# P10 31 Chart P10 31 10 36 by 3kQWm23H

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```									Problem 10-36
The Nautilus Company, which is under contract to the U.S. Navy, assembles troop deployment boats.
As part of its research program, it completes the assembly of the first of a new model (PT109) of
deployment boats. The Navy is impressed with the PT109. It requests that Nautilus submit a proposal
on the cost of producing another 6 PT109s.

Nautilus reports the following cost information for the first PT109 assembled and uses an 90%
cumulative average-time learning model as a basis for forecasting direct manufacturing labor-hours
for the next 6 PT109s. (An 90% learning curve means b = -0.152004.)

Direct materials                                                 \$200,000
Direct manufacturing labor time for first boat                      15,000   labor-hours
Direct manufacturing labor rate                                       \$40    per direct manufacturing labor-hour
Variable manufacturing overhead cost                                  \$25    per direct manufacturing labor-hour
Other manufacturing overhead                                          20%    of direct manufacturing labor costs
Tooling costs (1)                                                \$280,000
Learning curve for manufacturing labor time per boat                  90%    cumulative average time (2)

(1) Tooling can be reused at no extra cost because all of its cost has been assigned to the first deployment boat.
(2) Using the formula (p. 359), for an 90% learning curve, b = ln.90/ln2 = (-0.105361/.693147) = -0.152004

Required:
1. Calculate predicted total costs of producing the six PT109s for the Navy. (Nautilus will keep the first
deployment boat assembled, costed at \$1,575,000, as a demonstration model for potential customers.)

Calculation of the direct manufacturing labor-hours                 b=           -0.152003093
to produce the 2nd to 8th boats can be calculated
as follows: y = aX to the power of b where                                    Cumulative
y = cumulative average time per unit in labor-hours                              # of
a = labor hours required for first unit                                         Units
X = cumulative number of units                                                    1
b = ln(learning-curve % in decimal form) / ln2                                    2
b = ln 0.90 / ln2 = -0.152003093                                                  3
-0.105360516                         4
0.693147181                        5
-0.152003093                         6
7
Extra unit           8

The DLHs required to produce the 2nd through the 7th boats
Cumulative
Average-time
Cost to produce the 2nd through 7th boats                                    Learning Model
Direct materials, 6 X \$200,000                                                \$1,200,000.00
Direct manufacturing labor (DML)                                              \$2,524,580.90
Other mfg. Overhead (20% of DML\$)                                               \$504,916.18
Total costs for boats 2 through 7                                         \$5,807,360.15

2. What is the dollar amount of the difference between (a) the predicted total costs for producing the
six PT109s in requirement 1, and (b) the predicted total costs for producing the six PT109s,
assuming that there is no learning curve for direct manufacturing labor? That is, for (b) assume a
linear function for units produced and direct manufacturing labor-hours.

Assumption
Cost to produce the 2nd through 7th boats                                         (a)
Direct labor hours required based on assumption                                  63,114.52

Learning Curve
Direct materials, 6 X \$200,000                                              \$1,200,000.00
Direct manufacturing labor (DML)                                            \$2,524,580.90
Other mfg. Overhead (25% of DML\$)                                             \$504,916.18
Total costs for boats 2 through 7                                        \$5,807,360.15
Difference

Learning curve effects are most prevalent in large manufacturing industries such as airplanes and
boats where costs can run into the millions or hundreds of millions of dollars, resulting in very large
and monetarily significant differences between the two methods.

Problem 10-37
Assume the same information for the Nautilus Company as in Problem 10-36 with one exception. This exception is th
Nautilus uses an 90% incremental unit-time learning model as a basis for predicting direct manufacturing labor-hours
in its assembling operations.

1. Calculate predicted total costs of producing the 6 additional PT109s for the Navy. (Nautilus will keep the first
deployment boat assembled, costed at \$1,575,000, as a demonstration model for potential customers.)

Calculation of the direct manufacturing labor-hours                 b=           -0.15200309
to produce the 2nd to 7th boats can be calculated
as follows: y = aX to the power of b where                                   Cumulative
y = Time (in labor-hours) to produce the most recent unit                       # of
a = labor hours required for first unit                                        Units
X = cumulative number of units                                                   1
b = ln(learning-curve % in decimal form) / ln2                                   2
b = ln 0.90 / ln2 = -0.152003093                                                 3
-0.105360516                        4
0.693147181                       5
-0.152003093                        6
7
Extra unit          8

The DLHs required to produce the 2nd through the 7th boats

Incremental
Unit-time Learning
Cost to produce the 2nd through 7th boats                                         Model
Direct materials, 6 X \$100,000                                                 \$1,200,000.00
Direct manufacturing labor (DML)                                               \$2,906,835.56
Other mfg. Overhead (20% of DML\$)                                                \$581,367.11
Total costs for boats 2 through 7                                             \$6,504,974.89
Difference

2. Compare the cost of the 2nd - 7th boats using the "Incremental Unit-time Learning Model" with the costs of the 2nd
boats using the "Cumulative Average-time Learning Model:
Incremental
Unit-time Learning
Cost to produce the 2nd through 7th boats                                     Model
Direct materials, 6 X \$200,000                                             \$1,200,000.00
Direct manufacturing labor (DML)                                           \$2,906,835.56
Other mfg. Overhead (20% of DML\$)                                            \$581,367.11
Total costs for boats 2 through 7                                      \$6,504,974.89
Difference

Why are the predictions different?

