Question Four (36 minutes)
Krystal Carrington was given the task of developing a cost function for predicting
indirect overhead costs for the Denver personal computer manufacturing plant for
Electron Horizons. The production plant is highly automated. The following
information has been collected:
Month
January
February
March
April
May
June
July
August
September
October
November
December
Indirect
Overhead Costs
in 000’s of
dollars
2,530
1,900
4,710
1,270
4,380
4,020
3,730
3,070
4,980
3,310
1,270
3,510
Machine Hours
Direct Labour
Hours
2,730
1,810
3,403
2,200
3,411
2,586
3,364
2,411
3,964
2,897
2,207
2,864
324
210
347
331
272
202
342
247
347
328
293
307
She examines three different possible cost functions using regression analysis
on Excel. The data is attached to the end of the examination.
Correlation between Machine Hours and Direct labour hours is shown below:
Machine Hours
Machine Hours
Direct Labour Hours
1
0.582388818
Direct Labour
Hours
1
Required:
a) Complete the attached chart showing your evaluation of the equations
considered under the various criteria. If the criterion is not relevant to your
decision, please indicate. If you desire additional information to make
your decision, please indicate what additional information you would want.
See attached chart at end.
1
b) Provide a 95% confidence interval for your estimate of total indirect
overhead costs if machine hours are 3,070.
Y
= [A + b1X1] +/- Se(t.025, 10 df)
= [-1,707 + 1.74823 (3,070)] +/- Se (t.025, 10 df)
=3,660.07 +/- (657.4396) (2.228)
= 2,195.29 5.124.85
c) Krystal is required to submit a bid for a government contract. Company
policy is to use marginal (variable) costing and require a 20% margin
based upon selling price. Using the equation Y = a + b1X1 (machine
hours), prepare a quote sheet for Krystal. The contract will require 900
machine hours, 125 labour hours at $25 and 1,000 kilos of materials at
$1.25 per kilo.
Direct Labour
Direct Materials
Variable Overhead
Total Variable Costs
Markup
Selling Price
125 hrs @ $25.00
1000 kilos @ $1.25
900 @ 1.74823
20% of selling price
$5,948.41/0.8
$3,125.00
1,250
1,573.41
$5,948.41
1,487.10
$7,435.51
d) If Krystal wished to be 95% confident of not running a loss on this project,
what price would she quote?
This is a one tailed test. We wish to find the value of “b” such that we
have 95% confidence that “b” will be less than this value.
b1 + Sb (t.05, df=10)
=1.74823 + (0.3166) (1.812)
=2.32191
Direct Labour
Direct Materials
Variable Overhead
Total Variable Costs
Markup
Selling Price
125 hrs @ $25.00
1,000 kilos @ $1.25
900 @ 2.32191
20% of selling price
$6,464.72 / 0.8
$3,125.00
1,250.00
2,089.72
$6,464.72
1,616.18
$8,080.90
2
Student name_________________________
ID _________________
Criterion
Y = a + b1X1
Y = a + b2X2
Y = a + b1X1 +
(machine hours) (direct labour
b2X2 (both
hours)
independent var)
Economic
Plausibility
Goodness of Fit
Significance of
Independent
Variables
Plausible
Not plausible,
since the plant is
highly automated
Mixed response
R2 = 0.753, good
Se = 657.44
R2 = 0.033, not
good
Se = 1,301 higher
R2 = 0.8912 best
Se = 415.99
t = 5.52
T > 2 significant
t = 0.59
T< 2 insignificant
F = good
t1 = 9.42
t2 = -4.00 both
greater than |2|
No plot provided
Linearity
Reasonable from
plot
Questionable from
plot
Need plot to be
certain
Homoscedasticity Constant
Unsure from plot
Multi-collinearity
Not relevant
Not relevant
Correlation matrix
indicates 0.58, =>
multicollinearity
Serial Correlation
Would like DW,
but can’t see any
in residuals plot
Would like DW,
but can’t see any
in residuals
Would like DW,
but can’t see any
in residuals
Optional (other
comments)
Could use residual plot against time to better examine for
serial correlation
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4