Deck 15: Least-Squares Regression Computations

Question 1

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.

$\begin{array}{cc}&\text { Activity } & \text { Cost } \\\text { Period 1}&46 & \$ 292 \\\text {Period 2 }&40 & \$ 271 \\\text {Period 3 }&42 & \$ 279 \\\text {Period 4 }&41 & \$ 267\end{array}$

Required:
Using the least-squares regression method,estimate the cost formula for this cost.

Answer 1

The solution using Microsoft Excel functions is:
Variable cost = Slope = $3.94
Fixed cost = Intercept = $110.80
Therefore,the cost formula is $110.80 per period plus $3.94 per unit of activity or:
Y = $110.80 + $3.94X

The solution using the formulas in the text is:
n = 4
sumX = 169
sumY = 1,109
sumXY = 46,937
sumX^2 = 7,161

b = [n(sumXY)-(sumX)(sumY)]/[n(sumX^2)-(sumX)^2]
= [4(46,937)-(169)(1,109)]/[4(7,161)-(169)^2]
= $3.94 (rounded to nearest whole cent)

a = [(sumY)-b(sumX)]/n
= [(1,109)-3.94(169)]/4
= $111 (rounded to nearest whole dollar)

Cost formula: Y = $111 + $3.94X.

Question 2

The least-squares regression method:

A)fits a line to data by minimizing the sum of the squared errors from the line.
B)is generally less accurate than the high-low method.
C)can be used only if the fixed cost element is larger than the variable cost element.
D)can be used only if the fixed cost element is smaller than the variable cost element.

Answer 2

A

Question 3

The Stephens Leadership Center provides training seminars in personal development and time management.The company is relatively new and management is seeking information regarding the Center's cost structure.The following information has been gathered since the inception of the business in January of the current year: $\begin{array}{lcc}\text { Month }&\text { Seminars Offered } & \text { Costs Incurred } \\\text {January }&10 & \$ 17,000 \\\text {February }&12 & \$ 18,800 \\\text {March }&15 & \$ 20,900 \\\text {April }&18 & \$ 23,762 \\\text {May }&16 & \$ 21,800 \\\text {June }&13 & \$ 19,400\end{array}$
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 method,estimate the variable cost per seminar and the total fixed cost per month.

Answer 3

a.High-Low Method:
$\begin{array}{lcc}\text {Month. }&\text { Number of Seminars } & \text { Costs Incurred } \\\text {April (high activity level). }&18 & \$ 23,762 \\\text {January (low activity level) }&\underline{10} & \underline{17,000} \\\text {Change observed }&\underline{8} & \underline{\$ 6,762}\end{array}$

Variable cost = Change in Cost/Change in activity = $6,762/8 seminars = $845.25 per seminar

Fixed cost element = Total cost - Variable cost element
= $23,762 - ($845.25 per seminar $\times$ 18 seminars)= $8,547.50

Cost formula for seminar costs: $8,547.50 per month plus $845.25 per seminar held
b.Least-Squares Method:
n = 6
sumX = 84
sumY = 121,662
sumXY = 1,737,816
sumX^2 = 1,218

b = [n(sumXY)-(sumX)(sumY)]/[n(sumX^2)-(sumX)^2]
= [6(1,737,816)-(84)(121,662)]/[6(1,218)-(84)^2]
= $822.57 (rounded to the nearest whole cent)

a = [(sumY)-b(sumX)]/n
= [(121,662)-822.57(84)]/6
= $8,761 (rounded to the nearest whole dollar)

The cost formula is $8,761 per month plus $822.57 per seminar.A similar answer can be obtained using Microsoft Excel.

Question 4

In least-squares regression,independent variables are not included in the computations of the slope and intercept.

Question 5

Least-squares regression selects the values for the intercept and slope of a straight line that minimize the sum of the squared errors.

Question 6

Which of the following methods of analyzing mixed costs can be used to estimate an equation for the mixed cost?

