Deck 5: Least-Squares Regression Computations

Question 1

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

Answer 1

Y = $15.80 + $1.70X

Question 2

CPE for CPAs,Inc. ,provides continuing professional education for certified public accountants.The company is relatively new and management is seeking information regarding the company's cost structure.The following information has been gathered for the first six months of the current year:
Required:
a.Using the high-low method,estimate the variable cost per seminar and the total fixed cost per month.
b.Using the least-squares regression method,estimate the variable cost per seminar and the total fixed cost per month.

Answer 2

a.High-Low Method
Variable cost = Change in cost ÷ Change in activity
Variable cost = $6,600 ÷ 8 seminars = $825 per seminar
Fixed cost = Total cost - Variable cost
Fixed cost = $21,800 - (16 seminars × $825 per seminar)= $8,600
Y = $8,600 + $825X
b.Least-squares regression method
Using Microsoft Excel functions,the estimates are:
Variable cost per seminar = Slope = $9,000
Total fixed cost per month = Intercept = $800
Y = $9,000 + $800X

Question 3

Magnano Inc.'s inspection costs are listed below:
Management believes that inspection cost is a mixed cost that depends on units produced.
$\begin{array}{c}\begin{array}{lll}\\ \text {February...............}\\ \text {March...................}\\ \text {April.....................}\\ \text {May......................}\\ \text {June.....................}\\ \text {July......................}\\ \text {August.................}\\ \text {September............}\end{array}\begin{array}{cc}\text { Units Produced } & \text { Inspection Costs } \\933 & \$ 4,592 \\945 & \$ 4,619 \\959 & \$ 4,692 \\922 & \$ 4,542 \\950 & \$ 4,669 \\889 & \$ 4,443 \\970 & \$ 4,723 \\878 & \$ 4,400\end{array}\end{array}$


-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 3

$3.54

Question 4

Recent maintenance costs of Pavelko Corporation are listed below:
Management believes that maintenance cost is a mixed cost that depends on machine-hours.
$\begin{array}{c}\begin{array}{lll}\\ \text {March..............}\\ \text {April................}\\ \text {May.................}\\ \text {June................}\\ \text {July................}\\ \text {August............}\\ \text {September......}\\ \text {October..........}\end{array}\begin{array}{cc}\text { Machine-Hours } & \text { Maintenance Costs } \\620 & \$ 8,027 \\577 & \$ 7,904 \\571 & \$ 7,897 \\616 & \$ 8,017 \\549 & \$ 7,826 \\552 & \$ 7,832 \\623 & \$ 8,067 \\621 & \$ 8,029 \end{array}\end{array}$


-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

Question 5

Donner Company would like to estimate the variable and fixed components of its maintenance costs and has compiled the following data for the last five months of operations.
$\begin{array}{lcc}&\text { Labor Hours } & \text { Maintenance Cost }\\ \text { January ....... } & 160 & \$ 617 \\\text { February ...... } & 130 & \$ 553 \\\text { March ........ } & 180 & \$ 596 \\\text { April......... } & 190 & \$ 623 \\\text { May ........... } & 110 & \$ 532\end{array}$

-Using the high-low method of analysis,the estimated total fixed cost per month for maintenance is closest to:

A)$440
B)$407
C)$470
D)$0

Question 6

Donner Company would like to estimate the variable and fixed components of its maintenance costs and has compiled the following data for the last five months of operations.
$\begin{array}{lcc}&\text { Labor Hours } & \text { Maintenance Cost }\\ \text { January ....... } & 160 & \$ 617 \\\text { February ...... } & 130 & \$ 553 \\\text { March ........ } & 180 & \$ 596 \\\text { April......... } & 190 & \$ 623 \\\text { May ........... } & 110 & \$ 532\end{array}$

-Using the least-squares regression equation,the total maintenance cost for March is:

A)above the regression line.
B)on the regression line.
C)below the regression line.
D)outside the relevant range.

Question 7

Donner Company would like to estimate the variable and fixed components of its maintenance costs and has compiled the following data for the last five months of operations.
$\begin{array}{lcc}&\text { Labor Hours } & \text { Maintenance Cost }\\ \text { January ....... } & 160 & \$ 617 \\\text { February ...... } & 130 & \$ 553 \\\text { March ........ } & 180 & \$ 596 \\\text { April......... } & 190 & \$ 623 \\\text { May ........... } & 110 & \$ 532\end{array}$

-Using the least-squares regression method,the estimated variable cost per labor hour for maintenance is closest to:

A)$1.88
B)$1.52
C)$1.09
D)$1.96

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

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 10

Meleski Corporation's recent utility costs are listed below:
Management believes that utility cost is a mixed cost that depends on machine-hours.
$\begin{array}{c}\begin{array}{lll}\\ \text { April...................}\\ \text { May....................}\\ \text { June...................}\\ \text { July....................}\\ \text { August...............}\\ \text { September..........}\\ \text { October..............}\\ \text { November...........}\end{array}\begin{array}{cc}\text { Machine-Hours } & \text { Utility Costs } \\3,546 & \$ 16,979 \\3,539 & \$ 16,954 \\3,554 & \$ 16,980 \\3,516 & \$ 16,850 \\3,536 & \$ 16,955 \\3,578 & \$ 17,065 \\3,551 & \$ 16,994 \\3,556 & \$ 17,023 \end{array}\end{array}$


