Supplemental Instruction Handouts
Statistical Analysis
Final Review
1. Given the following sales of a certain company:
Years
Sales
2010
18.9
2011
19.4
2012
20.2
2013
16.3
2014
13.7
2015
15.3
2016
16.2
A. What is the regression equation? Round your final answer to 2 decimal places.
B. Forecast the sales for 2017 using the regression equation.
C. What is the smoothed value for 2012? Use an exponential smoothing constant of 0.3.
D. Forecast the sales for 2017 using the Autoregressive forecasting model.
2. You have been asked to perform a study on absenteeism for your department at work. You have
been given the following table representing the absenteeism of your fellow employees over the last
three years.
Year
2014
2015
2016
I
4
5
6
II
10
12
16
III
7
9
12
IV
3
4
4
A. Using the tables provided, calculate a four quarter moving average.
B. Calculate the seasonal indexes.
C. Deseasonalize the absenteeism and come up with a trend equation.
D. Predict the absenteeism for the four quarters of 2017.
3. For the actual and forecast values of a time series shown here, calculate MAD and SSE for both
models.
Period
Model 1
Model 2
Actual Value
1
78
82
85
2
75
78
67
3
71
73
75
4
76
81
83
If the goal is to choose a model that consistently produces moderately accurate forecasts, which
model would you choose?
4. A municipal bond service has three rating categories, A, B and C. Suppose that in the past year, of
the municipal bonds issued throughout Canada, 70% were rated A, 20% were rated B, and 10% were
rated C. Of the municipal bonds rated A, 50% were issued by cities, 40% by suburbs and 10% by rural
areas. Of the municipal bonds rated B, 60% were issued by cities, 20% by suburbs and 20% by rural
areas. Of the municipal bonds rated C, 90% were issued by cities, 5% by suburbs and 5% by rural
areas. Given that a city issued a bond, what is the probability it was Rated A?
Academic Success Centre
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These questions were compiled by Michael Reimer for the Academic Success Centre.
5. You have been asked to see if the machines are producing bags of corn chips that have 70 grams in
each bag. You test a bag coming off the production line every 15 minutes from 7am to 12pm. Here
are your results:
Hour
7 – 8 am
8 – 9 am
9 – 10 am
10 – 11 am
11 – 12 am
Bag 1
69
73
70
71
68
Bag 2
71
68
68
70
69
Bag 3
72
69
72
68
70
Bag 4
74
70
74
66
70
Complete a mean chart. Assume the S is 2.125.
6. You have been asked to test the quality control of your sandwich makers over the lunch time for
this past week. For each of the days you take a sample of 25 customers and ask them if they were
dissatisfied with their sandwich. Here are the results you obtained:
Day of the Week
Monday
Tuesday
Wednesday
Thursday
Friday
Number
Sampled
25
25
25
25
25
Dissatisfied
Customers
2
4
3
5
3
Calculate the upper and lower control limits.
7. An author is trying to choose between two publishing companies that are competing for the
marketing rights to her new novel. Company A has offered the author $10,000 plus $2 per book
sold. Company B has offered the author $2,000 plus $4 per book sold. The author believes that five
levels of demand for the book are possible: 1,000 (45%), 2,000 (20%), 5,000 (15%), 10,000 (10%), and
50,000 (10%).
A. Develop a Payoff Table
B. Compute the Expected Monetary Value for Companies A and B.
C. Compute the Expected Value of Perfect Information.
D Develop an Opportunity Lose Table.
E. Compute the Expected Opportunity Loss for Companies A and B.
F. Which company should this author go with?
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These questions were compiled by Michael Reimer for the Academic Success Centre.
8. A recently retired schoolteacher is meeting with an investment advisor to determine how to invest
her cash payout for unused sick days. The advisor presents two options, A and B. The payoff for
each option depends on possible changes in the bond rate, which can increase, decrease or stay the
same. The payoffs for the two options and the probabilities associated with the states of nature are
presented below:
Options
A
B
Probabilities
States
Increase
$-2,000
$4,000
0.5 (S1)
Of Nature
Decrease
$12,000
$ 2,000
0.2 (S2)
Stay the Same
$5,000
$3,000
0.3 (S3)
A. Calculate EMV*.
B. The investment advisor has hired an economist to forecast the bank rate. The economist’s past
record is as follows:
I1
I2
I3
P (FI/I) = 0.6
P (FI/D) = 0.4
P (FI/SS) = 0.5
P (FD/I) = 0.2
P (FD/D) = 0.5
P (FD/SS) = 0.1
P (FSS/I) = 0.2
P (FSS/D) = 0.1
P (FSS/SS) = 0.4
Where: FI = forecast increase
FD = forecast decrease
FSS = forecast stay the same
I = increase in bank rate
D = decrease in bank rate
SS = bank rate stays the same
The economist has forecast a decrease in the bank rate. Based on the past record of the economist,
recalculate the probabilities for each of the states of nature. (Round to 3 decimals)
C. Calculate the new expected monetary value (EMV) for each option.
D. Calculate the EMV`. Use your answers from b and c.
E. Calculate EVSI.
9. El Cheapo Glass Co. produces two products, doors and windows. El Cheapo Glass Co. uses three
different machines to produce these two items. Machine one has 14 hours available for use per day.