The incremental unit-time learning curve has a slower rate of decline in the time required to produce successive un
than does the cumulative average-time learning curve even though the same 90% factor is used for both curves.
The reason is that, in the incremental unit-time learning model, as the number of units double, only the last unit
produced has a time of 90% of the initial time. In the cumulative average-time learning model, doubling the numbe
of units causes the average time of all the additional units produced (not just the last unit) to be 90% of the initial ti

Cumulative
# of
Units
1
2
3
4
5
6
7
8

How should Nautilus decide which model it should use?

The company should examine its own internal records on past jobs and seek information from engineers, plant managers, and
when deciding which learning curve better describes the behavior of direct manufacturing labor-hours on the production of the
boats.
deployment boats.
del (PT109) of
s submit a proposal

uring labor-hours

manufacturing labor-hour
manufacturing labor-hour
manufacturing labor costs

ve average time (2)

d to the first deployment boat.
.693147) = -0.152004

us will keep the first
r potential customers.)

90% LC           90% LC
Average          Average
Time per         Time per       Cumulative
Unit (y):        Unit (y):     Total Time:
Labor-Hrs.       Labor-Hrs.     Labor-Hrs.
15,000.00         15,000.00  15,000.00
13,500.00         13,500.00  27,000.00
12,693.09                    38,079.27
12,150.00         12,150.00  48,600.00
11,744.80                    58,724.00
11,423.78                    68,542.68
11,159.22                    78,114.52
10,935.00         10,935.00  87,480.00

63,114.52

s for producing the
six PT109s,
s, for (b) assume a

Assumption
(b)
90,000.00

No
Learning Curve
\$1,200,000.00
3,600,000.00
2,250,000.00
720,000.00          Proof
\$7,770,000.00          \$7,770,000.00
\$1,962,639.85

h as airplanes and
esulting in very large

ne exception. This exception is that
g direct manufacturing labor-hours

y. (Nautilus will keep the first
r potential customers.)

90% LC              90% LC
Incremental         Incremental
Unit Time for       Unit Time for    Cumulative
Xth Unit (y)        Xth Unit (y)    Total Time:
Labor-Hrs.          Labor-Hrs.      Labor-Hrs.
15,000.00            15,000.00  15,000.00
13,500.00            13,500.00  28,500.00
12,693.09                       41,193.09
12,150.00            12,150.00  53,343.09
11,744.80                       65,087.89
11,423.78                       76,511.67
11,159.22                       87,670.89
10,935.00            10,935.00  98,605.89

72,670.89
ng Model" with the costs of the 2nd - 7th

Cumulative
Average-time
Learning Model
\$1,200,000.00
\$2,524,580.90
\$1,577,863.06
\$504,916.18
\$5,807,360.15
(\$697,614.75)

required to produce successive units
% factor is used for both curves.
f units double, only the last unit
arning model, doubling the number
e last unit) to be 90% of the initial time.

Cumulative            Incremental
Average-time        Unit-time Learning
Learning Model              Model
Cumulative            Cumulative
Total Time:           Total Time:
Labor-Hrs.             Labor-Hrs.
15,000.00              15,000.00
27,000.00              28,500.00
38,079.27              41,193.09
48,600.00              53,343.09
58,724.00              65,087.89
68,542.68              76,511.67
78,114.52              87,670.89
87,480.00              98,605.89

n from engineers, plant managers, and workers
ng labor-hours on the production of the PT109
Problem 10-31

Ken Howard, financial analyst at KMW Corporation, is examining the behavior of quarterly maintenance costs
for budgeting purposes. Howard collects the following data on machine-hours worked and maintenance costs
for the past 12 quarters:

Machine      Maintenance
Quarter      Hours          Costs
1         100,000         \$205,000
2         120,000         \$240,000
3         110,000         \$220,000
4         130,000         \$260,000
5          95,000         \$190,000
6         115,000         \$235,000
7         105,000         \$215,000
8         125,000         \$255,000
9         105,000         \$210,000
10         125,000         \$245,000
11         115,000         \$200,000
12         140,000         \$280,000

1. Estimate the cost function for the quarterly data using the high-low method.

Machine
Total Cost       Hours
\$280,000          140,000
\$190,000           95,000
\$90,000           45,000                \$2 VC per Machine Hour

Total           Total
Total Cost   Variable Costs    Fixed Costs
\$280,000          \$280,000             \$0 No fixed costs
\$190,000          \$190,000             \$0 No fixed costs

Cost Function: Y = \$2 (Machine Hours)

2. Plot and comment on the estimated cost function.

Actual          Estimated
Machine      Maintenance      Maintenance
Quarter      Hours         ACosts           ECosts
1         100,000         \$205,000        \$200,000
2         120,000         \$240,000        \$240,000
3         110,000         \$220,000        \$220,000
4         130,000         \$260,000        \$260,000
5          95,000         \$190,000        \$190,000
6         115,000         \$235,000        \$230,000
7         105,000         \$215,000        \$210,000
8         125,000         \$255,000        \$250,000
9         105,000         \$210,000        \$210,000
10         125,000         \$245,000        \$250,000
11          115,000           \$200,000         \$230,000
12          140,000           \$280,000         \$280,000

See P10-31(Chart)

There appears to be a clear-cut relationship between machine
hours and maintenance costs.

