Question

Required Information 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 1 2 3 4 5 6 Units 5 7 10 5 16 17 60 Total Etching Cost $ 22 21 25 20 28 32 $ 148 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. 2-b. Express these estimates in the form Y = a + bx. Complete this question by entering your answers in the tabs below. Req 2A Reg 2B Using the least-squares regression method, estimate the variable etching cost per unit and the total fixed etching cost per week. (Round your answers to 2 decimal places.) Fixed etching cost per week Variable etching cost per unit

Answer 1

2-a) calculation of variable etching cost per unit and total fixed etching cost per week using least square regression method :

week	x (units)	y (total etching cost in $)	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
n = 6	$\sum$x = 60	$\sum$y = 148	$\sum$x2 = 744	$\sum$xy = 1599

normal equations are :

$\sum$y = na + b$\sum$x

$\sum$xy = a$\sum$x + b$\sum$x²

^{putting the values in normal equations :}

^{148 = 6a + 60 b (equation 1)}

^{1599 = 60a + 744b (equation 2)}

^{10 multiply in equation 1 and we get equation 3) as under:}

^{148 x 10 = 6a x 10 + 60b x 10}

^{1480 = 60a + 600b (equation 3)}

^{equation 3 is subtracted from equation 2 and we get as under :}

^{1599 = 60a + 744b (equation 2)}

^{-(1480 = 60a + 600b) (equation 3)}

^{1599-1480 = (60a -60a) + (744b-600b)}

^{119 = 0 + 144b}

^{b = 119/144 = 0.8263 or 0.83}

^{variable cost per unit = $0.83}

^{put the value in equation 1 as under :}

^{148 = 6a + 60 b}

^{148 = 6a + 60 bx 0.83}

^{148 = 6a + 49.8}

^{148-49.8 = 6a}

^{a = 98.2/6 = 16.3666 or 16.37}

^{fixed cost = $16.37}

2-b) expression of above estimates in the form of y = a +bx

y = $16.37 + $0.83 x

3) if the company processes 14 units (x = 14) next week, expected total etching cost :

y = a + bx

y = $16.37 + $0.83 x 14

y = $16.37 + $11.62 = $27.99

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