Modelling Approach to Determining Profitability in the Movie Industry between 2009 and 2011 - Statistics Project Example

GLOBAL MOVIES REPORT: A MODELLING APPROACH TO DETERMINING PROFITABILITY IN THE MOVIE INDUSTRY BETWEEN 2009 AND By Presented to Introduction This report examines and explains the profitability of the movie industry based on 414 movies produced between 2009 and 2011. The analysis examines three basic queries that bear great importance for a distributor within the film industry. It uses information gathered shortly after the release of the sample movies to determine conclusive responses to the following questions: 1) Is it possible to predict the total revenue and profits? 2) Is a US movie likely to make more money outside the US than in the country? The report details how the optimal prediction model was picked from a host of many other models developed in search of the best placed one for the purposes listed above. Details pertaining to inevitable/ necessary transformations and modifications, corrections, and removal of certain entries to suit the high standards required for the laid out purposes have been clearly indicated. Further, the results of the analysis process and corresponding interpretations have been provided. Background A client (whose name will remain anonymous in this report) has asked for our assistance with determining if it is possible to determine the profitability of a new release (movie) using parameters set out in several variables. For this reason, data pertaining to several aspects of a movie’s production, distribution and sale have been put into consideration. These include: 1) The year that the movie was released 2) The title of the film 3) The lead studio that produced the film 4) A combined, percentage critics’ rating as obtained from the group Rotten Tomatoes 5) The rating offered by the audience (also obtained from the Rotten Tomatoes) 6) The story type in the movie 7) The genre of the movie 8) The production budget 9) The number of cinemas within the Us that show the film 10) The average revenue per cinema generated from sales within the opening weekend 11) Total revenues generated within the opening weekend 12) The total, gross revenue generated from the film’s sales within the US 13) The total, gross revenue generated from the film’s sales outside the US 14) The total worldwide revenue 15) Records of whether the film won the Oscars, and 16) Records of whether the film won the Bafta award The data is compiled from the book Information is Beautiful by David McCandless (2012). The revenue sections of the data were all reported in millions of US million dollars. In order to achieve this, the variable Average Opening Week was transformed from dollars to millions of dollars by dividing the initially provided values by one million. This was intended to provide uniformity of units of measurement among all variables measured in million dollars. The new variable was renamed Average Opening Week 1. The variable Opening Weekend is the product of the variables Cinemas Open Week and Average Open Week. Worldwide Gross is the sum of Domestic Gross and Foreign Gross. The following section describes further changes made to the data and how the optimal model was obtained. The Modelling Approach The data was explored for errors, outliers, and other specific characteristics that would warrant forfeiture of certain variables, their modifications, or simply encourage their retention. There was no immediate information regarding missing values to the “feeder variables” for Opening Weekend. Consequently, all values for this column derived from Cinemas Open Week and Average Open Week were deleted alongside any other values in corresponding rows. Review of the initial data indicates inconsistencies in the way the summation variable was obtained – both incomplete and inexistent values were treated as zeroes alongside genuine zeroes. In order to correct this error, all rows for which either or both of the variables Domestic Gross and Foreign Gross were deleted before commencing the analysis. In conformity with the above criteria, films for which certain values within the variables were not indicated were removed from the final sample. As a result, the number of films considered for the final analysis were 380, down from 414. Further modifications to the data included the insertion of a new variable, Profitability, which is a quotient of the World Wide Gross and Budget. The variable indicates the ability of the film’s sale to surpass the allocated budget, and hence benefit the relevant entities