QM 662 Exam II
1. The table below features three forecasting models used on the same set of data.
Model 1
Model 2
Model 3
Type
Exponential
Smoothing
Regression
Seasonal & Trend
MSE
8755.3
4876.2
5945.8
Based solely on the information in this output, which of the following is the best answer? (5)
a.
b.
c.
d.
e.
The data set contains no trend or seasonality.
The data set contains trend but no seasonality.
The data set contains seasonality but no trend.
The data set probably contains cyclicality.
The data set contains both trend and seasonality.
2. In a forecasting application for 20 time periods, there are 10 negative errors and 10
positive errors. This indicates the model is performing well. (2)
a. True
b. False
3. Refer to the following graph:
Quarterly Sales (in $)
70000
60000
50000
40000
30000
20000
10000
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
Which of the following apply? (8)
a.
b.
c.
d.
The data contain a trend component.
The data contain a seasonal component.
The data ,contain a cyclical component.
The data contain an irregular (random) component.
4. In #3, which method (if any) is most appropriate? (4)
a.
b.
c.
d.
Exponential smoothing.
Regression.
Regression with seasonal indices.
None of the above.
5. In #3, which of the following is most appropriate regarding sales? (4)
a.
b.
c.
d.
e.
We should use all of the data in our model.
We should use only periods 5-16 in our model.
We should use only periods 9-16 in our model.
We should use only periods 13-16 in our model.
We should use only periods 1-12 in our model.
6. Refer to the Excel output on the final pages. Here, we are tracking the number of orders
placed by week for a 20-week period. The first set of output is for an exponential
smoothing model with α = 0.25. The second set of output is for a regression. Which of
the following is most appropriate? (3)
a. The exponential smoothing model is most appropriate.
b. The regression is most appropriate.
c. Another model would be more appropriate.
7. The model with the lower MSE is always the most appropriate model. (2)
a. True
b. False
8. In a given application, we are using regression with seasonal indices. The regression
model is y = 42 + 2.5t. The seasonal indices for quarters 1-4 are 0.85, 0.92, 0.98, and
1.25, respectively. The predicted value for period 20 is ___________. (5)
9. If our data contains seasonality but no trend, exponential smoothing is appropriate. (2)
a. True
b. False
10. Annual data can exhibit seasonality. (2)
a. True
b. False
11. We can assess quarterly seasonality with one year of data. (2)
a. True
b. False
Week
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
Orders
45
56
65
63
54
60
54
60
56
57
50
61
47
56
55
Forecast
#N/A
45
47.75
52.0625
54.79688
54.59766
55.94824
55.46118
56.59589
56.44691
56.58519
54.93889
56.45417
54.09063
54.56797
Error
#N/A
11
17.25
10.9375
-0.79688
5.402344
-1.94824
4.538818
-0.59589
0.553085
-6.58519
6.06111
-9.45417
1.909375
0.432031
Error^2
121
297.5625
119.6289
0.63501
29.18532
3.795648
20.60087
0.35508
0.305903
43.36467
36.73706
89.38128
3.645712
0.186651
16
17
18
19
20
52
57
58
61
47
54.67598
54.00698
54.75524
55.56643
56.92482
-2.67598
2.993017
3.244763
5.433572
-9.92482
7.160852
8.958153
10.52849
29.52371
98.50207
MSE =
48.47673
SUMMARY OUTPUT
Regression Statistics
Multiple R
R Square
Adjusted R Square
Standard Error
Observations
0.139263
0.019394
-0.03508
5.524367
20
ANOVA
df
1
18
19
SS
10.86466
549.3353
560.2
Coefficients
57.04211
-0.12782
Standard
Error
2.566242
0.214226
Regression
Residual
Total
Intercept
Week
MS
10.86466
30.51863
F
0.356001
t Stat
22.22787
-0.59666
P-value
1.54E-14
0.558166
Exponential Smoothing
70
60
Orders
50
40
30
Actual
20
Forecast
10
0
1
3
5
7
9
11 13 15 17 19
Week
Significance F
0.558166112
Data for Samantha's Super Sectional Sofas
Quarter
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
%Defective
7,31
6,19
7,44
6,61
7,33
7,43
6,74
7,35
6,86
11,40
6,08
6,65
8,24
7,33
6,27
7,03
7,52
7,80
7,21
7,23
7,27
6,92
7,55
7,75
Note: These data represent her percentage of defective units produced for each quarter.