A)Option A
B)Option B
C)Option C
D)Option D

Question 7

Descoteaux 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)$1,979
B)$6,033
C)$5,624
D)$2,021

Question 8

Gelrud 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)$19,733
B)$5,809
C)$19,962
D)$5,628

Question 9

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 = $156.64 + $9.20X
B)Y = $0.00 + $16.01X
C)Y = $164.54 + $8.86X
D)Y = $169.97 + $6.10X

Question 10

Moeller 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)$51.76 per unit plus $2,621 per month
B)$51.99 per unit plus $2,584 per month
C)$67.86 per unit plus $11,053 per month
D)$52.23 per unit plus $2,550 per month

Question 11

The management of Ferry 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)$1.64 per machine-hour plus $29,566 per month
B)$0.92 per machine-hour plus $31,132 per month
C)$1.37 per machine-hour plus $30,157 per month
D)$15.39 per machine-hour plus $33,096 per month

Question 12

Carr Company reports the following data for the first six months of the year:

-Using the least-squares regression method,the estimated variable electrical cost per machine hour is closest to:

A)$0.91
B)$0.10
C)$0.20
D)$0.25

Question 13

Descoteaux 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)$9.87
B)$14.84
C)$9.26
D)$9.97

Question 14

Executive Training,Inc. ,provides a personal development seminar that is popular with many companies.The number of seminars offered over the last five months,along with the total costs of offering these seminars,follows:

$\begin{array}{lcc}&\text { Seminars Offered } & \text { Costs Incurred } \\\text {April }&55 & \$ 15,400 \\\text {May }&45 & \$ 14,000 \\\text {June }&60 & \$ 18,000 \\\text { July}&50 & \$ 14,700 \\\text {August }&75 & \$ 19,000\end{array}$

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,compute the variable cost per seminar and the total fixed cost per month.(Round off to the nearest whole dollar. )

Question 15

Recent maintenance costs of Prideaux 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)$9.36
B)$9.49
C)$14.06
D)$9.23

Question 16

Recent maintenance costs of Prideaux 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)$2,859
B)$8,241
C)$8,550
D)$2,782

Question 17

Dillenbeck Printing Corp. ,a book printer,has provided the following data: $\begin{array}{lcc}&\text { Titles Printed } & \text { Press Setup Cost } \\\text {February. }&33 & \$ 3,170 \\\text {March. }&34 & \$ 3,203 \\\text { April}&46 & \$ 3,688 \\\text {May. }&28 & \$ 2,996 \\\text {June }&44 & \$ 3,607 \\\text {July }&42 & \$ 3,551 \\\text {August }&43 & \$ 3,586 \\\text {September }&39 & \$ 3,413\end{array}$ 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 18

Gelrud 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)$8.15
B)$5.78
C)$5.57
D)$5.85

Question 19

Carr Company reports the following data for the first six months of the year:

-Using the least-squares regression method,the estimated monthly fixed component of the electrical cost is closest to:

A)$5
B)$20
C)$6
D)$10

Question 20

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 is very high.

Question 21

Galarneau 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: $\begin{array}{lcc}&\text { Calls Taken } & \text { Call Center Cost } \\\text { February.}&7,851 & \$ 85,115 \\\text {March. }&7,820 & \$ 84,934 \\\text {April. }&7,861 & \$ 85,178 \\\text {May. }&7,860 & \$ 85,161 \\\text {June }&7,825 & \$ 84,965 \\\text {July . }&7,836 & \$ 85,009 \\\text {August. }&7,879 & \$ 85,262 \\\text {September }&7,866 & \$ 85,201\end{array}$

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 22

The management of Ferriman 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: $\begin{array}{lcc}&\text { Product Returns } & \text { Warranty Cost } \\\text {April }&24 & \$ 2,972 \\\text { May.}&23 & \$ 2,928 \\\text { June.}&27 & \$ 3,141 \\\text {July }&39 & \$ 3,752 \\\text {August }&36 & \$ 3,569 \\\text {September }&35 & \$ 3,551 \\\text { October}&26 & \$ 3,071 \\\text { November.}&37 & \$ 3,636\end{array}$ 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.