Quantitative Methods Research to Determine per Theatre Gross - Example

Predicting per theater gross: This report highlights the main findings in the movie industry, conclusions about this industry are made with reference to statistics determined, an analysis of 25 movies for the period 1977 to 2010 indicate that science fiction movies have the highest average and standard deviation value(497,768,775 and 238,314,536 respectively) . Black comedies on the other hand have the lowest average and standard deviation values (29, 862,967 and 19,854,281 respectively), the average values indicate the expected value for each genre and therefore science fiction movies have a higher expected gross. There Phantom invasion movie being produced is expected to have a gross value of 497,768,775 and a standard deviation of 238,314,536. An analysis of original movie transformers and the movie transformers revenge of the fallen indicates that the original movie transformers had a lower per theater gross (3,359) compared to the transformers revenge of the fallen (3,735.75), this implies that there is a high possibility that the movie phantom invasion is expected to have a higher per theater average compared to the original movie phantom. The frequency distribution and histogram indicate that transformers revenge of the fallen has a possibility that per theater earnings will be higher than 6,000 compared to transformers, this shows that the original movie phantom has a lower probability to gain higher earnings compared to phantom invasion Regression analysis to find an appropriate model to estimate gross value was undertaken, assuming that the opening gross value is the independent variable then the resulting regression indicates that the slope is 2.1946 while the constant value is 55.042, and the R squared value is 0.5757. This means that if opening gross was to increase by 1 million then the gross value will increase by 2.19 million. The chart below summarizes the trend line: However one outlier identified in this trend line is the movie transformers and this value is indicated in the above chart. When budget is assumed to be the independent variable then the resulting regression indicates that the slope is 0.4385 while the constant value is 136.16, and the R squared value is 0.1635. Due to unavailability of budget values only the first 30 units of data was considered. This means that if opening gross was to increase by 1 million then the gross value will increase by 0.4385 million. The chart below summarizes the trend line: However one outlier identified in this trend line is the movie transformers: revenge of the fallen and this value is indicated in the above chart. Given these two model the model that takes opening gross as the independent variable is more appropriate due to the high correlation of determination compared to the other model. Analysis of preference by gender shows the following results: From the chart more male prefer science fiction and action movies than female, while more female prefer romance and fantasy movies than male. There is a 50 -50 preference of drama movies. Generation preference is summarized below: The charts indicate that more generation X (those aged 26 to 49) individuals prefer science fiction movies than any other generation; there are also more generation Y (those aged 13 to 25) individuals who prefer science fiction movies than baby boomers. Therefore the target market should be male individuals and also those aged between 13 to 49 years for the science fiction movie phantom invasion. Probability analysis indicate that there is a 0.086 probability that an individual prefers science fiction movies, further analysis indicate that there is a 0.245 probability that an individual will choose science fiction if they are generation Y and a 0.16 probability if they were generation X, this shows that the phantom invasion movie should focus on male viewers and also on those aged 13 to 49 years. From the above analysis therefore a number of consideration should be taken in decision making, analysis show that phantom invasion is more likely to have higher gross value than the original movie phantom, this is evident by comparing the movies transformers and transformer: revenge of the fallen. Another finding is that science fiction movies are more likely to have higher gross values those other movie genres, therefore given that phantom is a science fiction movie then there is a high probability that earnings will be higher than earnings gained by other movie genres. Other findings show that the opening gross is more appropriate in estimating the gross earnings, applying this model to the phantom invasion mopvie indicate that the expected gross value is 219.64 million, however in order to achieve higher earnings the market