Data for Colleen's Cajun Cannery
Week
1
2
3
4
5
6
7
8
9
10
11
12
13
# OT Hours
13
16
18
17
19
21
23
22
25
29
34
42
55
Note: These data represent her weekly number of overtime hours used.
Simpson's Inc.
Quarter
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
# of rolls
ordered
56
48
58
67
59
51
64
71
73
67
78
84
77
70
82
89
83
74
84
93
86
78
85
93
Note: Simpson's produces nonwoven fabric rolls.
Sally's Sensational Stationery Sales Data
Quarter
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
Sales
6455
8779
13897
18920
24225
26190
27440
37562
29895
29120
28540
39985
33255
32110
30875
41234
36476
34860
32197
43940
39723
37890
35230
46115
41432
39243
36922
Note: The sales figures are in dollars.
Data for Upper Flutzland
Year
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
GDP
62,6
66,7
68,8
64,5
63,2
55,6
54,5
63,8
65,3
67,4
65,9
78,9
80,8
81,3
82,5
Note: These data are the real GDP (in $000,000,000) indexed to Year 1 dollars.
Forecasting Homework
1. For each of the five worksheets on here, answer the following:
a. What forecasting method is most appropriate? Explain.
b. Use the method indicated in a., and discuss the efficacy of the model (i.e., how well does it fit the data).
c. What is your recommendation regarding future forecasts?
2. Discuss at least two potential application of forecasting in your job or field.
es it fit the data).
Forecasting Homework
1. For each of the five worksheets on here, answer the following:
a. What forecasting method is most appropriate? Explain.
b. Use the method indicated in a., and discuss the efficacy of the model (i.e., how well does it fit the data).
c. What is your recommendation regarding future forecasts?
2. Discuss at least two potential applications of forecasting in your job or field.
1. Forecasting monthly registrations in the Commercial Vehicle Training Program and other program areas that have regularly s
2. Forecasting quarterly registrations in all program areas (our Continuing Ed catalogs and "terms" are set up quarterly)
3. Forecasting expense budgets of consumable supplies in large program areas with significant consumable material costs (for
(comments are also made on some of the five worksheets)
r program areas that have regularly scheduled monthly classes
icant consumable material costs (for "instructional/student supplies)
Data for Samantha's Super Sectional Sofas
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
%Defective
7.31
6.19
7.44
6.61
7.33
7.43
6.74
7.35
6.86
11.40
6.08
6.65
8.24
7.33
6.27
7.03
7.52
7.80
7.21
7.23
7.27
6.92
7.55
7.75
% Defective Scatterplot
% Defective
Quarter
y = 0.0129x + 7.1518
R² = 0.008
12.00
10.00
8.00
6.00
4.00
2.00
0.00
Series1
Linear (Series1)
0
5
10
15
20
25
30
Quarter
Note: These data represent her percentage of defective units produced for each quarter.
