Rand Mcnally
Rand Mcnally
Relationship Between The Domestic Gross Income And The Total Running Time Of A Film
Introduction:
This paper tends to investigate the relationship between the domestic gross income and the total running time of a film, it is evident that films that have shorter running time films will earn more income than the films with longer running time films. Secondary data is used to analyse this relationship because of the availability of data and also time and financial constraints associated with primary data. Data therefore was retrieved form the box office MOJO where a total of 214 films was collected based on the US figures, a sample of 50 was selected using systematic sampling and regression analysis and measures of central tendencies determined.
Hypothesis:
Hypothesis one involves testing whether the shorter the totals running time of a film then the less the total income, this is done through the estimation of a model and testing the statistical significance of the estimated coefficients.
The next hypothesis involves testing whether the mean running time for high income films is less than the mean running time for the low income films, this is done by grouping films into low and high income films and testing the hypothesis that the mean running time for the high income films is less than the running time for the low income films.
Method:
The method that is intended to be applied in the analysis of the hypothesis include statistical tests of the hypothesis and the regression of income against total time, the results will help us determine the relationship between total running time of the film and the total income generated.
Data used:
Data was collected from a secondary source because of the availability of data and also time and financial constraints associated with primary data, Data therefore was retrieved form the box office MOJO where a total of 214 films was collected based on the US figures. Due to calculation difficulties a sample of 50 was generated through systematic sampling, every forth observation was selected to come up with the sample, the total time was converted into minutes and the total revenue was rounded off to the nearest million dollars.
Statistical analysis:
After the sample was generated statistical measures were undertaken, the following table summarises some of central measures of the data:
Income to the nearest million
minutes
total
$10,037.00
6247
mean
$200.74
124.94
median
$182.00
124.5
mode
$206.00
133
standard deviation
$76.48
26.82
The correlations coefficient for the two data series is equal to 0.13 meaning that there is a positive relationship between the revenue and the running time of a film.
The following graph portrays a scatter diagram of both variables and the trend line:
Having selected our sample the next step is to analyse the relationship between the variables, the following table summarises some of central measures of the data:
Income to the nearest million
minutes
total
$10,037.00
6247
mean
$200.74
124.94
median
$182.00
124.5
mode
$206.00
133
standard deviation
$76.48
26.82
The correlations coefficient for the two data series is equal to 0.13 meaning that there is a positive relationship between the revenue and the running time of a film.
The following graph portrays a scatter diagram of both variables and the trend line:
From the above chart is is evident that as the running time of the film increases then the total income increases.
Regression:
We estimate the model stating that Y = MX + C where Y is the total income while X is the total running time and C is the constant of the autonomous value,
M mis the slope or the coefficient of X.
After estimating the following are the results:
Y = 0.3731X + 154.13
The model means that if we increase the level of running time by unit then the level of total income increases by 0.3731 and if the running time was zero then the level of income is 154 million dollars. This means that as we increase the running time then the level of income increases, however there is a need to check for statistical significance of the estimated coefficients, The correlation of determination value is equal to 0.0171
Variance and standard deviation:
In order to undertake statistical test there is a need to determine the variance and standard deviation of the coefficients, the table below summarises the standard error and variance of the variables:
coefficient
variance
standard error
M
0.166436
0.407966
C
135771.6
368.472
Hypothesis test:
Having determined the variance and standard error of the coefficients the statistical test are as follows:
For the constant C
Null hypothesis:
C = 0
Alternative hypothesis:
C ≠ 0
Our T statistics will be determined as follows:
=C / std error c
= 154.13/ 368.472
T statistics = 0.418289
At 98% level of test using a two tail test the T critical value is 2.32635, this means that we accept the null hypothesis, the reason being the fact that the T calculated value is less than the T critical value, for this reason therefore we conclude that the constant coefficient is not statistically significant.