Machine two has 12 hours available for use per day. And, machine three has 18 hours available for
use per day. To produce a door, the company needs to use 2 hour of machine one, 1 hours of
machine two and 3 hours of machine three. To produce a window, the company needs to use 2
hours of machine one, 2 hours of machine two and 2 hours of machine three. The profit that the
company can realize on doors is $300 and on windows is $500.
A. Define the maximization equation.
B. Define the decision variables.
C. Define the constraint equations.
D. Graph the constraint equations.
E. Determine the extreme points.
F. Determine the optimal solution/maximum profit.
G. Determine which constraints are binding and which are non – binding.
H. Determine the shadow price of the binding constraints.
I. If a constraint is non – binding then what is its’ shadow price.
J. Determine the slack/surplus.
K. Determine the range of optimality.
L. In analyzing the machine 2 constraint, you determined that it could be increased by 6 or decreased
by 3. Specify the range of feasibility for machine 2.
Academic Success Centre
www.rrc.mb.ca/asc
These questions were compiled by Michael Reimer for the Academic Success Centre.
10. Consider the following Linear Programming Problem:
s.t.:
Department 1: 2A + 3B ≤ 1,500 Hours
Department 2: 3A + 2B ≤ 1,500 Hours
Department 3: A + B ≤ 540
A, B ≥ 0
The problem was solved by the computer program (Excel) discussed in the notes with the following results:
Variable Cells
Name
A
B
Constraints
Name
Department 1
Department 2
Department 3
Final
Value
120
420
Final
Value
1,500
1,200
540
Reduced
Cost
0
0
Shadow
Price
2.00
0.00
6.00
Objective
Coefficient
$10
$3
$12
$5
Allowable
Allowable
IncreaseDecrease
$3.50
$4.25
Constraint
Allowable
Right Hand Side IncreaseDecrease
1,500
400
220
1,500
1E + 30 300
540
260
140
Allowable
A. Determine the optimal quantities.
B. Determine the optimal solution/maximum profit.
C. Determine which constraints are binding and which are non – binding.
D. Determine the shadow price of the binding constraints.
E. If a constraint is non – binding then what is its’ shadow price.
F. Determine the slack/surplus.
G. Determine the range of optimality.
H. Determine the right hand side ranges (range of feasibility).
For each of the remaining questions, calculate the amount requested. If you cannot, then put “Rerun
the Model.”
I. If product A’s coefficient changed to $15, calculate the value of the optimal solution.
J. If product B’s coefficient changed to $8, calculate the value of the optimal solution.
K. If Department 1’s right – hand side changed to 1,850, calculate the change in the optimal solution.
L. If Department 2’s right – hand side changed to 1,175, calculate the change in the optimal solution.
M. If Department 3’s right – hand side changed to 425, calculate the change in the optimal solution.
N. If overtime can be scheduled for one of the departments, which department would you
recommend?
Academic Success Centre
www.rrc.mb.ca/asc
These questions were compiled by Michael Reimer for the Academic Success Centre.
2. A. Determine the seasonal adjusted indices for this data using the table provided. Answer all
the question marks.
Year Qt
2004 1
2
3
Sick Days
4
4 QT
MT
4 QT
MA
24
A=?
2005 1
2
7
27
6.75
29
7.25
5
12
2006 1
2
J=?
F=?
K=?
7
71.429
G=?
L=?
H=?
M=?
I=?
N=?
9.125
65.753
9.5
168.411
C=?
9
31
4
E=?
Deseasonalized
B=?
3
30
3
Seasonalized
10
25
4
CMA
D=?
4
35
8.75
38
9.5
6
16
38
3
12
4
4
9.5
2007 1
2
3
4
Academic Success Centre
www.rrc.mb.ca/asc
These questions were compiled by Michael Reimer for the Academic Success Centre.
b)
Answer all the question marks on the sheet.
Year
1
2004
2005 71.429
2006 65.753
2
162.712
168.411
3
114.289
118.0328
46.154
48.485
4
Total A=?
B=?
C=?
D=?
Total
Mean E=?
F=?
G=?
H=?
I=?
Seasonal J=?
Index
K=?
L=?
M=?
N=?
Correction Factor = 400/?
Seasonal Index Quarter 1:
Seasonal Index Quarter 2:
Seasonal Index Quarter 3:
Seasonal Index Quarter 4:
Academic Success Centre
www.rrc.mb.ca/asc
These questions were compiled by Michael Reimer for the Academic Success Centre.