Excel Single Parameter Exponential Smoothing - EXAMPLE FOR COMPARISON WITH……
a = 0.10
Period=Quarter
Excel Damping Factor = 1 - α (1 - .10 = .90)
Period Percent % Forecast
Defective, Yt Sales, Ft
t
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
7.31
6.19
7.44
6.61
7.33
7.43
6.74
7.35
6.86
11.40
6.08
6.65
8.24
7.33
6.27
7.31
7.20
7.22
7.16
7.18
7.20
7.16
7.18
7.14
7.57
7.42
7.34
7.43
7.42
Management Scientist FORECASTING WITH EXPONENTIAL SMOOTHING
**************************************
THE SMOOTHING CONSTANT IS 0.1
Forecast
Error
-1.12
0.24
-0.61
0.17
0.25
-0.46
0.19
-0.32
4.26
-1.49
-0.77
0.90
-0.10
-1.16
TIME PERIOD
=======
Instead of a smoothing constant,
Excel uses a Dampin g Factor,
which is shown above.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
TIME SERIES VALUE
=======
7.31
6.19
7.44
6.61
7.33
7.43
6.74
7.35
6.86
11.40
6.08
6.65
8.24
7.33
6.27
FORECAST
========
7.31
7.20
7.22
7.16
7.18
7.20
7.16
7.18
7.14
7.57
7.42
7.34
7.43
7.42
FORECAST ERROR
========
-1.12
0.24
-0.61
0.17
0.25
-0.46
0.19
-0.32
4.26
-1.49
-0.77
0.90
-0.10
-1.15
16
17
18
19
20
21
22
23
24
25
7.03
7.52
7.80
7.21
7.23
7.27
6.92
7.55
7.75
7.31
7.28
7.30
7.35
7.34
7.33
7.32
7.28
7.31
7.35
-0.28
0.24
0.50
-0.14
-0.11
-0.06
-0.40
0.27
0.44
0.43 Sum of Forecast Errors
16
17
18
19
20
21
22
23
24
7.03
7.52
7.80
7.21
7.23
7.27
6.92
7.55
7.75
7.31
7.28
7.30
7.35
7.34
7.33
7.32
7.28
7.31
0.00 Sum of Forecast Errors
THE MEAN SQUARE ERROR
MSE =
-0.28
0.24
0.50
-0.14
-0.11
-0.06
-0.40
0.27
0.44
1.13
1.13
THE FORECAST FOR PERIOD 25
7.35
Model Comparison Table - Exponential Smoothing - (See worksheets)
ES - α .10 ES - α .20 ES - α .30
MSE
Forecast for Period 25
1.13
7.35
1.24
7.39
1.35
7.43
a. What forecasting method is most appropriate? Explain.
No linear (pos or neg) trend based on scatterplot. Would use
exponential smoothing based on appearance of the scatterplot.
Based on Model Comparions the Exponential Smoothing using smoothing constant of .10
(in Excel damping factor .90 ((1 - .10)) is the best model.
b. Use the method indicated in a., and discuss the efficacy of the model (i.e., how well does it fit the data).
Fits well as there are no large differences between forecast and actuals except for
the outlier in period 10.
Residuals are both negative and positive with no obvious patterns
Forecast errors (residuals) sum to zero.
c. What is your recommendation regarding future forecasts?
Use exponential smoothing based on previous 12 periods (3 yrs - qtrly data),
unless series of unusual spikes occur. In this case, using the most current data
can produce even lower MSE (minimum data needed is at least 2 yrs.
to test for presence of repeated seasonal trend)