The slope coefficient:
Null hypothesis:
m = 0
Alternative hypothesis:
m ≠ 0
Our T statistics will be determined as follows:
=m / std error m
= 0.3731/ 0.407966
T statistics = 0.914479
At 98% level of test using a two tail test the T critical value is 2.32635, this means that we accept the null hypothesis, the reason being the fact that the T calculated value is less than the T critical value, for this reason therefore we conclude that the slope coefficient is not statistically significant.
Following our rejection of our coefficients then there is need to specify the model again with other variables in order to get statistically significant estimated coefficients, we can also use another sample to estimate our model. However our results from the model show that the more the time does not mean that a film will earn more.
Further hypothesis tests:
We now group the sample according to their earnings, the first 25 being the top earnings and the next 325 being the low earning films, in this was we will be able to determine whether the top earning films earn more amounts and are characterised by shorter running time using the other group of data that contains low earning films, the table below summarises the two sets of groups:
25 Low income
income
Time in minutes
25 High income
income
Time in minutes
total
$3,679.00
2979
total
$6,358.00
3268
Mean (L)
147.16
119.16
Mean (H)
254.32
130.72
standard deviation
28.2174296
23.16369285
standard deviation
71.86139
29.37618
Hypothesis:
We now tend to test the hypothesis that the mean running time for the high income films is lower than the mean running time for the low income films:
Null hypothesis:
H0: Ht = Lt
Alternative hypothesis:
Ha: Ht < Lt
Where Ht is the mean running time for the high income group and that Lt is the mean running time for the low income group.
We test the hypothesis as follows:
Ht – Lt
Z = ___________
[(σ12/ n1) + (σ22/ n2)] ½
σ1 is the standard deviation of Ht
σ2 is the standard deviation of Lt
n is the sample size which is equal to 50
After calculation Z = 2.185012
At 95% two tail test level of test the critical value is 1.95996, because the critical value is less then the critical value we reject the null hypothesis that the mean running time for the low income films is equal to the mean running time for the high income films.
We therefore conclude that the mean time for the high income film group is less than the mean running time for the low income. For this reason therefore following our hypothesis test it is clear that the higher the running time then the lower the income.
Conclusion:
In above discussion the total running time of a movie will determine the income level of the film, our first analysis involved the estimation of the model Y = MX + C whereby
Y is the income level and X is the running time of films, after estimation it was evident that the more the time then the higher the income, however statistical tests show that our estimated model is not statistically significant, this therefore means that there is a need to specify the model including other dependent variables or the use of a different sample.
Further analysis involve the grouping of films into high income movies and the other group includes the low income films, this is done by sorting the films in ascending order using excel and then picking the first 25 as low income films and the next 25 as high income films, from the hypothesis test on time used it is clear that the high income films have a lower running time than the low income films, this decision is made through the test hypothesis of the difference in the two means.
References:
Box office MOJO (2008) films income and running time data, retrieved on , available at
Bluman A. (2000) Elementary Statistics: A Step by Step Approach, McGraw Hill press, New York
Cochran (1997) Sampling Techniques, Wiley publishers, New York
