# Chapter 1 Chapter 4 – Forecasting … Case Study #2 Markov Processes Case Study 2: Forecasting Box Office Returns For years, people in the motion picture industry – critics, film historians, and others...

Chapter 1
Chapter 4 – Forecasting … Case Study #2
Markov Processes
Case Study 2: Forecasting Box Office Returns
For years, people in the motion picture industry – critics, film historians, and others – have eagerly awaited the second issue in January of Variety. Long considered the show business bible, Variety is a weekly trade newspaper that reports on all aspects of the entertainment industry; movies, television, recordings, concert tours, and so on. The second issue in January, called the Anniversary Edition, summarizes how the entertainment industry fared in the previous year, both artistically and commercially.
In this issue, Variety publishes its list of All Time Film Rental Champs. This list indicates, in descending order, motion pictures and the amount of money they returned to the studio. Because a movie theater rents a film from a studio for a limited time, the money paid for admission by ticket buyers is split between the studio and theater owner. For example, if a ticket buyer pays \$12 to see a particular movie, the theater owner keeps about \$6 and the studio receives the other \$6. The longer a movie plays in a theater, the greater the percentage of the admission price returned to the studio. A film playing for an entire summer could eventually return as much as 90% of the \$12 to the studio. The theater owner also benefits from such a success because although the owner’s percentage of the admission price is small, the sales of concessions (candy, soda and so on) provide greater profits. Thus, both the studio and the theater owner win when a film continues to draw audiences for a long time. Variety lists the rental figures (the actual dollar amounts returned to the studios) that the films have accrued in their domestic releases (United States and Canada).
In addition, Variety provides a monthly Box-Office Barometer of the film industry, which is a profile of the month’s domestic box-office returns. This profile is not measured in dollars, but scaled according to some standard. By the late 1980’s, for example, the scale was based on numbers around 100, with 100 representing the average box-office return of 1990. The figures from 1997 to 2006 are given in the table below and in the file BoxOffice.xlsx in blackboard.
All the figures are scaled around the 1990’s box-office returns, but instead of dollars, artificial numbers are used. Film executives can get a relative indication of the box-office figures compared to the a
itrary 1990 scale. For example, in January 1997 the box-office returns to the film industry were 95% of the average that year, whereas in January 1998 the returns were 104% of the average of 1990 (or, they were 4% above the average of 1990’s figure).
Month
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
Jan
104
101
88
132
125
111
127
119
147
145
Fe
100
96
110
109
118
123
129
147
146
149
Ma
99
82
129
101
121
121
132
164
133
148
Ap
88
84
113
111
140
139
108
135
148
148
May
89
85
114
140
141
119
115
124
141
148
Jun
108
124
169
179
201
156
149
168
191
201
Jul
109
134
131
145
152
154
155
159
178
184
Aug
101
109
139
140
138
136
129
137
156
166
Sep
106
121
120
120
137
105
117
149
119
151
Oct
102
111
115
129
138
132
166
159
138
166
Nov
78
101
116
118
144
123
152
175
175
170
Dec
111
112
128
139
148
164
173
195
188
194
From the time series given in the above table, you will make a forecast for the 12 months of the next year, 2007.
Managerial Report
1. Produce a time series plot of the data. From this graph, do you see a pattern? Can you see any seasonality in the data?
2. Use exponential smoothing to fit the data. Select an appropriate constant  based on the variation you see in the data. Comment on the appropriateness of exponential smoothing on this data set. Plot the predictions from this model on the graph with the original data. How well does this technique fit the data? Make forecasts for each month in 2007.
3. Use regression to build a linear trend model. Comment on the goodness-of-fit of this model to the data (or, how well does R2 explain the variance in the data?). Plot the predictions from this model on the graph with the original data.
4. Develop multiplicative seasonal indices for the linear trend model developed in question 3. Use these indices to adjust predictions from the linear trend model from question 3 above for seasonal effects. Plot the predictions from this model on the graph with the original data. How well does this technique fit the data? Make forecasts for the next 12 months of 2007 using this technique.
5. Which forecasting method of those that you tried do you have the most confidence for making accurate forecasts for 2007? Use MAPE (mean absolute percent e
Enrichment (5 pts): Use Optimization (and Solver in Excel) to find the optimal smoothing constant in problem 2 above (by minimizing the Mean Squared E
or or MSE).

