Relationship Between The Domestic Gross Income and The Total Running Time af 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.

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Relationship Between The Domestic Gross Income and The Total Running Time af a Film

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:

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Relationship Between The Domestic Gross Income and The Total Running Time af a Film

Income to the nearest  million

minutes

total

\$10,037.00

6247

mean

\$200.74

124.94

median

\$182.00

124.5

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Relationship Between The Domestic Gross Income and The Total Running Time af a Film

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:

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Relationship Between The Domestic Gross Income and The Total Running Time af a Film

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

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Relationship Between The Domestic Gross Income and The Total Running Time af a Film

median

\$182.00

124.5

mode

\$206.00

133

standard  deviation

\$76.48

26.

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.

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Relationship Between The Domestic Gross Income and The Total Running Time af 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

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Relationship Between The Domestic Gross Income and The Total Running Time af a Film

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

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Relationship Between The Domestic Gross Income and The Total Running Time af a Film

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

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Relationship Between The Domestic Gross Income and The Total Running Time af a Film

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:

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Relationship Between The Domestic Gross Income and The Total Running Time af a Film

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.

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Relationship Between The Domestic Gross Income and The Total Running Time af a Film

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

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Relationship Between The Domestic Gross Income and The Total Running Time af a Film

\$3,679.00

2979

total

\$6,358.00

3268

Mean (L)

147.16

119.16

Mean (H)

254.32

130.72

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Relationship Between The Domestic Gross Income and The Total Running Time af a Film

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:

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Relationship Between The Domestic Gross Income and The Total Running Time af a Film

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

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Relationship Between The Domestic Gross Income and The Total Running Time af a Film

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.

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Relationship Between The Domestic Gross Income and The Total Running Time af a Film

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

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Relationship Between The Domestic Gross Income and The Total Running Time af a Film

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

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Relationship Between The Domestic Gross Income and The Total Running Time af a Film

(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

19/54

Relationship Between The Domestic Gross Income and The Total Running Time af a Film

161

The Lion King

\$329.00

89

Independence Day

\$306.00

153

Star Wars

\$461.00

121

Transformers

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Relationship Between The Domestic Gross Income and The Total Running Time af a Film

\$319.00

143

Ice Age; The Meltdown

\$195.00

90

The Lost World; Jurassic Park

\$229.00

129

Men in Black

\$251.00

97

21/54

Relationship Between The Domestic Gross Income and The Total Running Time af a Film

King Kong

\$218.00

187

\$194.00

86

Meet the Fockers

\$279.00

144

Twister

22/54

Relationship Between The Domestic Gross Income and The Total Running Time af a Film

\$242.00

133

Saving Private Ryan

\$217.00

170

Charlie and the Chocolate Factory

\$206.00

106

Cars

\$244.00

116

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Relationship Between The Domestic Gross Income and The Total Running Time af a Film

\$188.00

155

Pearl     Harbour

\$199.00

183

Mrs Doubtfire

\$219.00

125

Cast Away

\$234.00

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Relationship Between The Domestic Gross Income and The Total Running Time af a Film

143

The Mummy

\$155.00

124

X-Men United

\$215.00

134

Robin Hood; Prince of Thieves

\$165.00

143

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Relationship Between The Domestic Gross Income and The Total Running Time af a Film

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

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Relationship Between The Domestic Gross Income and The Total Running Time af a Film

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

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Relationship Between The Domestic Gross Income and The Total Running Time af a Film

\$165.00

140

Dinosaur

\$138.00

82

I

\$145.00

105

Alvin  and the Chipmunks

\$212.00

92

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Relationship Between The Domestic Gross Income and The Total Running Time af a Film

Indiana  Jones and the Temple       of Doom

\$180.00

118

The Golden Compass

\$70.00

113

Seven

\$100.00

127

Schindler’s List

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Relationship Between The Domestic Gross Income and The Total Running Time af a Film

\$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

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Relationship Between The Domestic Gross Income and The Total Running Time af a Film

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

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Relationship Between The Domestic Gross Income and The Total Running Time af a Film

130

The Bourne Supremacy

\$176.00

108

Lethal Weapon 4

\$130.00

127

XXX

\$142.00

113

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Relationship Between The Domestic Gross Income and The Total Running Time af a Film

