 $20

3 12 $31

4 6 $20

5 8 $24

6 11 $30

Total 54 $ 152

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

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

Variable etching Cost ____

Fixed Etching cost _____

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

Answer 1

2a.

x	y	xy	x^2
10	27	270	100
7	20	140	49
12	31	372	144
6	20	120	36
8	24	192	64
11	30	330	121
54	152	1424	514

Unit Variable Cost (b) =	nΣxy − (Σx)(Σy)
nΣx2 − (Σx)2
Variable cost =	(6*1424) - (54*152)	=   2
	(6*514) - (54^2)
Total Fixed Cost (a) =	Σy − bΣx / n
	152 -( 2*54) / 6	= 7.33
2b.
Y = 7.33+ 2x