Forecasting Case Study #2
Box-Office Returns
Month    1997    1998    1999    2000    2001    2002    2003    2004    2005    2006
Jan    104    101    88    132    125    111    127    119    147    145
Feb    100    96    110    109    118    123    129    147    146    149
Mar    99    82    129    101    121    121    132    164    133    148
Apr    88    84    113    111    140    139    108    135    148    148
May    89    85    114    140    141    119    115    124    141    148
Jun    108    124    169    179    201    156    149    168    191    201
Jul    109    134    131    145    152    154    155    159    178    184
Aug    101    109    139    140    138    136    129    137    156    166
Sep    106    121    120    120    137    105    117    149    119    151
Oct    102    111    115    129    138    132    166    159    138    166
Nov    78    101    116    118    144    123    152    175    175    170
Dec    111    112    128    139    148    164    173    195    188    194
Answered 4 days AfterApr 04, 2022

## Solution

Rochak answered on Apr 09 2022
Forecasting Case Study #2
Box-Office Returns
Month    1997    1998    1999    2000    2001    2002    2003    2004    2005    2006
Jan    104    101    88    132    125    111    127    119    147    145
Feb    100    96    110    109    118    123    129    147    146    149
Mar    99    82    129    101    121    121    132    164    133    148
Apr    88    84    113    111    140    139    108    135    148    148
May    89    85    114    140    141    119    115    124    141    148
Jun    108    124    169    179    201    156    149    168    191    201
Jul    109    134    131    145    152    154    155    159    178    184
Aug    101    109    139    140    138    136    129    137    156    166
Sep    106    121    120    120    137    105    117    149    119    151
Oct    102    111    115    129    138    132    166    159    138    166
Nov    78    101    116    118    144    123    152    175    175    170
Dec    111    112    128    139    148    164    173    195    188    194
Exponential Smoothing
Month    Box-Office Returns    Exponential Smoothing (a=0.17)
Jan-97    104    104
Feb-97    100    104
Mar-97    99    103
Apr-97    88    103
May-97    89    100
Jun-97    108    98
Jul-97    109    100
Aug-97    101    101
Sep-97    106    101
Oct-97    102    102
Nov-97    78    102
Dec-97    111    98
Jan-98    101    100
Feb-98    96    100
Mar-98    82    100
Apr-98    84    97
May-98    85    94
Jun-98    124    93
Jul-98    134    98
Aug-98    109    104
Sep-98    121    105
Oct-98    111    108
Nov-98    101    108
Dec-98    112    107
Jan-99    88    108
Feb-99    110    105
Mar-99    129    105
Apr-99    113    109
May-99    114    110
Jun-99    169    111
Jul-99    131    121
Aug-99    139    122
Sep-99    120    125
Oct-99    115    124
Nov-99    116    123
Dec-99    128    122
Jan-00    132    123
Feb-00    109    124
Mar-00    101    122
Apr-00    111    118
May-00    140    117
Jun-00    179    121
Jul-00    145    131
Aug-00    140    133
Sep-00    120    134
Oct-00    129    132
Nov-00    118    131
Dec-00    139    129
Jan-01    125    131
Feb-01    118    130
Mar-01    121    128
Apr-01    140    127
May-01    141    129
Jun-01    201    131
Jul-01    152    143
Aug-01    138    144
Sep-01    137    143
Oct-01    138    142
Nov-01    144    142
Dec-01    148    142
Jan-02    111    143
Feb-02    123    138
Mar-02    121    135
Apr-02    139    133
May-02    119    134
Jun-02    156    131
Jul-02    154    135
Aug-02    136    139
Sep-02    105    138
Oct-02    132    133
Nov-02    123    132
Dec-02    164    131
Jan-03    127    136
Feb-03    129    135
Mar-03    132    134
Apr-03    108    134
May-03    115    129
Jun-03    149    127
Jul-03    155    131
Aug-03    129    135
Sep-03    117    134
Oct-03    166    131
Nov-03    152    137
Dec-03    173    139
Jan-04    119    145
Feb-04    147    141
Mar-04    164    142
Apr-04    135    146
May-04    124    144
Jun-04    168    140
Jul-04    159    145
Aug-04    137    147
Sep-04    149    146
Oct-04    159    146
Nov-04    175    148
Dec-04    195    153
Jan-05    147    160
Feb-05    146    158
Mar-05    133    156
Apr-05    148    152
May-05    141    151
Jun-05    191    150
Jul-05    178    157
Aug-05    156    160
Sep-05    119    160
Oct-05    138    153
Nov-05    175    150
Dec-05    188    154
Jan-06    145    160
Feb-06    149    158
Mar-06    148    156
Apr-06    148    155
May-06    148    154
Jun-06    201    153
Jul-06    184    161
Aug-06    166    165
Sep-06    151    165
Oct-06    166    163
Nov-06    170    163
Dec-06    194    164
Jan-07        169
Feb-07        174
Mar-07        177
Apr-07        180
May-07        182
Jun-07        184
Jul-07        186
Aug-07        187
Sep-07        188
Oct-07        189
Nov-07        190
Dec-07        191