D Amaratunga and et al (2002) Quantitative and qualitative research, McGraw Hill publishers, New York
D. Bridge (1993) Statistics: An Introduction to Quantitative Economic Research, Rand McNally publishers, Michigan
Patton M. (1990) Qualitative evaluation and research method, Sage publishers, Newbury
Chambers and Skinner (2003) Analysis of Survey Data, Wiley publishers, New York
Appendixes:
Y
X
(NEAREST MILLION)
(MINUTES)
Harry Potter and the Philiosphers Stone
$318.00
153
Star Wars:Episode 1-The Phantom Menace
$431.00
133
Harry Potter and the Chamber of Secrets
$262.00
161
The Lion King
$329.00
89
Independence Day
$306.00
153
Star Wars
$461.00
121
Transformers
$319.00
143
Ice Age; The Meltdown
$195.00
90
The Lost World; Jurassic Park
$229.00
129
Men in Black
$251.00
97
King Kong
$218.00
187
Madagascar
$194.00
86
Meet the Fockers
$279.00
144
Twister
$242.00
133
Saving Private Ryan
$217.00
170
Charlie and the Chocolate Factory
$206.00
106
Cars
$244.00
116
Gladiator
$188.00
155
Pearl Harbour
$199.00
183
Mrs Doubtfire
$219.00
125
Cast Away
$234.00
143
The Mummy
$155.00
124
X-Men United
$215.00
134
Robin Hood; Prince of Thieves
$165.00
143
Live Free or Die Hard
$135.00
130
Beauty and the Beast
$171.00
84
The Fugitive (1993)
$184.00
130
Shark Tale
$161.00
90
Planet of the Apes
$180.00
119
Home Alone 2; Lost in New York
$174.00
120
Rain Man
$173.00
133
Catch Me If You Can
$165.00
140
Dinosaur
$138.00
82
I
$145.00
105
Alvin and the Chipmunks
$212.00
92
Indiana Jones and the Temple of Doom
$180.00
118
The Golden Compass
$70.00
113
Seven
$100.00
127
Schindler's List
$96.00
194
Air Force One
$173.00
124
Austin Powers; The Spy who Shagged Me
$206.00
95
The Pursuit of Happyness
$164.00
116
Close Encounters of the Third Kind
$132.00
137
Rocky IV
$128.00
91
Look Who's Talking
$140.00
93
What Lies Beneath
$155.00
130
The Bourne Supremacy
$176.00
108
Lethal Weapon 4
$130.00
127
XXX
$142.00
113
The Silence of the Lambs
$131.00
118
total
$10,037.00
6247
mean
$200.74
124.94
median
$182.00
124.5
mode
$206.00
133
standard deviation
$76.48
26.82
low income
high income
Y
X
Y
X
The Golden Compass
$70.00
113
The Fugitive (1993)
$184.00
130
Schindler's List
$96.00
194
Gladiator
$188.00
155
Seven
$100.00
127
Madagascar
$194.00
86
Rocky IV
$128.00
91
Ice Age; The Meltdown
$195.00
90
Lethal Weapon 4
$130.00
127
Pearl Harbour
$199.00
183
The Silence of the Lambs
$131.00
118
Charlie and the Chocolate Factory
$206.00
106
Close Encounters of the Third Kind
$132.00
137
Austin Powers; The Spy who Shagged Me
$206.00
95
Live Free or Die Hard
$135.00
130
Alvin and the Chipmunks
$212.00
92
Dinosaur
$138.00
82
X-Men United
$215.00
134
Look Who's Talking
$140.00
93
Saving Private Ryan
$217.00
170
XXX
$142.00
113
King Kong
$218.00
187
I
$145.00
105
Mrs Doubtfire
$219.00
125
The Mummy
$155.00
124
The Lost World; Jurassic Park
$229.00
129
What Lies Beneath
$155.00
130
Cast Away
$234.00
143
Shark Tale
$161.00
90
Twister
$242.00
133
The Pursuit of Happyness
$164.00
116
Cars
$244.00
116
Robin Hood; Prince of Thieves
$165.00
143
Men in Black
$251.00
97
Catch Me If You Can
$165.00
140
Harry Potter and the Chamber of Secrets
$262.00
161
Beauty and the Beast
$171.00
84
Meet the Fockers
$279.00
144
Rain Man
$173.00
133
Independence Day
$306.00
153
Air Force One
$173.00
124
Harry Potter and the Philiosphers Stone
$318.00
153
Home Alone 2; Lost in New York
$174.00
120
Transformers
$319.00
143
The Bourne Supremacy
$176.00
108
The Lion King
$329.00
89
Planet of the Apes
$180.00
119
Star Wars:Episode 1-The Phantom Menace
$431.00
133
Indiana Jones and the Temple of Doom
$180.00
118
Star Wars
$461.00
121
total
$3,679.00
2979
total
$6,358.00
3268
mean
147.16
119.16
mean
254.32
130.72
standard deviation
28.2174296
23.16369285
standard deviation
71.86139
29.37618083
variance
796.2233333
536.5566667
variance
5164.06
862.96
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