Question

Exercise 5A-5 (Algo) Least-Squares Regression [LO5-11]

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		5			$	22
2		7				21
3		10				25
4		5				20
5		16				28
6		17				32
		60			$	148

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

Exercise 5A-5 Part 2 (Algo)

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

Fixed etching cost per week
Variable etching cost per unit

1-b.

Express these estimates in the form Y = a + bX. (Round your answers to 2 decimal places.)

Y =

+

X

2c.  If the company processes fourteen units next week, what would be the expected total etching cost? (Round your intermediate calculations and final answer to 2 decimal places.)

Expected total etching cost

Answer 1

1-a.

Week	X (units)	Y ($)	X²	XY
1	5	22	25	110
2	7	21	49	147
3	10	25	100	250
4	5	20	25	100
5	16	28	256	448
6	17	32	289	544
	60	148	744	1599

Variable cost per unit =

(6 * 1599) - (60 * 148) ÷ (6 * 744) - 60²

= (9594 - 8880) ÷ (4464 - 3600)

= 714 ÷ 864

= $ 0.826

Fixed cost = 148 - ( 0.826 × 60) /6

= 98.44 /6

= $16.40

1.b. Y = a + bx

Y = 98.44 + 0.82x

2. C

If the company produces 14 units then the expected total etching cost will be

98.44 + 0.82 × 14

= 109.92