Practice Exam Questions 2
For each of the following short scenarios, describe briefly and specifically how you would respond to the issue
raised:
1. What are the purposes of looking at each of leverage, studentized residuals and Cook’s D?
2. You expected from theory, that a particular X variable of the 5 you have in the equation should have a direct
relationship with Revenues, your dependent variable. However, when you look at your regression results you see a
negative slope with a significant P-value of .002. What problem does this suggest and what would you do about it?
3. You are at the final stages of a revenues forecasting project and now need to forecast revenues using values for your
independent variables for the next 4 quarters. Specify the two very different ways for obtaining values for these
independent variables for the next 4 quarters.
4. One of your models involves transforming sales by taking a natural log. Why can you no longer use the standard error
as a means of choosing a ‘best’ model? What should you use in this case?
5. The normal probability plot in Tools-Data Analysis- Regression gives you a normal probability plot of the dependent
variable and it shows the dependent variable to be normal. Is that sufficient to satisfy the normality assumption in
regression? If not, what should you do?
1
Data is available in Appendix A on household income for households sampled from 4 regions in a large city in the
Western United States.
6. We wish to determine whether or not a significant relationship exists between income and region. (a) Set up specific
hypotheses that reflect the type of relationship for situations like this and (b)use Appendix A to help you write up a statement
of how confident you are, and (c) Check the assumptions that are needed to do this test.
7. Use the post hoc analysis to help you write up a series of statements detailing how confident you are about which areas
have significantly higher incomes than which other areas.
Appendix B details a seasonal and trend analysis of 20 quarters of revenues from Lowe’s Home Improvement
($Millions)
8a. Describe the type and strength of the trend in Lowe’s revenues.
b.
Describe the seasonal nature of Lowe’s revenues.
c. Calculate a seasonal forecast for the 21st quarter (a first quarter) using the results of a and b above.
2
Appendix C and following Appendices deal with forecasting revenues for Lowe’s. Definitions for all the variables
are found at the bottom of page 6.
9. Look at Appendix C. Explain why the VIF process is used and what you would do as a next step in this process.
10. Look at Appendix D. The dependent variable is seasonally adjusted revenues for Lowe’s Home
Improvement.
a. Interpret the numbers 0.5556 and 1.2902 across from GDP. Make sure you use the proper units and interpret the
numbers in terms of revenues and GDP.
b. Does a relationship exist between revenues and housing starts (HSN1F)? Set up appropriate hypotheses and write a
conclusion stating your confidence.
c. Interpret the number 1.3617 for HSN1F. Make sure you use the proper units.
11. Look at Appendix E. (a) What assumption does this plot address? (b). Does the assumption hold? (c) This plot
comes from an equation that has a negative coefficient for MRIME. If you were to use the ladder approach and wanted a
better fitting model what would your next step be? Be very specific.
3
12. Look at Appendix F. The dependent variable in the left equation is adjusted revenues and the right is the natural
log of adjusted revenues. Being careful of units, interpret the slope for GDP in each equation.
13. Look at Appendix G. This plot comes from Model D. What assumption does it address? Does this assumption
hold?
14. Look at Appendix H. This plot comes from Model D. What assumption does it address? Does this assumption
hold? If you could ask for other statistical evidence, what would you ask for?
15. Since this data is time series, the D-W statistic is appropriate. In Model D, the D-W statistic was 1.1. What does this
say about the independence assumption? How might you make this a better model?
4
16. For the following charts: State whether or not the process is in control or out of control, and describe the reason(s)
why using Rules 1, 2 and 3.
6.00
5.00
4.82
4.00
3.00
2.00
1.34
1.00
0.00
0
0
10
20
30
40
1.85
1.75
1.7221
1.65
1.55
1.45
1.35
1.33277
1.25
1.15
1.05
0.95
0.94345
0.85
0
10
20
30
40
50
The following situations call for the use of a control chart. Look at each situation and decide which type of control
chart is appropriate for the situation.
17. Customers are surveyed leaving the teller window to find out if their transaction was satisfactory. They sample 50
customers each day and record the number of unsatisfactory transactions. What chart is called for?
18. A chart is constructed by looking at a sample of 25 applications for a consumer loan. Each application is checked
thoroughly to see how many questions on the application are not filled out properly. You are to analyze the data but you
have only the number of questions not filled out properly. What chart is called for?
19. A mail-order clothing retailer is interested in improving the time of its customer service agents who enter customer
orders into the computerized record system. A manager records how long it takes to enter an order in a daily sample of 15
customer orders. He does this over the course of one month’s time. . What type of chart should they use?