with a profit. A binary variable, High outside US was created by comparing the gross sales for domestic and foreign sales. The digit 1 was assigned to every case in which the foreign gross exceeded the corresponding domestic gross. All cases for which the domestic gross exceeded the foreign gross were assigned the digit 2. There were no cases of equality between the two. Descriptive Statistics Descriptive statistics were obtained for the continuous variables as shown in the minitab output table below. Table 1. Descriptive statistics for the raw variables. Variable N N* Mean SE Mean StDev Minimum Maximum RottenTomatoes 412 2 50.58 1.32 26.70 4.00 99.00 AudienceScore 412 2 59.364 0.814 16.527 19.000 93.000 Budget 408 6 55.36 2.54 51.24 0.01 260.00 CinemasOpenWeek 403 11 2670.6 49.5 993.4 2.0 4468.0 AverageOpenWeek 400 14 8297 409 8185 1003 93230 OpeningWeekend 413 1 21.36 1.15 23.43 0.03 169.19 DomesticGross 414 0 70.36 3.91 79.61 0.54 760.50 ForeignGross 409 5 97.29 8.28 167.41 0.03 2021.00 WorldwideGross 414 0 166.3 11.8 239.4 1.1 2781.5 As shown in table 1 above, the average Rotten Tomatoes rating for all the 414 movies is 50.58 (SD = 26.70), and the average audience score is 59.364 (SD = 16.53). Other variable means are budget (mean = $55.36 M, SD = 51.24), cinema’s opening sales week (mean = $2670.6 M, SD = 993.4), average opening week sales (mean = $8297M, SD = 8185.0), opening weekend sales (mean = $21.36, SD = 23.43), domestic gross revenue (mean = $70.36M, SD = 79.61), foreign gross revenue (mean = $97.29M, SD = 167.41), and worldwide gross revenue (mean = $166.3M, SD = 239.4). Further descriptive analysis involved the frequency determination of the categorical variables. The graphical interpretations of the categorical variables is contained in the appendix (figures 6,7,8,9,10,11, and 12). Exploratory Data Analysis The data was explored for in-depth understanding of the various characteristics associated with the various variables, both hypothetically related (for instance, the gross revenues collected across the geographical regions in consideration) and the unrelated (for instance, movie ratings and gross revenues reported). The techniques used in the current phase include box plots, and scatter plots/ matrix plots. The figures below indicate the outputs obtained regarding the features of the data. Figure 1. Box plots for comparative ratings. Out of a rating range between 0% and 100%, the average Rotten Tomatoes rating is visibly lower on compared to the Audience Score rating. Equally, Rotten Tomatoes had a larger spread for the distribution of movie ratings, beginning several scores below the minimum rating for the Audience Score, and attaining a top ranking slightly lower than the highest rating accorded the movies by the audience. The initial box plots obtained comparing all the revenues’ variables indicated that the variables can be further subdivided into two categories based on observed differences in scales. The box plot is provided in the appendix. Therefore, the following two plots were created for comparison purposes. Sales for the opening week were substantially higher than those made during the first weekend of a movie’s launch, and equally so compared to the average weekly sales. Therefore, the variable Cinemas Open Week could not be favourable compared with the other sales variables for the first week following the launch of a movie. The average opening week’s sales were observed to be too low even when compared to the slightly lower revenues accumulated over the weekends. This presented an uncertain situation depicting a possible inconsistency in the variable Average Open Week1. It is ideally impossible to get lower figures for the average weekly sales than were obtained for the weekend and weekly sales. For this reason, the variable Average Open Week1, a modification of Average Open Week, was omitted in the eventual analysis. The comparisons that advised its removal are provided simply in the box plots below. Figure 2. Box plots depicting the inconsistency in recording Average Open Week. The variables Opening Weekend and Cinemas Open Week were both observed to have large numbers of outliers. In order to overcome this hurdle, their logarithms were preferred to the original figures. The three categories of gross revenues also appeared to have large numbers of outliers, which ultimately advised the use of their logarithms. Figure 3 below shows box plots corresponding to the three variables in this category and how values are distributed within each variable. Evidently, World Wide Gross is a