The Silence of the Lambs

\$131.00

118

total

\$10,037.00

6247

mean

\$200.74

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Relationship Between The Domestic Gross Income and The Total Running Time af a Film

124.94

median

\$182.00

124.5

mode

\$206.00

133

standard deviation

\$76.48

26.82

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Relationship Between The Domestic Gross Income and The Total Running Time af a Film

low  income

high  income

Y

X

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Relationship Between The Domestic Gross Income and The Total Running Time af a Film

Y

X

The Golden Compass

\$70.00

113

The Fugitive (1993)

\$184.00

130

Schindler’s List

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Relationship Between The Domestic Gross Income and The Total Running Time af a Film

\$96.00

194

\$188.00

155

Seven

\$100.00

127

37/54

Relationship Between The Domestic Gross Income and The Total Running Time af a Film

\$194.00

86

Rocky IV

\$128.00

91

Ice Age; The Meltdown

\$195.00

90

Lethal Weapon 4

\$130.00

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Relationship Between The Domestic Gross Income and The Total Running Time af a Film

127

Pearl      Harbour

\$199.00

183

The Silence of the Lambs

\$131.00

118

Charlie and the Chocolate Factory

\$206.00

106

39/54

Relationship Between The Domestic Gross Income and The Total Running Time af a Film

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

40/54

Relationship Between The Domestic Gross Income and The Total Running Time af a Film

Alvin  and the Chipmunks

\$212.00

92

Dinosaur

\$138.00

82

X-Men United

\$215.00

134

Look Who’s Talking

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Relationship Between The Domestic Gross Income and The Total Running Time af a Film

\$140.00

93

Saving Private Ryan

\$217.00

170

XXX

\$142.00

113

King Kong

42/54

Relationship Between The Domestic Gross Income and The Total Running Time af a Film

\$218.00

187

I

\$145.00

105

Mrs Doubtfire

\$219.00

125

The Mummy

\$155.00

43/54

Relationship Between The Domestic Gross Income and The Total Running Time af a Film

124

The Lost World; Jurassic Park

\$229.00

129

What Lies Beneath

\$155.00

130

Cast Away

\$234.00

143

44/54

Relationship Between The Domestic Gross Income and The Total Running Time af a Film

Shark Tale

\$161.00

90

Twister

\$242.00

133

The Pursuit of Happyness

\$164.00

116

45/54

Relationship Between The Domestic Gross Income and The Total Running Time af a Film

Cars

\$244.00

116

Robin Hood; Prince of Thieves

\$165.00

143

Men in Black

\$251.00

97

Catch Me If You Can

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Relationship Between The Domestic Gross Income and The Total Running Time af a Film

\$165.00

140

Harry Potter and the Chamber of Secrets

\$262.00

161

Beauty and the Beast

\$171.00

84

Meet the Fockers

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Relationship Between The Domestic Gross Income and The Total Running Time af a Film

\$279.00

144

Rain Man

\$173.00

133

Independence Day

\$306.00

153

Air Force One

\$173.00

48/54

Relationship Between The Domestic Gross Income and The Total Running Time af a Film

124

Harry Potter and the Philiosphers Stone

\$318.00

153

Home Alone 2; Lost in New York

\$174.00

120

Transformers

\$319.00

143

49/54

Relationship Between The Domestic Gross Income and The Total Running Time af a Film

The Bourne Supremacy

\$176.00

108

The Lion King

\$329.00

89

Planet of the Apes

\$180.00

119

50/54

Relationship Between The Domestic Gross Income and The Total Running Time af a Film

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

51/54

Relationship Between The Domestic Gross Income and The Total Running Time af a Film

\$3,679.00

2979

total

\$6,358.00

3268

mean

147.16

119.16

mean

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Relationship Between The Domestic Gross Income and The Total Running Time af a Film

254.32

130.72

standard  deviation

28.2174296

23.16369285

standard  deviation

71.86139

29.37618083

variance

796.2233333

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Relationship Between The Domestic Gross Income and The Total Running Time af a Film

536.5566667

variance

5164.06

862.96

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