Exam 5: Least-Squares Regression Computations
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.
Calls Taken Call Center Cost April ............ 2,613 \ 60,339 May ............... 2,614 \ 60,345 June ............ 2,640 \ 60,495 July .......... 2,644 \ 60,533 August .......... 2,616 \ 60,346 September...... 2,646 \ 60,537 October........ 2,639 \ 60,501 November...... 2,604 \ 60,263
The solution using Microsoft Excel functions is:
slope = $6.38 per call
intercept = $43,652 per month
The solution using the formulas in the text is:
n = 8
sumX = 21,016
sumY = $483,359
sumXY = $1,269,796,718
sumX2 = 55,211,010
b = [n(sumXY)- (sumX)(sumY))]/[n(sumX^2)- (sumX)^2]
= [8($1,269,796,718)- (21,016)($483,359))]/[8(55,211,010)- (21,016)^2]
= $6.38
a = [(sumY)- b(sumX)]/n
= [($483,359)- $6.38(21,016)]/8
= $43,652
Any difference in the solutions is due to rounding errors when the formulas are used.
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.
Labor Hours Maintenance Cost January ....... 160 \ 617 February ...... 130 \ 553 March ........ 180 \ 596 April......... 190 \ 623 May ........... 110 \ 532
-Using the least-squares regression equation,the total maintenance cost for March is:
C
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.
Activity Cost Period 1 ..... 47 \ 357 Period 2 ..... 46 \ 351 Period 3 ..... 43 \ 334 Period 4\ldots\ldots. 44 \ 340
n = 4
sumX = 180
sumY = 1,382
sumXY = 62,247
sumX^2 = 8,110
b = [n(sumXY)-(sumX)(sumY)]/[n(sumX^2)-(sumX)^2]
= [4(62,247)-(180)(1,382)]/[4(8,110)-(180)^2]
= $5.70 (rounded to nearest whole cent)
a = [(sumY)-b(sumX)]/n
= [(1,382)-5.70(180)]/4
= $89 (rounded to nearest whole dollar)
Cost formula: Y = $89 + $5.70X.
Recent maintenance costs of Pavelko Corporation are listed below:
Management believes that maintenance cost is a mixed cost that depends on machine-hours.
March.............. April................ May................. June................ July................ August............ September...... October.......... Machine-Hours 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
-Using the least-squares regression method,the estimate of the variable component of maintenance cost per machine-hour is closest to:
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.
Seminars Offered Costs Incurred January \ldots\ldots. 8 \ 15,200 February \ldots\ldots. 10 \ 17,000 March \ldots\ldots\ldots. 13 \ 19,400 April ........ 16 \ 21,800 May .......... 14 \ 20,000 June ........ 11 \ 18,200
Recent maintenance costs of Pavelko Corporation are listed below:
Management believes that maintenance cost is a mixed cost that depends on machine-hours.
March.............. April................ May................. June................ July................ August............ September...... October.......... Machine-Hours 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
-Using the least-squares regression method,the estimate of the fixed component of maintenance cost per month is closest to:
Magnano Inc.'s inspection costs are listed below:
Management believes that inspection cost is a mixed cost that depends on units produced.
February............... March................... April..................... May...................... June..................... July...................... August................. September............ Units Produced 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
-Using the least-squares regression method,the estimate of the fixed component of inspection cost per month is closest to:
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.
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.
Number of Total Sporting Clean-up Events Cost July ........... 28 \ 30,900 August ........ 34 \ 34,200 September..... 16 \ 20,700 October......... 22 \ 28,200
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.
Labor Hours Maintenance Cost January ....... 160 \ 617 February ...... 130 \ 553 March ........ 180 \ 596 April......... 190 \ 623 May ........... 110 \ 532
-Using the high-low method of analysis,the estimated total fixed cost per month for maintenance is closest to:
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.
Labor Hours Maintenance Cost January ....... 160 \ 617 February ...... 130 \ 553 March ........ 180 \ 596 April......... 190 \ 623 May ........... 110 \ 532
-Using the least-squares regression method,the estimated total fixed cost per month for maintenance is closest to:
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.
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.
Labor Hours Maintenance Cost January ....... 160 \ 617 February ...... 130 \ 553 March ........ 180 \ 596 April......... 190 \ 623 May ........... 110 \ 532
-Using the least-squares regression method,the estimated variable cost per labor hour for maintenance is closest to:
Meleski Corporation's recent utility costs are listed below:
Management believes that utility cost is a mixed cost that depends on machine-hours.
April................... May.................... June................... July.................... August............... September.......... October.............. November........... Machine-Hours 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
-Using the least-squares regression method,the estimate of the variable component of utility cost per machine-hour is closest to:
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.
Labor Hours Maintenance Cost January ....... 160 \ 617 February ...... 130 \ 553 March ........ 180 \ 596 April......... 190 \ 623 May ........... 110 \ 532
-Using the high-low method of analysis,the estimated variable cost per labor hour for maintenance is closest to:
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:
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.
Product Returns Warranty Cost May .............. 30 \ 3,929 June ............. 33 \ 3,975 July .............. 26 \ 3,859 August .......... 36 \ 3,996 September....... 42 \ 4,072 Oetober......... 34 \ 3,963 November....... 35 \ 3,976 December ....... 39 \ 4,022
Magnano Inc.'s inspection costs are listed below:
Management believes that inspection cost is a mixed cost that depends on units produced.
February............... March................... April..................... May...................... June..................... July...................... August................. September............ Units Produced 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
-Using the least-squares regression method,the estimate of the variable component of inspection cost per unit produced is closest to:
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?
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.
February............. March.................. April.................... May..................... June..................... July...................... Augus................... September............ Titles Printed Press Setup Cost 39 \ 2,197 40 \ 2,218 36 \ 2,134 31 \ 2,044 48 \ 2,424 47 \ 2,377 29 \ 1,997 45 \ 2,353
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