The high-low line appears to "fit" the data well. The vertical
differences between the actual and predicted costs appear
to be quite small.

3. Howard anticipates that KMW will operate machines for
100,000 hours in quarter 13. Calculate the predicted
maintenance costs in quarter 13 using the cost function
estimated in requirement 1.

Estimated maintenance costs = 100,000 X \$2 = \$200,000

90,000 hours?
aintenance costs
aintenance costs
Estimated Cost Function & Actual Costs

\$300,000

\$250,000

\$200,000

\$150,000

\$100,000

\$50,000

\$0
0   20,000   40,000        60,000         80,000         100,000       120,000   140,000   160,000

ACosts Machine Hours
ECosts     Linear (ECosts)
Exercise 10-40

Fashion Bling operates a chain of 10 retail department stores. Each department store makes its own purchasing deci
Fashion Bling, is interested in better understanding the drivers of purchasing department costs. For many years, Fas
costs to products on the basis of the dollar value of merchandise purchased. A \$100 item is allocated 10 times as ma
department as a \$10 item.

Barry Lee recently attended a seminar titled "Cost Drivers in the Retail Industry." In a presentation at the seminar, a le
system reported that "number of purchase orders" and "number of suppliers" were the two most important cost drive
value of merchandise purchased in each purchase order was not found to be a significant cost driver. Barry Lee inter
Department at Fashion Bling's Miami store. They believed that the competitors conclusions regarding cost drivers fo
Department. Mr. Barry Lee collects the following data for the most recent year for Fashion Bling's 10 retail departmen

\$ Value of        Number of
Merchandise        Purchase        Number of
Department         Purchased           Orders        Suppliers
Store            (MP\$)            (# of PO)       (# of S)
Baltimore                 \$68,307,000            4,345             125
Chicago                    33,463,000            2,548             230
LA                        121,800,000            1,420               8
Miami                     119,450,000            5,935             188
NYC                        33,575,000            2,786              21
Phoenix                    29,836,000            1,334              29
Seattle                   102,840,000            7,581             101
St. Louis                  38,725,000            3,623             127
Toronto                   139,300,000            1,712             202
Vancouver                 130,110,000            4,736             196

Lee decides to use simple regression analysis to examine whether one or more of three variables are reasonable cost
Summary results for these regressions are as follows:

Regression 1: PDC = a + (b X MP\$)
SUMMARY OUTPUT
Regression 1 (MP\$)
\$2,500,000      Regression Statistics
Multiple R                 0.651131304
R Square                   0.423971975
Standard Error             401027.6454
\$2,000,000
Observations                        10

ANOVA
df               SS              MS
Purchase Dept. Dollars

Regression                          1    9.46961E+11     9.46961E+11
\$1,500,000
Residual                            8    1.28659E+12     1.60823E+11
Total                               9    2.23355E+12

Coefficients    Standard Error       t Stat
Intercept
\$1,000,000                         730715.82    265418.8246      2.753067048
(# of PO)                156.9660646     64.68655284      2.426564065
Purchase Dept. Do

\$500,000

\$0
\$0            \$20,000,000          \$40,000,000            \$60,000,000          \$80,000,000
Dollar Value of Merchandise

SUMMARY OUTPUT                                                     Regression 1: PDC = a + (b X MP\$)
PDC = \$1,041,421.37 + .003126704 (MP\$)
Regression Statistics: Regression 1
Multiple R                0.282507267
R Square                  0.079810356
Standard Error            510550.3505
Observations                        10
2.60662E+11
ANOVA
df                     SS                 MS
Regression                                  1       1.80863E+11        1.80863E+11
Residual                                    8       2.08529E+12        2.60662E+11
Total                                       9       2.26616E+12

Coefficients   Standard Error                 t Stat
Intercept                    1041421.366    346708.5474                3.003737214
(MP\$)                        0.003126704    0.003753624                0.832982632

From a t-table for df=8 and one tail equal to .025 (95% confidence interval), the t-value is:
Therefore the intercept confidence intervals are:
And the b-coefficient confidence intervals are:

For a normal curve: "+/-" 1.96 standard errors for 95% confidence interval.
For a normal curve: "+/-" 2.58 standard errors for 99% confidence interval.