Box-Office Returns    35431    35462    35490    35521    35551    35582    35612    35643    35674    35704    35735    35765    35796    35827    35855    35886    35916    35947    35977    36008    36039    36069    36100    36130    36161    36192    36220    36251    36281    36312    36342    36373    36404    36434    36465    36495    36526    36557    36586    36617    36647    36678    36708    36739    36770    36800    36831    36861    36892    36923    36951    36982    37012    37043    37073    37104    37135    37165    37196    37226    37257    37288    37316    37347    37377    37408    37438    37469    37500    37530    37561    37591    37622    37653    37681    37712    37742    37773    37803    37834    37865    37895    37926    37956    37987    38018    38047    38078    38108    38139    38169    38200    38231    38261    38292    38322    38353    38384    38412    38443    38473    38504    38534    38565    38596    38626    38657    38687    38718    38749    38777    38808    38838    38869    38899    38930    38961    38991    39022    39052    104    100    99    88    89    108    109    101    106    102    78    111    101    96    82    84    85    124    134    109    121    111    101    112    88    110    129    113    114    169    131    139    120    115    116    128    132    109    101    111    140    179    145    140    120    129    118    139    125    118    121    140    141    201    152    138    137    138    144    148    111    123    121    139    119    156    154    136    105    132    123    164    127    129    132    108    115    149    155    129    117    166    152    173    119    147    164    135    124    168    159    137    149    159    175    195    147    146    133    148    141    191    178    156    119    138    175    188    145    149    148    148    148    201    184    166    151    166    170    194    Exponential Smoothing    35431    35462    35490    35521    35551    35582    35612    35643    35674    35704    35735    35765    35796    35827    35855    35886    35916    35947    35977    36008    36039    36069    36100    36130    36161    36192    36220    36251    36281    36312    36342    36373    36404    36434    36465    36495    36526    36557    36586    36617    36647    36678    36708    36739    36770    36800    36831    36861    36892    36923    36951    36982    37012    37043    37073    37104    37135    37165    37196    37226    37257    37288    37316    37347    37377    37408    37438    37469    37500    37530    37561    37591    37622    37653    37681    37712    37742    37773    37803    37834    37865    37895    37926    37956    37987    38018    38047    38078    38108    38139    38169    38200    38231    38261    38292    38322    38353    38384    38412    38443    38473    38504    38534    38565    38596    38626    38657    38687    38718    38749    38777    38808    38838    38869    38899    38930    38961    38991    39022    39052    104    104    103.32    102.58559999999999    100.10604799999999    98.218019839999982    99.880956467199979    101.43119386777597    101.35789091025406    102.14704945551085    102.12205104807401    98.021302369901434    100.22768096701819    100.35897520262509    99.617949418178824    96.622898017088417    94.47700535418339    92.865914443972216    98.15870898849694    104.25172846045245    105.05893462217553    107.76891573640569    108.31820006121671    107.07410605080987    107.9115080221722    104.52655165840292    105.45703787647443    109.45934143747378    110.06125339310324    110.7308403162757    120.63659746250883    122.39837589388233    125.22065199192232    124.33314115329553    122.74650715723529    121.59960094050528    122.68766878061939    124.27076508791409    121.67473502296869    118.16003006906401    116.94282495732313    120.86254471457819    130.74591211309991    133.16910705387292    134.33035885471452    131.89419784941305    131.40218421501282    129.12381289846064    130.80276470572232    129.81629470574953    127.8075246057721    126.65024542279085    128.91970370091641    130.97335407176064    142.87788387956132    144.4286436200359    143.33577420462979    142.25869258984272    141.53471484956947    141.95381332514265    142.98166505986839    137.54478199969077    135.07216905974335    132.67990031958698    133.75431726525719    131.24608333016346    135.45424916403567    138.60702680614961    138.16383224910416    132.52598076675645    132.43656403640784    130.83234815021851    136.47084896468135    134.8608046406855    133.86446785176895    133.54750831696822    129.20443190308362    126.7896784795594    130.56543313803431    134.71930950456849    133.74702688879185    130.90003231769722    136.86702682368869    139.43963226366162    145.14489477883913    140.70026266643646    141.77121801314226    145.55011095090808    143.7565920892537    140.39797143408057    145.09031629028686    147.4549625209381    145.6776188923786    146.24242368067425    148.41121165495963    152.93130567361649    160.08298370910168    157.85887647855441    155.84286747720014    151.95958000607612    151.28645140504318    149.53775466618583    156.58633637293423    160.22665918953538    159.50812712731437    152.62174551567091    150.13604877800685    154.36292048574569    160.08122400316893    157.51741592263022    156.06945521578308    154.69764782909994    153.55904769815294    152.61400958946695    160.83962795925754    164.77689120618376    164.98481970113252    162.60740035193999    163.18414229211018    164.34283810245145
Regression
Month    Box-Office Returns    Prediction
1    104    100        SUMMARY OUTPUT
2    100    101
3    99    101        Regression Statistics
4    88    102        Multiple R    0.7218305936
5    89    103        R Square    0.5210394059
6    108    103        Adjusted R Square    0.5169804178
7    109    104        Standard E
or    19.0392570528
8    101    104        Observations    120
9    106    105
10    102    105        ANOVA
11    78    106            df    SS    MS    F    Significance F
12    111    107        Regression    1    46532.114523578    46532.114523578    128.3668232008    1.38377144273321E-20
13    101    107        Residual    118    42774.210476422    362.4933091222
14    96    108        Total    119    89306.325
15    82    108
16    84    109            Coefficients    Standard E
or    t Stat    P-value    Lower 95%    Upper 95%    Lower 95.0%    Upper...
SOLUTION.PDF