Deck 16: Least-Squares Regression Computations

Question 1

Delreal Inc.'s inspection costs are listed below: Management believes that inspection cost is a mixed cost that depends on the number of units produced.Using the least-squares regression method,the estimates of the variable and fixed components of inspection cost would be closest to:

A)$20.27 per unit plus $5,905 per month
B)$44.44 per unit plus $10,867 per month
C)$20.68 per unit plus $5,807 per month
D)$20.57 per unit plus $5,837 per month

Answer 1

D
Explanation: The solution using Microsoft Excel functions is:
slope = $20.57 per unit
intercept = $5,837 per month
The solution using the formulas in the text is:
n = 8
sumX = 1,956
sumY = $86,933
sumXY = $21,334,856
sumX2 = 482,118
b = [n(sumXY) - (sumX)(sumY))]/[n(sumX^2) - (sumX)^2]
= [8($21,334,856) - (1,956)( $86,933))]/[8(482,118) - (1,956)^2]
= $20.57
a = [(sumY) - b(sumX)]/n
= [($86,933) - $20.57(1,956)]/8
= $5,837
Any difference in the solutions is due to rounding errors when the formulas are use

Question 2

Magnano Inc.'s inspection costs are listed below: Management believes that inspection cost is a mixed cost that depends on units produced.
Using the least-squares regression method,the estimate of the variable component of inspection cost per unit produced is closest to:

A)$3.51
B)$3.49
C)$4.93
D)$3.54

Answer 2

D
Explanation: The solution using Microsoft Excel functions is:
slope = $3.54 per unit
intercept = $1,290 per month
The solution using the formulas in the text is:
n = 8
sumX = 7,446
sumY = $36,680
sumXY = $34,166,530
sumX2 = 6,937,884
b = [n(sumXY) - (sumX)(sumY))]/[n(sumX^2) - (sumX)^2]
= [8($34,166,530) - (7,446)( $36,680))]/[8(6,937,884) - (7,446)^2]
= $3.54
a = [(sumY) - b(sumX)]/n
= [($36,680) - $3.54(7,446)]/8
= $1,290
Any difference in the solutions is due to rounding errors when the formulas are use

Question 3

Recent maintenance costs of Pavelko Corporation are listed below: Management believes that maintenance cost is a mixed cost that depends on machine-hours.
Using the least-squares regression method,the estimate of the variable component of maintenance cost per machine-hour is closest to:

A)$3.26
B)$13.45
C)$2.00
D)$2.96

Answer 3

D
Explanation: The solution using Microsoft Excel functions is:
slope = $2.96 per machine-hour
intercept = $6,199 per month
The solution using the formulas in the text is:
n = 8
sumX = 4,729
sumY = $63,599
sumXY = $37,616,495
sumX2 = 2,802,701
b = [n(sumXY) - (sumX)(sumY))]/[n(sumX^2) - (sumX)^2]
= [8($37,616,495) - (4,729)( $63,599))]/[8(2,802,701) - (4,729)^2]
= $2.96
a = [(sumY) - b(sumX)]/n
= [($63,599) - $2.96(4,729)]/8
= $6,199
Any difference in the solutions is due to rounding errors when the formulas are use

Question 4

Below are cost and activity data for a particular cost over the last four periods.Your boss has asked you to analyze this cost so that management will have a better understanding of how this cost changes in response to changes in activity. Required:
Using the least-squares regression method,estimate the cost formula for this cost.

Question 5

Your boss would like you to estimate the fixed and variable components of a particular cost.Actual data for this cost over four recent periods appear below. Using the least-squares regression method,what is the cost formula for this cost?

A)Y = $24.51 + $1.08X
B)Y = $10.33 + $1.92X
C)Y = $0.00 + $2.32X
D)Y = $15.80 + $1.70X

Question 6

Magnano Inc.'s inspection costs are listed below: Management believes that inspection cost is a mixed cost that depends on units produced.
Using the least-squares regression method,the estimate of the fixed component of inspection cost per month is closest to:

A)$4,400
B)$1,290
C)$4,585
D)$1,318

Question 7

The management of Smoots Corporation would like for you to analyze their repair costs,which are listed below: Management believes that repair cost is a mixed cost that depends on the number of machine-hours.Using the least-squares regression method,the estimates of the variable and fixed components of repair cost would be closest to:

A)$4.64 per machine-hour plus $34,603 per month
B)$2.09 per machine-hour plus $19,018 per month
C)$2.79 per machine-hour plus $13,787 per month
D)$2.00 per machine-hour plus $19,649 per month

Question 8

Mccatty Inc.maintains a call center to take orders,answer questions,and handle complaints.The costs of the call center for a number of recent months are listed below: Management believes that the cost of the call center is a mixed cost that depends on the number of calls taken.
Required:
Estimate the variable cost per call and fixed cost per month using the least-squares regression method.

Question 9

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

Question 10

The management of Archie Corporation would like to better understand the behavior of the company's warranty costs.Those costs are listed below for a number of recent months: Management believes that warranty cost is a mixed cost that depends on the number of product returns.
Required:
Estimate the variable cost per product return and the fixed cost per month using the least-squares regression method.

Question 11

Recent maintenance costs of Pavelko Corporation are listed below: Management believes that maintenance cost is a mixed cost that depends on machine-hours.
Using the least-squares regression method,the estimate of the fixed component of maintenance cost per month is closest to:

A)$7,826
B)$6,036
C)$7,950
D)$6,199

Question 12

Meleski Corporation's recent utility costs are listed below: Management believes that utility cost is a mixed cost that depends on machine-hours.
Using the least-squares regression method,the estimate of the variable component of utility cost per machine-hour is closest to:

A)$4.40
B)$4.79
C)$3.47
D)$3.37

Question 13

Meleski Corporation's recent utility costs are listed below: Management believes that utility cost is a mixed cost that depends on machine-hours.
Using the least-squares regression method,the estimate of the fixed component of utility cost per month is closest to:

A)$4,649
B)$5,028
C)$16,975
D)$16,850

Question 14

The R² (i.e. ,R-squared) indicates the proportion of a mixed cost that is variable.