Evaluation of the information:                  Regression 1: MP\$

Criterion
1. Economic Plausibility                        A leading competitor found little support for MP\$ as a significa
Purchasing personnel at the Miami store also believe MP\$ is n

2. Goodness of fit                              r2 = 0.0798 indicates a poor fit.

3. Significance of "X" Variable                 t-value of 0.832982632 is insignificant; the larger the t-value the
From a t-table for df=8 and one tail equal to .025 (95% confidence inte

4. Specification Analysis: The testing of the assumptions of regression analysis
pg. 369                             A. Linearity within the relevant range   Appears questionable (See Scatter diagram)

B. Constant variance of residuals        Appears questionable, but no strong evidence against constant varia

C. Independence of residuals             Durbin-Watson Statistic = 2.41 (Assumption of independence is not r
For samples of 10-20 observations, a D/W statistic in the range of 1.1
that the residuals are independent.

D. Normality of residuals                Too few data points to make reliable inferences.

Regression 2: PDC = a + (b X (# of PO))

\$2,500,000                                                        Regression 2 (Number of Purchase Orders)

\$2,000,000
Purchase Dept. Dollars

\$1,500,000

\$1,000,000

\$500,000

\$0
0                 1,000               2,000                3,000
Number of Purchase Orders

SUMMARY OUTPUT                                                Regression 2: PDC = a + (b X (# of PO))
PDC = \$722,537.85 + \$159.48 (# of PO)
Regression Statistics: Regression 2
Multiple R                0.656228523
R Square                  0.430635874
Standard Error            401601.1595
Observations                        10
1.61283E+11
ANOVA
df                     SS                 MS
Regression                                     1       9.75888E+11        9.75888E+11
Residual                                       8       1.29027E+12        1.61283E+11
Total                                          9       2.26616E+12

Coefficients    Standard Error                t Stat
Intercept                         722537.851    265834.6274               2.717997494
(# of PO)                       159.4842168     64.83547006               2.459829731

From a t-table for df=8 and one tail equal to .025 (95% confidence interval), the t-value is:
Therefore the intercept confidence intervals are:
And the b-coefficient confidence intervals are:

For a normal curve: "+/-" 1.96 standard errors for 95% confidence interval.
For a normal curve: "+/-" 2.58 standard errors for 99% confidence interval.

Evaluation of the information:                     Regression 2: # of PO

Criterion
1. Economic Plausibility                           Economically plausible. Increasing the number of purchase or

2. Goodness of fit                                 r2 = 0.430635874 indicates a reasonable fit.

3. Significance of "X" Variable                    t-value of 2.459829731 is significant; the larger the t-value the b

4. Specification Analysis: The testing of the assumptions of regression analysis

pg. 369                             A. Linearity within the relevant range       Appears reasonable (See Scatter diagram)

B. Constant variance of residuals            Appears reasonable

C. Independence of residuals                 Durbin-Watson Statistic = 1.97 (Assumption of independence is not r
For samples of 10-20 observations, a D/W statistic in the range of 1.1
that the residuals are independent.

D. Normality of residuals                    Too few data points to make reliable inferences.

Regression 3: PDC = a + (b X (# of S))

\$2,500,000                                                                    Regression 3 (Number of Suppliers)

\$2,000,000
hase Dept. Dollars
Purchase Dept. Dollars
\$1,500,000

\$1,000,000

\$500,000

\$0
0                             50                                  100
Number of Suppliers

SUMMARY OUTPUT                                                 Regression 3: PDC = a + (b X (# of S))
PDC = \$828,814.24 + \$3,815.69 (# of S)
Regression Statistics
Multiple R                 0.621971696
R Square                   0.386848791
Standard Error             416757.7672
Observations                        10
1.73687E+11
ANOVA
df                    SS                 MS
Regression                               1       8.7666E+11         8.7666E+11
Residual                                 8       1.3895E+12        1.73687E+11
Total                                    9      2.26616E+12

Coefficients   Standard Error                t Stat
Intercept                 828814.2417    246570.4694               3.361368633
(# of S)                  3815.694852    1698.407173                2.24663138

From a t-table for df=8 and one tail equal to .025 (95% confidence interval), the t-value is:
Therefore the intercept confidence intervals are:
And the b-coefficient confidence intervals are:

For a normal curve: "+/-" 1.96 standard errors for 95% confidence interval.
For a normal curve: "+/-" 2.58 standard errors for 99% confidence interval.

Evaluation of the information:               Regression 3: # of Suppliers

Criterion
1. Economic Plausibility                     Economically plausible. Increasing the number of suppliers in
the Fashion Bling-supplier relationships.

2. Goodness of fit                           r2 = 0.386848791 indicates a reasonable fit.

3. Significance of "X" Variable              t-value of 2.24663138 is significant.

4. Specification Analysis

A. Linearity within the                   Appears reasonable (See Scatter diagram)
relevant range

B. Constant variance of residuals         Appears reasonable.

C. Independence of residuals              Durbin-Watson Statistic = 2.01 (Assumption of independence
For samples of 10-20 observations, a D/W statistic in the range
that the residuals are independent.

