Question

Furlan Printing Corp., a book printer, has provided the following data: Titles Printed Press Setup Cost May 26 $ 3,385 June 27 $ 3,418 July 39 $ 3,903 August 21 $ 3,211 September 37 $ 3,822 October 35 $ 3,766 November 36 $ 3,768 December 32 $ 3,380 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.) Required: Estimate the variable cost per title printed and the fixed cost per month using the least-squares regression method. (Round the "Variable cost" to 2 decimal places and the "Fixed cost" to the nearest dollar amount.)

Furlan Printing Corp., a book printer, has provided the following data: Titles Printed 26 27 Press Setup Cost $3,385 $3,418 $3,903 $3,211 $ 3,822 $ 3,766 $ 3,768 $3,380 May June July August September October November December 21 35 32 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.) Required: Estimate the variable cost per title printed and the fixed cost per month using the least-squares regression method. (Round the "Variable cost" to 2 decimal places and the "Fixed cost" to the nearest dollar amount.) Variable costſ Fixed cost $ $ 38.44 per title printed 2,386 per month

Answer 1

The general for the linear regression equation is given as

Y = a + b X

where a = intercept

b = slope

Y = dependent variable

X = independent variable

In this example, the press setup cost is considered as the dependent variable and titles printed as the independent variable.

The value of the intercept a is the fixed cost per month

The value of the slope b is the variable cost per title.

The slope b is calculated using the following equation

b = ΣΧΥ – ηXY ΣΧ2 – ηX2

X² 26 Titles printed (X) Press Setup cost (Y) $3,385 27 $3,418 $3,903 21 $3.211 $3,822 $3,766 36 $3,768 $3,380 X = 253 Y = $28,653 XY $88,010 676 $92,286 729 $152,217 1521 $67,431 441 $141,414 1369 $131.810 1225 $135.648 1296 $108, 160 1024 XY = $916,976 5X2 = 8281

ř = 253 = 31.625

$28.653 - = 3581.625

b= 916976 -8 X 31.625 x 3582 8281 - 8 x 31.6252

b = 38.68

a= 7-bxX

a = 3581.625 - 38.68 $\times$ 31.625

a = 2358.48

Variable cost Fixed cost $38.68 Per tile printed $2,359 Per month