summation of the domestic and foreign gross revenues. Therefore, the summation variable has the largest outliers. Figure 3. Box plots for the gross revenues. Logarithmic transformations yielded the following relatively comparable plots for the presumed subsets. Each new variable was assigned the prefix “log” and the corresponding suffix. For instance, Log (Domestic Gross) obtained from “Domestic Gross” became “LogDometicGross”. One advantage observed from the transformation is that comparison was made much easier than when the raw scores were used. For the obvious advantages associated with using logarithms in place of raw values (including the reduction of relatively high-ranging values to more comparable forms (Osborne, 2002)), the new variables were adopted for subsequent computations in the logarithmic form. Osborne (2002) further noted that data obtained from such transformations hardly loses its initial characteristics except in the situations where an unfavourable base to the logarithm is used. The values that were remarkably closer to the extreme ends were evidently distributed across both sides of the mean, implying that the choice of log to base 10 used was in accordance with Osborne’s advice. Figure 4. Box plots for opening weeks’ sales in logarithmic form. Figure 5. Box plots for the gross revenues in logarithmic form. Further explorations were provided in the form of condensed scatter plots as produced in the matrix plots below. Figure 6. Matrix plot comparing multiple variables. Considered per row from left to right, the associations between Cinemas Open Week and Worldwide Gross, Cinemas Open Week and Domestic Gross, and Cinemas Open Week and Foreign Gross were all relatively non-linear. Consequently, Cinemas Open Week is not expected to significantly predict the revenues collected. All associations between Opening Weekend and each of Worldwide Gross, Domestic Gross and Foreign Gross were all seemingly linear in nature. Consequently, Opening Weekend is hypothesized to have a strong linear relationship with each of the gross revenue variables. The various scale variables were then assessed for linear relationships with the variable Profitability. The movie Paranormal Activity (2009) was omitted due to the abnormally large value associated with its profitability. The number of points lying further away from the line of best fit were quite few, which indicates that most of the variables could be suitable for predicting profitability. Figure 7. Matrix plots for various revenues. Selecting the Regression Models Stepwise elimination was used to select the optimum model for the data, with profitability set as the response. The following results were obtained from the analysis. Linear Regression Model. The model selection criteria followed several addition steps as provided in the stepwise elimination method. The output corresponding to the steps is contained in the appendix. The entry and elimination for alpha was set at 0.15, the default values provided by Minitab. The first model included the constant and the variable “Log Worldwide Gross”. The coefficient for the variable was significant (p ˂ 0.001, adjusted R-square = 7.89). In the second step, budget was introduced and the coefficients still remained significant (p ˂ 0.001, adjusted R-square = 24.78). In the third step, the third variable “Rotten Tomatoes” was included. It was significant (p = 0.003, adjusted R-square = 26.33). In the fourth step, “Log Cinemas Open Week” was introduced. The variable coefficient was not significant (p = 0.107) and the overall increase in the adjusted R-square was only marginal (from 26.33 to 26.65). This was the first “would-be” predictor to be eliminated from the linear regression model. Equally, the fifth variable introduced (Audience Score) did not have a significant coefficient (p = 0.142, adjusted R-square = 26.87). Together with the sixth variable (Log Foreign Gross – p = 0.149, adjusted R-square = 27.09), this variable was also eliminated for having a coefficient that was not significant at the 5% level of significance. Thus, the new model developed is derived from the table of outputs shown below. Table 2. Regression coefficients for the profitability model. Model Summary S R-sq R-sq(adj) R-sq(pred) 4.30684 26.91% 26.33% 25.07% Coefficients Term Coef SE Coef T-Value P-Value VIF Constant -7.58 1.06 -7.13 0.000 RottenTomatoes 0.02535 0.00851 2.98 0.003 1.04 Budget -0.05413 0.00594 -9.11 0.000 1.93 LogWorldwideGross 6.557 0.627 10.46 0.000 1.98 The regression equation becomes: Profitability = 0.02535*Rotten Tomatoes Rating – 0.05413*Budget + 6.557*Log Worldwide Gross – 7.58. We realize that every unitary rise in a movie’s profitability corresponds with a 0.02535 increase in the Rotten Tomatoes rating for the same. As such, the Rotten Tomatoes rating is a positive contributor to profitability. For every unit rise in profitability there is a corresponding rise by 6.557 units in the Log (worldwide gross revenues), corresponding to $3,605,786.43. The worldwide gross revenues have a positive impact on the profitability of a movie. As such, increase in the revenues corresponds to higher profitability. Every unit increase in profitability corresponds to a 0.05413 units decrease in the budget. This shows that a budget size is inversely proportional to profitability. As such, for a movie to attain higher profitability, it has to have a lower budget assigned to it. The Binary Logistic Model. A similar approach to that used above was used in determining the best suited model for predicting whether sales exclusively sourced outside the US led to inferior revenues compared to those collected outside the country. The stepwise elimination approach was used, with the variables “Rotten Tomatoes Rating”, “Audience Score”, “Budget”, “Log Cinemas Open Week”, “Log Opening Weekend”, “Log Domestic Gross”, “Log Foreign Gross”, and “Log Worldwide Gross”. The response was the assigned score “High Outside US”, which is a dichotomous variable with 1 denoting that revenues outside the US were more than those collected within the country for each particular movie. The output corresponding to the analysis are shown below. Table 3. Regression coefficients for the sales model. Stepwise Selection of Terms Candidate terms: RottenTomatoes, AudienceScore, Budget, LogCinemasOpenWeek, LogOpeningWeekend, LogDomesticGross, LogForeignGross, LogWorldwideGross ----Step 1---- Coef P Constant 4.621 LogForeignGross -2.897 0.000 Deviance R-Sq 31.09% Deviance R-Sq(adj) 30.90% AIC 365.75 The model appears to adopt only one out of the eight predictors initially selected. As such, the other seven predictors are dropped to retain “Log Foreign Gross” as the only predictor for the binary regression model. The variable has a significant predictor (p ˂ 0.001, Deviance adjusted R-square = 31.09). The model becomes: “Higher Sales outside US” = 4.621 – 2.897*Log Foreign Gross. From this model we realize that whenever movie sales are higher outside the US market, the Log (foreign gross revenues) falls by 2.897 units – which translates into $0.0013. The figure is seemingly marginal. In order to determine whether sales outside the US are more likely to be higher than the domestic sales, we develop the odds ratio for each expected outcome. This is obtained as: Odds ratio = Exp(all coefficients in the equation). For the case when non-US sales revenues are higher than domestic sales, we multiply each coefficient with 1, and 2 for cases when US sales revenue exceeds the foreign market revenues. The multipliers 1 and 2 are in line with the values assigned each case in the data file. P(non-US) = exp(Y)/(1 + exp (Y)) = 5.60/ (1 + 5.60) = 0.848 P(US) = 31.44/ (1 + 31.44) = 0.969 From these figures, we realize that there are higher odds for a movie making more sales in the US (P = 96.9%, Odds = 31.44) than in the foreign markets (P = 84.8%, Odds = 5.60). As such, a movie is 5.61 (31.44/ 5.60) times more likely to make higher sales revenues in the US market than it can in the foreign markets. Conclusion This analysis provides a fair outlook of the movie market by comparing the sales made within and outside the US. Several shortcomings were observed in the data, which effectively prompted the use of transformational data analysis techniques to address them. Equally, some variables and columns were eliminated for inaccuracy or failure to report details under certain columns. The final verdict is that using variables identified using the regression inclusion/ exclusion technique of best subsets, sales revenues within the US were found to be 5.61 times higher than outside the country. Therefore, for an effective distribution chain to thrive conveniently, it is important that the marketers understand the importance of establishing a strong foothold within the US, as this is obviously going to fetch much higher sales and, consequently, revenues and profits. References Osborne, J. 2002. Notes on the use of data transformations. Practical Assessment, Research and Evaluation. 