D. Normality of residuals                 Too few data points to make reliable inferences.

2. Do the regression results support the competitor's presentation about the purchasing department's cost drivers?

Fashion Bling can either (a) develop a multiple regression equation for estimating purchasing departme
suppliers as cost allocation bases, or (2) divide the purchasing department cost pool into two separate
and another for costs related to suppliers, and estimate a separate simple regression equation for each

3. How might Lee gain additional evidence on drivers of Purchasing Department costs at each store?

a. Use physical relationships or engineering relationships to establish cause-and-effect links.
Lee could observe the purchasing department operations to gain insight into how costs are driven.

b. Use knowledge of operations.
Lee could interview operating personnel in the purchasing department to obtain their insight on cost

Exercise 10-41
Barry Lee decides that the simple regression analysis used in P10-40 could be extended to a multiple regression analy

Regression 4: PDC = a + (b1)(# of PO) + (b2)(# of S)

SUMMARY OUTPUT                                  PDC = \$484,521.6364 + \$126.6639997 (# of PO) + \$2903.2977

Regression Statistics: Regression 4
Multiple R                 0.797723096
R Square                   0.636362138
Standard Error             343107.6721
Observations                        10                             7.21048E+11
1.17723E+11
ANOVA
df                   SS                MS
Regression                               2        1.4421E+12       7.21048E+11
Residual                                   7       8.2406E+11        1.17723E+11
Total                                      9      2.26616E+12

Coefficients   Standard Error                t Stat
Intercept                   484521.6346    256684.0955               1.887618451
(# of PO)                   126.6639997     57.7952084               2.191600362
(# of S)                    2903.297788    1458.922564                1.99002871

From a t-table for df=7 and one tail equal to .025 (95% confidence interval), the t-value is:
Therefore the intercept confidence intervals is:
And the b-coefficient confidence intervals are:
Number of purchase orders
Number of Suppliers

For a normal curve: "+/-" 1.96 standard errors for 95% confidence interval.
For a normal curve: "+/-" 2.58 standard errors for 99% confidence interval.

Evaluation of the information:                 Regression 4: PDC = a + (b1)(# of PO) + (b2)(# of S)

Criterion
1. Economic Plausibility                       Economically plausible. Both independent variables are plaus
the findings of the competitor's research and Bling's own rese

2. Goodness of fit                             r2 = 0.636362138 indicates an excellent fit.

3. Significance of "X" Variables               t-value of 2.19 is significant for the (# of PO) variable
t-value of 1.99 is nearly significant for the (# of S) variable
4. Specification Analysis

A. Linearity within the                     Appears reasonable.
relevant range

B. Constant variance of residuals           Appears reasonable.

C. Independence of residuals                Durbin-Watson Statistic = 1.91 (Assumption of independence

D. Normality of residuals                   Too few data points to make reliable inferences.

1. Compare regression 4 with regression 2 and 3 in Problem 10-40. Which model would you recommend that Lee use

Regression 4 is economically feasible and has the highest r2 value. Lee should use the results from
regression 4 to predict PDC.

Regression 5: PDC = a + (b1 X (# of PO)) + (b2 X (# of S)) + (b3 X MP\$)

SUMMARY OUTPUT         PDC = \$483,559.95 + \$126.5778427 (# of PO) + \$2,900.7309 (# of S) + -.000194148 (M

Regression Statistics: Regression 5
Multiple R                0.797724783
R Square                      0.63636483
Standard Error               370597.2708
Observations                          10                            4.80701E+11
1.37342E+11
ANOVA
df                   SS                  MS
Regression                                3      1.4421E+12         4.80701E+11
Residual                                  6     8.24054E+11         1.37342E+11
Total                                     9     2.26616E+12

Coefficients    Standard Error               t Stat
Intercept                  483559.9493     312554.2588              1.547123214
(MP\$)                     0.0000194148     0.002913205              0.006664422
(# of PO)                  126.5778427     63.75031137              1.985525089
(# of S)                      2900.7309    1622.198995              1.788147391

From a t-table for df=6 and one tail equal to .025 (95% confidence interval), the t-value is:
Therefore the intercept confidence intervals is:
And the b-coefficient confidence intervals are:
Dollars of Merchandise Purchased
Number of purchase orders
Number of Suppliers

For a normal curve: "+/-" 1.96 standard errors for 95% confidence interval.
For a normal curve: "+/-" 2.58 standard errors for 99% confidence interval.

2. Compare regression 5 with regression 4. Which model would you recommend that Lee use?

Regression 4 should be used.
It is slightly less complicated (and therefore less costly), has about the same r 2, and the standard errors
regression variables are slightly smaller.

3. Lee estimates the following data for the Baltimore store for next year:
Dollar value of merchandise purchased                            \$75,000,000
Number of purchase orders                                              4,000
Number of suppliers                                                       95

Regression 4: PDC = a + (b1)(# of PO) + (b2)(# of S)

PDC = \$484,521.6364 + \$126.6639997 (# of PO) + \$2903.297788 (# of S)

PDC =                   \$1,266,990.92 Slightly preferred -- see above.

