Question

Stamp Printing Corp., a book printer, has provided the following data:

	Titles Printed	Press Setup Cost
February	39	$2,197
March	40	$2,218
April	36	$2,134
May	31	$2,044
June	48	$2,424
July	47	$2,377
August	29	$1,997
September	45	$2,353

Management believes that the press setup cost is a mixed cost that depends on the number of titles printed. (A specific book that is to be printed is called a "title". Typically, thousands of copies will be printed of each title. Specific steps must be taken to setup the presses for printing each title-for example, changing the printing plates. The costs of these steps are the press setup costs.)

On the basis of the above data, you are required to do the following:

• Estimate the variable cost per title printed and the fixed cost per month using the least-squares regression method.

Answer 1

Month	x(Titles printed)	y(Press setup cost)	x2	xy
Feb	39	$2,197	$1,521	$85,683
March	40	$2,218	$1,600	$88,720
April	36	$2,134	$1,296	$76,824
May	31	$2,044	$961	$63,364
June	48	$2,424	$2,304	$1,16,352
July	47	$2,377	$2,209	$1,11,719
August	29	$1,997	$841	$57,913
September	45	$2,353	$2,025	$1,05,885

315 $17,744 $12,757 $7,06,460

We have, n(no. of months) =8

x = 315

y = $17,744

  x² = $12,757

  xy = $7,06,460

Variable cost per title(b) = nxy - ( x ) (y)

nx² -  x²  

b =8 *7,06,460 - 315*17,744

8*12,757 - 12,757

=56,51,680 - 55,89,360

1,02,056 - 12,757   

= 62320   

89299

=0.6978

Total fixed cost (a) = y - bx = 17,744 - 0.6978*315 = 17,744 - 219.807 =17,524.193 =2190.52

n 8 8 8

Fixed cost per month = 2190.52 = 182.54

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