8(6). [Online]. http://pareonline.net/getvn.asp?v=8&n=6 (12th December 2014). Appendix The plot below provided the hint that the variables on either side of the graph should be treated separately. Figure 6. Box plot comparing raw revenue data. Figure 7. Bar Chart for frequencies of regions with higher sales revenues. Figure 8. Bar chart for Oscar awards associated with the movies. Figure 9. Bar chart for Bafta awards associated with the movies. Figure 10. Bar chart for movie genres. Figure 11. Bar chart for story types. Figure 12. Bar chart for production studios. Table 4. Stepwise selection criteria for the regression model. Stepwise Selection of Terms α to enter = 0.15, α to remove = 0.15 Analysis of Variance Source DF Adj SS Adj MS F-Value P-Value Regression 6 2688.09 448.02 24.40 0.000 LogForeignGross 1 38.47 38.47 2.10 0.149 RottenTomatoes 1 137.92 137.92 7.51 0.006 AudienceScore 1 53.10 53.10 2.89 0.090 Budget 1 1610.50 1610.50 87.73 0.000 LogCinemasOpenWeek 1 77.36 77.36 4.21 0.041 LogWorldwideGross 1 840.18 840.18 45.77 0.000 Error 372 6829.21 18.36 Total 378 9517.30 Model Summary S R-sq R-sq(adj) R-sq(pred) 4.28463 28.24% 27.09% 25.19% Coefficients Term Coef SE Coef T-Value P-Value VIF Constant -5.39 1.78 -3.03 0.003 LogForeignGross -1.068 0.737 -1.45 0.149 6.02 RottenTomatoes 0.0347 0.0127 2.74 0.006 2.32 AudienceScore -0.0383 0.0225 -1.70 0.090 2.86 Budget -0.05564 0.00594 -9.37 0.000 1.95 LogCinemasOpenWeek -1.098 0.535 -2.05 0.041 1.55 LogWorldwideGross 9.11 1.35 6.77 0.000 9.23 Regression Equation Profitability = -5.39 - 1.068 LogForeignGross + 0.0347 RottenTomatoes - 0.0383 AudienceScore - 0.05564 Budget - 1.098 LogCinemasOpenWeek + 9.11 LogWorldwideGross Fits and Diagnostics for Unusual Observations Obs Profitability Fit Resid Std Resid 104 3.281 7.114 -3.833 -0.94 X 120 1.443 2.542 -1.099 -0.28 X 121 2.140 0.135 2.005 0.48 X 124 3.333 0.788 2.545 0.61 X 125 0.709 2.175 -1.466 -0.36 X 127 4.490 6.213 -1.723 -0.42 X 134 0.425 -1.885 2.310 0.56 X 135 2.339 4.558 -2.218 -0.54 X 141 25.338 10.812 14.526 3.43 R 143 9.574 4.269 5.305 1.28 X 148 1.312 1.890 -0.577 -0.14 X 153 1.417 3.049 -1.632 -0.40 X 183 1.797 3.496 -1.698 -0.43 X 218 0.345 0.727 -0.382 -0.09 X 220 0.431 1.422 -0.991 -0.24 X 222 2.276 -1.548 3.824 0.92 X 235 27.614 11.634 15.980 3.79 R 237 37.629 7.181 30.448 7.27 R 257 3.034 4.707 -1.674 -0.41 X 262 1.862 4.169 -2.306 -0.56 X 271 4.472 3.055 1.417 0.34 X 303 64.673 7.011 57.661 13.53 R 322 41.408 9.561 31.846 7.51 R 345 0.303 -1.518 1.821 0.44 X 367 1.697 6.836 -5.139 -1.26 X R Large residual X Unusual X Stepwise Selection of Terms Candidate terms: LogForeignGross, RottenTomatoes, AudienceScore, Budget, LogCinemasOpenWeek, LogWorldwideGross, LogOpeningWeekend, LogDomesticGross ----Step 1---- ------Step 2----- ------Step 3----- Coef P Coef P Coef P Constant -2.18 -6.88 -7.58 LogWorldwideGross 2.879 0.000 6.879 0.000 6.557 0.000 Budget -0.05540 0.000 -0.05413 0.000 RottenTomatoes 0.02535 0.003 LogCinemasOpenWeek AudienceScore LogForeignGross S 4.81579 4.35175 4.30684 R-sq 8.13% 25.18% 26.91% R-sq(adj) 7.89% 24.78% 26.33% R-sq(pred) 7.43% 23.50% 25.07% Mallows’ Cp 98.76 12.83 5.90 ------Step 4----- ------Step 5----- ------Step 6----- Coef P Coef P Coef P Constant -5.46 -4.82 -5.39 LogWorldwideGross 7.038 0.000 7.502 0.000 9.11 0.000 Budget -0.05459 0.000 -0.05536 0.000 -0.05564 0.000 RottenTomatoes 0.02034 0.025 0.0334 0.009 0.0347 0.006 LogCinemasOpenWeek -0.838 0.107 -0.906 0.082 -1.098 0.041 AudienceScore -0.0327 0.142 -0.0383 0.090 LogForeignGross -1.068 0.149 S 4.29758 4.29092 4.28463 R-sq 27.42% 27.84% 28.24% R-sq(adj) 26.65% 26.87% 27.09% R-sq(pred) 25.37% 24.85% 25.19% Mallows’ Cp 5.28 5.13 5.04 α to enter = 0.15, α to remove = 0.15 Analysis of Variance Source DF Adj SS Adj MS F-Value P-Value Regression 6 2688.09 448.02 24.40 0.000 LogForeignGross 1 38.47 38.47 2.10 0.149 RottenTomatoes 1 137.92 137.92 7.51 0.006 AudienceScore 1 53.10 53.10 2.89 0.090 Budget 1 1610.50 1610.50 87.73 0.000 LogCinemasOpenWeek 1 77.36 77.36 4.21 0.041 LogWorldwideGross 1 840.18 840.18 45.77 0.000 Error 372 6829.21 18.36 Total 378 9517.30 Model Summary S R-sq R-sq(adj) R-sq(pred) 4.28463 28.24% 27.09% 25.19% Coefficients Term Coef SE Coef T-Value P-Value VIF Constant -5.39 1.78 -3.03 0.003 LogForeignGross -1.068 0.737 -1.45 0.149 6.02 RottenTomatoes 0.0347 0.0127 2.74 0.006 2.32 AudienceScore -0.0383 0.0225 -1.70 0.090 2.86 Budget -0.05564 0.00594 -9.37 0.000 1.95 LogCinemasOpenWeek -1.098 0.535 -2.05 0.041 1.55 LogWorldwideGross 9.11 1.35 6.77 0.000 9.23 Regression Equation Profitability = -5.39 - 1.068 LogForeignGross + 0.0347 RottenTomatoes - 0.0383 AudienceScore - 0.05564 Budget - 1.098 LogCinemasOpenWeek + 9.11 LogWorldwideGross Read More