-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 11

Donner Company would like to estimate the variable and fixed components of its maintenance costs and has compiled the following data for the last five months of operations.
$\begin{array}{lcc}&\text { Labor Hours } & \text { Maintenance Cost }\\ \text { January ....... } & 160 & \$ 617 \\\text { February ...... } & 130 & \$ 553 \\\text { March ........ } & 180 & \$ 596 \\\text { April......... } & 190 & \$ 623 \\\text { May ........... } & 110 & \$ 532\end{array}$

-Using the least-squares regression method,the estimated total fixed cost per month for maintenance is closest to:

A)$470
B)$416
C)$400
D)$378

Question 12

Donner Company would like to estimate the variable and fixed components of its maintenance costs and has compiled the following data for the last five months of operations.
$\begin{array}{lcc}&\text { Labor Hours } & \text { Maintenance Cost }\\ \text { January ....... } & 160 & \$ 617 \\\text { February ...... } & 130 & \$ 553 \\\text { March ........ } & 180 & \$ 596 \\\text { April......... } & 190 & \$ 623 \\\text { May ........... } & 110 & \$ 532\end{array}$

-Using the high-low method of analysis,the estimated variable cost per labor hour for maintenance is closest to:

A)$0.83
B)$1.84
C)$1.30
D)$1.14

Question 13

The R2 (i.e. ,R-squared)indicates the proportion of a mixed cost that is variable.
The R² (i.e. ,R-squared)is a measure of the goodness-of-fit in least-squares regression.

Question 14

Meleski Corporation's recent utility costs are listed below:
Management believes that utility cost is a mixed cost that depends on machine-hours.
$\begin{array}{c}\begin{array}{lll}\\ \text { April...................}\\ \text { May....................}\\ \text { June...................}\\ \text { July....................}\\ \text { August...............}\\ \text { September..........}\\ \text { October..............}\\ \text { November...........}\end{array}\begin{array}{cc}\text { Machine-Hours } & \text { Utility Costs } \\3,546 & \$ 16,979 \\3,539 & \$ 16,954 \\3,554 & \$ 16,980 \\3,516 & \$ 16,850 \\3,536 & \$ 16,955 \\3,578 & \$ 17,065 \\3,551 & \$ 16,994 \\3,556 & \$ 17,023 \end{array}\end{array}$


-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 15

The management of Buff Sports Stadium believes that the number of sporting events each month is an measure of activity for total clean-up cost.Shown below are event figures and total clean up costs for the past four months:
Required:
a.Estimate Buff's cost formula for monthly clean-up cost using the high-low method.
b.Estimate Buff's cost formula for monthly clean-up cost using the least-squares regression method.

Question 16

Magnano Inc.'s inspection costs are listed below:
Management believes that inspection cost is a mixed cost that depends on units produced.
$\begin{array}{c}\begin{array}{lll}\\ \text {February...............}\\ \text {March...................}\\ \text {April.....................}\\ \text {May......................}\\ \text {June.....................}\\ \text {July......................}\\ \text {August.................}\\ \text {September............}\end{array}\begin{array}{cc}\text { Units Produced } & \text { Inspection Costs } \\933 & \$ 4,592 \\945 & \$ 4,619 \\959 & \$ 4,692 \\922 & \$ 4,542 \\950 & \$ 4,669 \\889 & \$ 4,443 \\970 & \$ 4,723 \\878 & \$ 4,400\end{array}\end{array}$


-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 17

Recent maintenance costs of Pavelko Corporation are listed below:
Management believes that maintenance cost is a mixed cost that depends on machine-hours.
$\begin{array}{c}\begin{array}{lll}\\ \text {March..............}\\ \text {April................}\\ \text {May.................}\\ \text {June................}\\ \text {July................}\\ \text {August............}\\ \text {September......}\\ \text {October..........}\end{array}\begin{array}{cc}\text { Machine-Hours } & \text { Maintenance Costs } \\620 & \$ 8,027 \\577 & \$ 7,904 \\571 & \$ 7,897 \\616 & \$ 8,017 \\549 & \$ 7,826 \\552 & \$ 7,832 \\623 & \$ 8,067 \\621 & \$ 8,029 \end{array}\end{array}$


-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 18

When analyzing a mixed cost,you should always plot the data in a scattergraph,but it is particularly important to check the data visually on a scattergraph when the R² from a least squares regression is low.A quick look at the scattergraph can reveal that there is little relation between the cost and the activity or that the relation is something other than a simple straight line.

Question 19

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

Question 20

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 21

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 22

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.