Regression 5: PDC = a + (b1)(# of PO) + (b2)(# of S) + (b3)(MP\$)

PDC = \$483,559.95 + \$126.5778427 (# of PO) + \$2,900.7309 (# of S) + .000194148 (MP\$)

PDC =                   \$1,266,896.87 More complicated, more costly, not much improvement.
4. What difficulties do not arise in simple regression analysis that may arise in multiple regression analysis?
Multicollinearity is a frequently encountered problem in cost accounting; it does not arise in simple reg
because there is only one independent variable in a simple regression. Multicollinearity exists when tw
more independent variables are highly correlated with each other.

One consequence of multicollinearity is an increase in the standard errors of the coefficients of the indi
variables. This frequently shows up in reduced t-values for the independent variables in the multiple
regression relative to their t-values in the simple regression.

t-value            t-value
Multiple            Simple
Variables           Regression         Regression
Regression 4
# of PO                     2.191600362      2.459829731
# of S                       1.99002871       2.24663138
Regression 5
# of PO                     1.985525089      2.459829731
# of S                      1.788147391       2.24663138
MP\$                         0.006664422      0.832982632

The decline in the t-values in the multiple regressions is consistent with some (but not very high)
collinearity among the independent variables.

Generally, users of regression analysis believe that a coefficient of correlation between independent va
greater than 0.70 indicates multicollinearity.

The coefficients of correlation between the potential independent variables for Fashion Bling are:

Pair-wise
Correlation Values                   # of PO
# of PO / # of S          0.285358                         # of Suppliers
# of PO / MP\$             0.270157
# of S / MP\$              0.296190                         MP\$
# of PO
No values are near the .70 benchmark.
MP\$
# of Suppliers

5. Give examples of decisions in which the regression results reported here could be informative.
Cost management decisions: Fashion Bling could restructure relationships with suppliers so that
fewer separate purchase orders are made. Alternatively, it may aggressively reduce the number
of existing suppliers.

Purchasing policy decisions: Fashion Bling could set up an internal charge system for individual
retail departments within each store. Separate charges to each department could be made for each
purchase order and each new supplier added to the existing ones. These internal charges would
signal to each department ways in which their own decisions affect the total costs of Fashion Bling.

Account system design decisions: Fashion Bling may want to discontinue allocating purchasing
department costs on the basis of dollar value of merchandise purchased. Allocation bases better
capturing cause-and-effect relations at Fashion Bling are the number of purchase orders and the
number of suppliers.
ent store makes its own purchasing decisions. Barry Lee, assistant to the president of
g department costs. For many years, Fashion Bling has allocated purchasing department
A \$100 item is allocated 10 times as many overhead costs associated with the purchasing

ry." In a presentation at the seminar, a leading competitor that has implemented an ABC
" were the two most important cost drivers of purchasing department costs. The dollar
a significant cost driver. Barry Lee interviewed several members of the Purchasing
ors conclusions regarding cost drivers for purchasing costs also applied to their Purchasing
ar for Fashion Bling's 10 retail department stores:

Department                          Merchandise       Number of
Costs                              Purchased        Suppliers
(PDC)                                (MP\$)           (# of S)
\$1,522,000                         \$68,307,000               125
1,095,000                          33,463,000               230
542,000                         121,800,000                 8
2,053,000                         119,450,000               188
1,068,000                          33,575,000                21
517,000                          29,836,000                29
1,544,000                         102,840,000               101
1,761,000                          38,725,000               127
1,605,000                         139,300,000               202
1,263,000                         130,110,000               196

ore of three variables are reasonable cost drivers of purchasing department costs.

Regression 1 (MP\$)

F          Significance F
5.888213164      0.041423692

P-value          Lower 95%        Upper 95%        Lower 95.0%       Upper 95.0%
0.024940453       118658.5171     1342773.123       118658.5171       1342773.123
0.041423692       7.798509836     306.1336195       7.798509836       306.1336195
\$80,000,000             \$100,000,000         \$120,000,000       \$140,000,000     \$160,000,000
Dollar Value of Merchandise

ession 1: PDC = a + (b X MP\$)
= \$1,041,421.37 + .003126704 (MP\$)
R2      0.079810356
Slope      0.003126704
Intercept      1041421.366

0.693860065

F              Significance F
0.693860065          0.429019986

3.003737214
0.832982632
P-value              Lower 95%           Upper 95%
0.016974731           241910.0229         1840932.71
0.429019986          -0.005529169        0.011782576

5 (95% confidence interval), the t-value is:                  2.306004133
241,910.0229       1,840,932.710
(0.005529169)       0.011782576

or 95% confidence interval.
or 99% confidence interval.

found little support for MP\$ as a significant driver.
l at the Miami store also believe MP\$ is not a significant driver.

(r2 >.30 passes).            0.079810356

2 is insignificant; the larger the t-value the better
nd one tail equal to .025 (95% confidence interval), the t-value is:             2.306004133

egression analysis
See Scatter diagram)

but no strong evidence against constant variance.

