Southwestern University Case Study 3. Develop a forecasting model, justifying it
ID: 385707 • Letter: S
Question
Southwestern University Case Study
3. Develop a forecasting model, justifying its selection over other techniques, and project attendance through 2017.
, 4.55-4.58 are cr 4.50-4.61 relate to Monitoring and Contralling Forecasts 100 80 4.9 Sales of tablet computers at Ted Ghckman's electron es store in Washington, D.C over the past 10 weeks are shown 104 105 DEMAND WEEK DEMAND 125 120 109 36 Decem 28 37 25 demand for each week. including week 10, using Additional prohlem 4.61 is available in MyOMLab tial smoothing with ,5 (initial forecast-20) What is the value of the tracking signal as of the end of December? 10 CASE STUDIES hired as its head coach in 2009 (in hopes of reaching the elusive number 1 each year incre by 10,000 just with the announcement of Stephenville and SWU were read Southwestern University: (B)* ollege in Stephenville, Texas, enrolls close to 20,000 students. The school is a dominant force in the small city, with more students during fall 20 in college football rankings. Since the legendary Phil Flamm was dance at the five Saturday home games mm's arrival, attendance generally 9.000 per game. Season ticket sales bumped up estern University (SWU), a large state c ranking), attend ased. Prior to Fla and spring than permanent residents. the new coach's arrival. Always a fothall owerhoume, SW U is usually in the top 20 by 000 ith the aount of the new soa Always a football powerhouse, SWU is usually in the top y to move to the big time! Southwestern University Football Game Attendance, 2010-2015 2010 2011 2012 GAME ATTENDEES OPPONENT ATTENDEES OPPONENT ATTENDEES OPPONENT 34.200 Rice 39,800 Texas 38,200 Duke 26,900 Arkansas 35,100 TCU 36,100 Miami 40,200 Nebraska 39,100 Ohio State 25,300 Nevada 36,200 Boise State 35,900 USC 46,500 Texas Tech 43,100 Alaska 27,900 Arizona 39,200 Baylor 2013 2014 2015 ATTENDEES OPPONENT GAME ATTENDEES OPPONENT 41,900 Arkansas 46,100 Missouri 43,900Florida 30,100Central ATTENDEES OPPONENT 42,500 Indian 46,900 LSU 48,200 North Texas 50,100 Texas 33,900 Southern 47,800 Oklahoma 4,200 Texas ABM 45900 South Flonida 45,900 South Florida 36,300 Montana Florida 40,500LSU 49,900 Arizona State " Homecoming games During the fourth week of each season, Stephenville hosted a hugely popular southwestern crafts fes- tival. This event brought tens of thousands of tourists to the town, especially on weekends, and had an obvious negative impact on game attendanceExplanation / Answer
. The time-series forecasting method “Trend projection” will fit in this case. In the trend projection, a trend line to a series of historical data points can be drawn and then we can project the line into the future for medium to long-range forecasts. We can have separate forecasting model or equation for each game. We will have a forecasting equation for each of the game and then we can project the data/line that into the future.
Game 1:
Game 1/Year
Year Ranked
Attendance
x2
y2
xy
2010
1
34200
1
1169640000
34200
2011
2
36100
4
1303210000
72200
2012
3
35900
9
1288810000
107700
2013
4
41900
16
1755610000
167600
2014
5
42500
25
1806250000
212500
2015
6
46900
36
2199610000
281400
x/n
3.50
y/n
39583.33
x2
91
xy
875600
y2
9523130000
B
2534.286
a
30713.333
r ( Correlation Coefficient)
0.959
coefficient of determination (r2)
0.921
Game 2:
Game 1/Year
Year Ranked
Attendance
x2
y2
xy
2010
1
39800
1
1584040000
39800
2011
2
40200
4
1616040000
80400
2012
3
46500
9
2162250000
139500
2013
4
46100
16
2125210000
184400
2014
5
48200
25
2323240000
241000
2015
6
50100
36
2510010000
300600
x/n
3.50
y/n
45150.00
x2
91
xy
985700
y2
12320790000
b
2145.714
a
37640.000
r ( Correlation Coefficient)
0.948
coefficient of determination (r2)
0.899
Game 3:
Game 1/Year
Year Ranked
Attendance
x2
y2
xy
2010
1
38200
1
1459240000
38200
2011
2
39100
4
1528810000
78200
2012
3
43100
9
1857610000
129300
2013
4
43900
16
1927210000
175600
2014
5
44200
25
1953640000
221000
2015
6
45900
36
2106810000
275400
x/n
3.50
y/n
42400.00
x2
91
xy
917700
y2
10833320000
b
1560.000
a
36940.000
r ( Correlation Coefficient)
0.954
coefficient of determination (r2)
0.911
Game 4:
Game 1/Year
Year Ranked
Attendance
x2
y2
xy
2010
1
26900
1
723610000
26900
2011
2
25300
4
640090000
50600
2012
3
27900
9
778410000
83700
2013
4
30100
16
906010000
120400
2014
5
33900
25
1149210000
169500
2015
6
36300
36
1317690000
217800
x/n
3.50
y/n
30066.67
x2
91
xy
668900
y2
5515020000
b
2142.857
a
22566.667
r ( Correlation Coefficient)
0.940
coefficient of determination (r2)
0.883
Game 5:
Game 1/Year
Year Ranked
Attendance
x2
y2
xy
2010
1
35100
1
1232010000
35100
2011
2
36200
4
1310440000
72400
2012
3
39200
9
1536640000
117600
2013
4
40500
16
1640250000
162000
2014
5
47800
25
2284840000
239000
2015
6
49900
36
2490010000
299400
x/n
3.50
y/n
41450.00
x2
91
xy
925500
y2
10494190000
b
3145.714
a
30440.000
r ( Correlation Coefficient)
0.966
coefficient of determination (r2)
0.933
Forecasting Model/Equation:
Taking the value of x as 7 for 2016
and 8 for 2017 and thus getting the
value for 2016 and 2017
(y = attendance and x = time)
Forecasting Model/Equation
Game
Model
2010
2011
R2
1
y = 30,713 + 2,534x
48451
50985
0.921
2
y = 37,640 + 2,146x
52662
54808
0.899
3
y = 36,940 + 1,560x
47860
49420
0.911
4
y = 22,567 + 2,143x
37567
39711
0.883
5
y = 30,440 + 3,146x
52462
55608
0.933
Total
239003
250532
(Where y = attendance and x = time)
Game 1/Year
Year Ranked
Attendance
x2
y2
xy
2010
1
34200
1
1169640000
34200
2011
2
36100
4
1303210000
72200
2012
3
35900
9
1288810000
107700
2013
4
41900
16
1755610000
167600
2014
5
42500
25
1806250000
212500
2015
6
46900
36
2199610000
281400
x/n
3.50
y/n
39583.33
x2
91
xy
875600
y2
9523130000
B
2534.286
a
30713.333
r ( Correlation Coefficient)
0.959
coefficient of determination (r2)
0.921
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