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Appendix A
One factor ANOVA
Mean
70,179.3
60,203.1
45,758.8
51,021.5
58,639.5
n
18
8
10
12
48
ANOVA table
Source
SS
Treatment
4,772,087,278.83
Error
10,014,453,691.09
Total
14,786,540,969.92
Std. Dev
15,997.59
16,211.27
14,843.42
12,937.56
17,737.17
NE
NW
SE
SW
Total
df
MS
3 1,590,695,759.6
44 227,601,220.3
47
F
6.99
p-value
.0006
NE
70,179.3
Post hoc analysis
p-values for pairwise t-tests
SE
SW
NW
NE
45,758.8
51,021.5
60,203.1
70,179.3
SE
45,758.8
SW
51,021.5
NW
60,203.1
.4196
.0497
.0002
.1893
.0014
.1268
SW
51,021.5
NW
60,203.1
1.33
3.41
1.56
Tukey simultaneous comparison t-values (d.f. = 44)
SE
45,758.8
SE
45,758.8
SW
51,021.5
0.81
NW
60,203.1
2.02
NE
70,179.3
4.10
critical values for experimentwise error rate:
0.05
0.01
NE
70,179.3
2.67
3.31
NE
NW
SE
SW
Skewness -0.178 0.012 1.011 -0.146
Kurtosis
-1.111 -2.093 -0.574 -0.047
Appendix B: 22 quarters of revenues from Lowe’s Home Improvement ($Millions)
2007
2008
2009
2010
2011
mean:
adjusted:
Calculation of Seasonal Indexes
1
2
3
0.961
1.008
1.138
0.962
1.008
1.144
0.939
1.009
1.126
0.961
1.029
1.149
1.013
1.139
0.956
1.014
1.140
0.956
4
0.886
0.891
0.908
0.876
0.890
0.890
Low e's Revenues and Adjusted Revenues
8100
7600
7100
6600
6100
5600
5100
4600
4100
3600
3100
y = 202.95x + 2713.2
R2 = 0.9873
0
5
10
15
20
6
Appendix C and Following appendices deal with forecasting revenues for Lowe’s and uses data as follows:
Adjusted –Seasonally adjusted revenues $Millions
GDP – Gross Domestic Product $Billions
DPI – Disposable Personal Income $Billions
CCONF – Consumer Confidence Index
CPI – Consumer price index
MORTG – Mortgage interest rate in percent
MPRIME – Prime interest rate in percent
UNRATE – Unemployment rate in percent
HSN1F – Single Family new housing starts (thousands)
PERMITS – Building permits (thousands)
Appendix C:
Regression output
variables
coefficients
Intercept
-19,619.8011
GDP
0.7690
DPI
-0.0194
CCONF
7.8018
CPI
81.5912
MORTG
-37.5298
MPRIME
-38.1043
UNRATE
316.5112
HSN1F
1.3720
PERMITS
0.00038802
Appendix D
Regression output
variables
coefficients
Intercept
-17,697.1195
GDP
0.9229
CPI
60.2911
UNRATE
399.8557
HSN1F
1.3617
std. error
0.3205
0.5798
7.6670
48.8790
87.1693
50.4449
140.6777
0.7371
0.0013
t (df=12) p-value
2.399
-0.033
1.018
1.669
-0.431
-0.755
2.250
1.861
0.302
confidence interval
95% lower 95% upper
.0336
0.0707
1.4673
.9739
-1.2827
1.2438
.3290
-8.9032
24.5069
.1209
-24.9069
188.0893
.6744
-227.4553
152.3957
.4646
-148.0143
71.8056
.0440
10.0007
623.0217
.0873
-0.2339
2.9779
.7680 -0.00241320 0.00318925
std. error
t (df=15)
p-value
0.1723
16.4430
35.7735
0.4717
5.356
3.667
11.177
2.887
.0001
.0023
1.13E-08
.0113
VIF
184.050
484.516
21.473
486.851
17.631
38.980
50.716
12.467
1.402
144.232
mean VIF
confidence interval
95% lower
95% upper
0.5556
25.2436
323.6063
0.3563
1.2902
95.3386
476.1051
2.3671
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Appendix E
MPRIME Residual Plot
200
2
150
y = 15.563x - 211.6x + 667.3
2
R = 0.2057
Residuals
100
50
0
-504.00
6.00
8.00
10.00
-100
-150
Appendix F
Y=Adjusted Coefficients
Intercept
-130009.4
MPRIME
-205.5678
Ln(GDP)
14842.41
Y = Ln AdjustedCoefficients
Intercept
5.255698
LnMPRIME
-0.164521
GDP
0.00036
Appendix G
Residuals vs Predicted
200
150
100
50
0
2000
-50
3000
4000
5000
6000
7000
8000
-100
-150
Appendix H
Normal Probability Plot of Residuals
1.63
1.13
0.63
0.13
-0.37
-0.87
-1.37
-1.87
-109.40
-59.40
-9.40
40.60
90.60
140.60
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