= 2.41 (Assumption of independence is not rejected.)
servations, a D/W statistic in the range of 1.10 - 2.90 range indicates

make reliable inferences.

sion 2 (Number of Purchase Orders)

4,000                  5,000                 6,000           7,000     8,000
Number of Purchase Orders

ession 2: PDC = a + (b X (# of PO))
= \$722,537.85 + \$159.48 (# of PO)
R2   0.430635874
Slope   159.4842168
Intercept    722537.851
6.050762303

F            Significance F
6.050762303        0.039329201

2.717997494
2.459829731
P-value            Lower 95%            Upper 95%
0.026330178         109522.1014           1335553.6
0.039329201         9.973354903         308.9950788

5 (95% confidence interval), the t-value is:                   2.306004133
109,522.1014         1,335,553.6
9.973354903        308.9950788

or 95% confidence interval.
or 99% confidence interval.

le. Increasing the number of purchase orders increases the purchasing tasks to be undertaken.

ates a reasonable fit.              (r2 >.30 passes).         0.430635874

1 is significant; the larger the t-value the better

egression analysis

e Scatter diagram)

= 1.97 (Assumption of independence is not rejected.)
servations, a D/W statistic in the range of 1.10 - 2.90 range indicates

make reliable inferences.

ression 3 (Number of Suppliers)
150                                 200                  250
Number of Suppliers

ession 3: PDC = a + (b X (# of S))
= \$828,814.24 + \$3,815.69 (# of S)
R2         0.386848791
Slope         3815.694852
Intercept         828814.2417

5.047352558

F            Significance F
5.047352558        0.054854897

3.361368633
2.24663138
P-value            Lower 95%           Upper 95%
0.00991164         260221.7201        1397406.763
0.054854897        -100.8391101        7732.228814

5 (95% confidence interval), the t-value is:                2.306004133
260,221.7201    1,397,406.763
(100.8391101)    7,732.228814

or 95% confidence interval.
or 99% confidence interval.

le. Increasing the number of suppliers increases the costs of certifying vendors and managing
pplier relationships.

ates a reasonable fit.           (r2 >.30 passes).       0.386848791

is significant.

See Scatter diagram)

tic = 2.01 (Assumption of independence is not rejected.)
observations, a D/W statistic in the range of 1.10 - 2.90 range indicates
independent.

o make reliable inferences.

purchasing department's cost drivers?                Yes. (See above analysis.)

ation for estimating purchasing department costs with the # of purchasee orders and the # of
g department cost pool into two separate cost pools, one for costs related to purchase orders
rate simple regression equation for each pool using the appropriate cost drive.

ment costs at each store?

o gain insight into how costs are driven.

department to obtain their insight on cost drivers.

e extended to a multiple regression analysis.

64 + \$126.6639997 (# of PO) + \$2903.297788 (# of S)

6.124960342

F           Significance F
6.124960342        0.02899625
1.887618451
2.191600362
1.99002871
P-value            Lower 95%           Upper 95%
0.10102841        -122439.8024        1091483.072
0.064526149        -9.999951709         263.327951
0.08688758        -546.5058866        6353.101463

5 (95% confidence interval), the t-value is:                2.364624251
confidence intervals is:                  (122,439.8024)   1,091,483.072
nfidence intervals are:
ber of purchase orders                     (9.999951709)      263.327951
ber of Suppliers                        (546.505886596)     6,353.101463

or 95% confidence interval.
or 99% confidence interval.

a + (b1)(# of PO) + (b2)(# of S)

le. Both independent variables are plausible and are supported by
mpetitor's research and Bling's own research.

ates an excellent fit.              (r2 >.30 passes).

ficant for the (# of PO) variable
y significant for the (# of S) variable

tic = 1.91 (Assumption of independence is not rejected.)

o make reliable inferences.

odel would you recommend that Lee use?

alue. Lee should use the results from

PO) + \$2,900.7309 (# of S) + -.000194148 (MP\$)
3.500018051

F            Significance F
3.500018051        0.089598866                        1.547123214
0.006664422
1.985525089
1.788147391
P-value            Lower 95%           Upper 95%
0.172797006        -281232.7692        1248352.668
0.994898658        -0.007108942        0.007147771
0.094299047        -29.41354943        282.5692348
0.123970458        -1068.647038        6870.108839

5 (95% confidence interval), the t-value is:                2.446911846
confidence intervals is:                  (281,232.7692)   1,248,352.668
nfidence intervals are:
rs of Merchandise Purchased                (0.007108942)     0.007147771
ber of purchase orders                   (29.413549432)      282.5692348
ber of Suppliers                          (1,068.647038)    6,870.108839

or 95% confidence interval.
or 99% confidence interval.

mend that Lee use?

bout the same r2, and the standard errors around the

of S) + .000194148 (MP\$)

ore costly, not much improvement.
in multiple regression analysis?
ccounting; it does not arise in simple regression
ression. Multicollinearity exists when two or

ndard errors of the coefficients of the individual
e independent variables in the multiple

stent with some (but not very high)

nt of correlation between independent variables

ent variables for Fashion Bling are:

# of PO         # of Suppliers
1        0.285358146
0.285358146                   1
MP\$              # of PO
1        0.270157066
0.270157066                   1
MP\$           # of Suppliers
1        0.296190300
0.296190300                   1

could be informative.
relationships with suppliers so that
y aggressively reduce the number

ternal charge system for individual
h department could be made for each
nes. These internal charges would
affect the total costs of Fashion Bling.

purchased. Allocation bases better
umber of purchase orders and the
Observation           X
1                 6
2                10
3                 8
4                11
5                 5
6                12
7                 9                                                              Hi-Low Method
8                 7                                                         Y
9                 4                                                        48
10                14                                                        18
Total              86                 310                                    30
Mean                                  31

Hi-Low                     Regression
b-value             3                      3.268398268                       3.268398268
Intercept            6                      2.891774892                       2.891774892
Formula         y = 6 + 3X        y=2.891774892+ 3.268398268(X)

Regression Statistics
Multiple R          0.988576473
R Square               0.977283443        0.977283443         0.977283443
Standard Error         1.693506825
Observations                    10

ANOVA
df                 SS                  MS                  F
Regression                        1       987.0562771         987.0562771         344.1660377
Residual                          8       22.94372294         2.867965368
Total                             9              1010

Coefficients      Standard Error          t Stat          P-value
Intercept             2.891774892         1.606987982         1.799500011      0.109636756
X                     3.268398268         0.176177712         18.55171253      7.34874E-08
1.799500011
18.55171253
Hi-Low
Actual value of Y when X is equal to 12 =                                         45
Best quess of Y, with knowledge of X equal to 12, is                               42
Best quess of Y, with no knowledge of X, is the mean                              31
Total Variation from the mean when X is = to 12                45 - 31 =          14
Explained Variation by knowing X is equal to 12                42 - 31 =           11
Unexplained Variation when X is equal to 12                    45 - 42 =           3
RESIDUAL OUTPUT (Regression)        Regression      Explained by X
Observation #        X      Y    Predicted Y       Residuals
1               6     22      22.5021645      -8.497835498
2              10     34     35.57575758       4.575757576
3               8     29     29.03896104      -1.961038961
4              11     40     38.84415584       7.844155844
5               5     19     19.23376623      -11.76623377
6              12     45     42.11255411       11.11255411
7               9     30     32.30735931       1.307359307
8               7     25     25.77056277      -5.229437229
9               4     18     15.96536797      -15.03463203
10              14     48     48.64935065       17.64935065
Total                                         310       0.000000000
60

50
Hi-Low Method
X
14
4                                                   40
10

30

y
20

10

0
0     2
Significance F
7.34874E-08                      344.1660377
987.0562771
2.867965368

Lower 95%          Upper 95%       2.306004133 = T-value for df =8
-0.813946037      6.597495821   -0.813946037        6.597495821
2.862131736      3.674664801    2.862131736        3.674664801

Regression
45
42.11255411
31
14
11.11255411       42.11233411 - 31
2.887445887       45 - 42.11255411
Unexplained
Squared        Residuals        Squared       Total Variation   Total Variation   Squared
72.21320815    -0.502164502    0.252169187         -9                -9            81
20.93755739    -1.575757576    2.483011938          3                 3             9
3.845673807    -0.038961039    0.001517963         -2                -2             4
61.53078091    1.155844156     1.335975713          9                 9            81
138.444257    -0.233766234    0.054646652         -12               -12           144
123.4888589    2.887445887     8.337343753         14                14            196
1.709188359    -2.307359307    5.323906973         -1                -1             1
27.34701374    -0.770562771    0.593766983         -6                -6            36
226.0401604    2.034632035     4.139727516         -13               -13           169
311.4995783    -0.649350649    0.421656266         17                17            289
987.0562771     0.000000000    22.94372294          0                 0           1010
0.977283443                                           1010
0.977283443
0.977283443
0.977283443
r= 0.988576473
Graph -- Data

4   6          8        10   12
x
Y

14   16
Anna Martinez is checking to see if there is any relationship between newspaper
advertising and sales revenue at the Casa Real restaurant where she is the financial
manager. She has obtained the following data for the past 10 months:

Month  Revenues            Costs
March         \$50,000           \$2,000
April         \$70,000           \$3,000
May           \$55,000           \$1,500
June          \$65,000           \$3,500
July          \$56,000           \$1,000
August        \$65,000           \$2,000
September     \$45,000           \$1,500
October       \$80,000           \$4,000
November      \$55,000           \$2,500
December      \$60,000           \$2,500

Using the high-low method, determine the cost function which could
be used to estimate restaurant revenues based on advertising costs.

Revenues        Costs
2      \$80,000        \$4,000
2      \$56,000        \$1,000
2      \$24,000        \$3,000       \$8.00

2       \$80,000      \$32,000    \$48,000
\$56,000       \$8,000    \$48,000

2 Y = \$48,000 + (\$8.00 X Advertising Costs)

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