3. Discuss at least two potential applications of forecasting in your job or field.
Forecasting monthly utility and fuel consumption in CDL program
and forecasting monthly equipment maintenance and repair expenses
FORECASTING WITH EXPONENTIAL SMOOTHING
**************************************
THE SMOOTHING CONSTANT IS 0.1
TIME PERIOD TIME SERIES VALUE
===========
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
FORECAST
=================
7.31
6.19
7.44
6.61
7.33
7.43
6.74
7.35
6.86
11.40
6.08
6.65
8.24
7.33
6.27
7.03
7.52
7.80
7.21
7.23
7.27
6.92
7.55
7.75
7.31
7.20
7.22
7.16
7.18
7.20
7.16
7.18
7.14
7.57
7.42
7.34
7.43
7.42
7.31
7.28
7.30
7.35
7.34
7.33
7.32
7.28
7.31
THE MEAN SQUARE ERROR
THE FORECAST FOR PERIOD 25
FORECAST ERROR
========
-1.12
0.24
-0.61
0.17
0.25
-0.46
0.19
-0.32
4.26
-1.49
-0.77
0.90
-0.10
-1.15
-0.28
0.24
0.50
-0.14
-0.11
-0.06
-0.40
0.27
0.44
1.13
7.35
FORECASTING WITH EXPONENTIAL SMOOTHING
**************************************
THE SMOOTHING CONSTANT IS 0.2
TIME PERIOD
===========
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
TIME SERIES VALUE
=================
7.31
6.19
7.44
6.61
7.33
7.43
6.74
7.35
6.86
11.40
6.08
6.65
8.24
7.33
6.27
7.03
7.52
7.80
7.21
7.23
7.27
6.92
7.55
7.75
7.31
7.09
7.16
7.05
7.10
7.17
7.08
7.14
7.08
7.95
7.57
7.39
7.56
7.51
7.26
7.22
7.28
7.38
7.35
7.32
7.31
7.23
7.30
THE MEAN SQUARE ERROR
THE FORECAST FOR PERIOD 25
FORECAST FORECAST ERROR
======== ==============
-1.12
0.35
-0.55
0.28
0.33
-0.43
0.27
-0.28
4.32
-1.87
-0.92
0.85
-0.23
-1.24
-0.23
0.30
0.52
-0.17
-0.12
-0.05
-0.39
0.32
0.45
1.24
7.39
FORECASTING WITH EXPONENTIAL SMOOTHING
**************************************
THE SMOOTHING CONSTANT IS 0.3
TIME PERIOD
===========
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
TIME SERIES VALUE
=================
7.31
6.19
7.44
6.61
7.33
7.43
6.74
7.35
6.86
11.40
6.08
6.65
8.24
7.33
6.27
7.03
7.52
7.80
7.21
7.23
7.27
6.92
7.55
7.75
7.31
6.97
7.11
6.96
7.07
7.18
7.05
7.14
7.06
8.36
7.67
7.37
7.63
7.54
7.16
7.12
7.24
7.41
7.35
7.31
7.30
7.19
7.30
THE MEAN SQUARE ERROR
THE FORECAST FOR PERIOD 25
FORECAST FORECAST ERROR
======== ==============
-1.12
0.47
-0.50
0.37
0.36
-0.44
0.30
-0.28
4.34
-2.28
-1.02
0.87
-0.30
-1.27
-0.13
0.40
0.56
-0.20
-0.12
-0.04
-0.38
0.36
0.45
1.35
7.43
Data for Colleen's Cajun Cannery
Week
1
2
3
4
5
6
7
8
9
10
11
12
13
# OT Hours
13
16
18
17
19
21
23
22
25
29
34
42
55
60
#
50
O 40
T 30
20
H
10
16
o
13
u 0
0
r
s
Note: These data represent her weekly number of overtime hours used.
Forecasting Thumbnail Notes - Page 1
1.
Determine if the response variable tends to vary over time in some repeatable pattern. If not, consider other statistical m
QM 670 Class Notes - Page 2 Scatterplot Examples
➢
➢
Positive
Nonlinear
Refer to Section 2.3 of QM 670 Class Notes (Other Model Types)
a. What forecasting method is most appropriate? Explain.
Because Colleen's data scatterplot shows an upward curve in the data, the data is non-linear and therefore out-of-scope for the
models we are using in this class. It is very important to choose the most appropriate model based on the characteristics displa
Refer to Section 2.3 and 3.0 of QM 670 Class Notes and the Forecasting Thumbnail Notes located in the Forecasting M
Colleen's
y = 2.7198x + 6.6538
R² = 0.8
55
42
13
25
21 23 22
19
16 18 17
5
29
# OT Hours
Linear (# OT Hours)
10
Week
34
15
Quarter
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
# of rolls
ordered
56
48
58
67
59
51
64
71
73
67
78
84
77
70
82
89
83
74
84
93
86
78
85
93
Note: Simpson's produces nonwoven fabric rolls.
# of rolls ordered (scatterplot)
100
90
80
# of Rolls Ordered
Simpson's Inc.
y = 1.5843x + 53.946
R² = 0.7536
70
60
50
# of rolls ordered
40
Linear (# of rolls ordered)
30
20
10
0
0
5
10
15
20
25
30
Quarter
Time Series Components (From Forecasting Thumbnail Notes)
1.
Trend – a gradual increase or decrease over time
2.
Seasonal – a pattern over a period of a year or less. The recurrence of the pattern will be seen over periods of more than a year.
3.
Cyclical – a pattern over a period of more than a year (generally many years)
4.
Irregular (random) – departures from a “perfect” recurring pattern
The irregular component will be present in any set of “real” data. In most cases, you will not encounter cyclical data unless your data covers a large time horizon.
When cyclical patterns exist, we often use the most recent data to develop our forecasts.
a. What forecasting method is most appropriate? Explain.
Because the scatterplot displays irregularity, trend and seasonality, the "Trend with Seasonal" forecasting (Classical Time Series) model is most appropriate.
b. Use the method indicated in a., and discuss the efficacy of the model (i.e., how well does it fit the data).
Some large forecasting errors and obvious patterns in negative and positive forecast values during first and and last two years.
Model does not fit as well as it could with adjustment .
Refer to "answer c" and "Trend w Season - 4 years" worksheet
c. What is your recommendation regarding future forecasts?
Examine the scatterplot chart and notice that the seasonal pattern begins to stabilize in quarter 9.
Drop the oldest data that occurs before the seasonal pattern stabilizes (in this case, the first 8 quarters);
Run the analysis again using the last 4 years of data.
The MSE drops and the forecasting errors stabilize. There are an equal number of positive and negative
errors, no large errors, no obvious forecast error patterns and errors sum to 0.
In the future I would examine the scatterplot data closely and be sure to adjust the input data according to the latest trend and seasonality patterns,
eliminating older data when these patterns change (To insure the recurrence of quarterly seaonality you need at least 2 years of data)..
FORECASTING WITH TREND AND SEASONAL COMPONENTS
**********************************************
SEASON
SEASONAL INDEX
------------------1
2
3
4
TIME
PERIOD
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
1.005
0.886
1.013
1.097
TIME SERIES
VALUE
56
48
58
67
59
51
64
71
73
67
78
84
77
70
82
89
83
74
84
93
86
78
85
93
FORECAST FORECAST
ERROR
56.50
51.15
60.00
66.65
62.60
56.53
66.15
73.31
68.71
61.92
72.30
79.98
74.81
67.30
78.45
86.64
80.91
72.68
84.60
93.30
87.02
78.06
90.75
99.96
THE MEAN SQUARE ERROR
THE FORECAST FOR PERIOD 25
THE FORECAST FOR PERIOD 26
THE FORECAST FOR PERIOD 27
THE FORECAST FOR PERIOD 28
-0.50
-3.15
-2.00
0.35
-3.60
-5.53
-2.15
-2.31
4.29
5.08
5.70
4.02
2.19
2.70
3.55
2.36
2.09
1.32
-0.60
-0.30
-1.02
-0.06
-5.75
-6.96
11.68
93.12
83.44
96.90
106.62
FORECASTING WITH TREND AND SEASONAL COMPONENTS
**********************************************
SEASON
SEASONAL INDEX
------------------1
2
3
4
TIME
PERIOD
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
1.000
0.895
1.014
1.091
TIME SERIES
VALUE
73
67
78
84
77
70
82
89
83
74
84
93
86
78
85
93
FORECAST FORECAST
ERROR
74.54
67.48
77.33
84.16
77.96
70.54
80.80
87.89
81.37
73.60
84.27
91.62
84.79
76.66
87.73
95.35
THE MEAN SQUARE ERROR
THE FORECAST FOR PERIOD 17
THE FORECAST FOR PERIOD 18
THE FORECAST FOR PERIOD 19
THE FORECAST FOR PERIOD 20
-1.54
-0.48
0.67
-0.16
-0.96
-0.54
1.20
1.11
1.63
0.40
-0.27
1.38
1.21
1.34
-2.73
-2.35
1.75
88.21
79.72
91.20
99.08
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