segment to target should be males who are aged between 13 to 49 years. Appendixes: Q1: A. descriptive: The table summarizes the 1977 to 2010 gross for 25 movies: Science Fiction Action Black Comedy Thriller Average 497,768,775 395,000,164 29,862,967 265,664,195 Std. Dev 238,314,536 113,439,411 19,854,281 175,964,950 Min 267,922,763 293,349,555 9,947,625 137,917,433 Max 1,221,103,103 738,932,505 92,308,740 966,233,033 A number of conclusions can be made from the above table; one is that science fiction movies have the highest average and standard deviation value (497,768,775 and 238,314,536 respectively) . Black comedies on the other hand have the lowest average and standard deviation values (29, 862,967 and 19,854,281 respectively), the average values indicate the expected value for each genre and therefore science fiction movies have a higher expected gross. B. Shortcoming: The above values cannot be used to make specific conclusion considering these are descriptive statistics, other statistics that could be determined include the overall average for the 25 movies as follows: (497,768,775+ 395,000,164+29,862,967+265,664,195)/ 4 = 297,074,025 Movie type whose average is greater is above average and therefore more profitable; the action and science fiction movies are therefore are more profitable. The variance is also an important value that is determined to indicate dispersion, it is determined as follows: standard deviation squared, the values are summarized by the table below: Science Fiction Action Black Comedy Thriller variance 5.67938E+16 1.28685E+16 3.94192E+14 3.09637E+16 Q2: Comparing the original movie transformers and transformers revenge of the fallen: A. descriptive statistics: transformers transformers revenge of the fallen mean $3,359 3735.75 standard deviation 4078.008844 6353.619247 q1 1267.25 878.75 q2 (median) 1942.5 1565 q3 3230 2770 q4 (max) 17577 25736 The table above summarizes the descriptive statistics; the average value indicates that the original movie transformers had a lower per theater gross (3,359) compared to the transformers revenge of the fallen (3,735.75), this implies that there is a high possibility that the movie phantom invasion is expected to have a higher per theater average compared to the original movie. Frequency distribution: transformers transformers revenge of the fallen Bin Frequency percentage frequency Frequency percentage frequency 1000 1 0.055555556 6 0.375 2000 8 0.444444444 5 0.3125 3000 4 0.222222222 1 0.0625 4000 2 0.111111111 1 0.0625 5000 0 0 0 0 6000 1 0.055555556 1 0.0625 7000 0 0 0 0 8000 0 0 0 0 9000 0 0 0 0 10000 1 0.055555556 1 0.0625 More 1 0.055555556 1 0.0625 18 16 Histogram: The table and histogram above summarizes the frequency distribution for each movie, these value indicate that for the movie transformers revenge of the fallen has a possibility that per theater earnings will be higher than 6,000 compared to transformers, this shows that the original movie phantom has a lower probability to gain higher earnings compared to phantom invasion B. shape of histogram: The shape of both histogram indicate that the variables are skewed, for the original movie the modal class is 2000 to 3000 while for the other movie the modal class is 1000 to 2000. There are outliers as indicated in the histogram and this include values greater than 10,000 and this include the value 17, 577 for transformers and 25, 736 for transformers revenge of the fallen. C. statistics that can be used to make conclusion regarding the two variables include the mean, quartiles and standard deviation, these values especially the mean value help in determining the expected gross value and also nature of the distribution. Q3: prediction using regression: A. scatter diagram (2009 gross and opening gross) The scatter diagram indicate a positive relations, this means an increase in opening gross means that 2009 gross is also increasing. B. trend line The trend line has a positive slope, the slope is 2.1946 while the constant value is 55.042, and the R squared value is 0.5757. C. unusual observations: The unusual observations are highlighted in the chart below: One outlier identified is the movie transformers; revenge of the fallen as indicated in the above diagram. D. predicting gross values using the budget values: Scatter diagram: Because some budget values were not available the first 30 units of data was considered: E. trend line: The trend line has a positive slope, the slope is 0.385 while the constant value is 136.16, and the R squared value is 0.1635. F. unusual observation G. appropriate model: The model that takes opening gross as the independent variable is more appropriate due to the high correlation of determination compared to the other model. The estimated value sin this case given that the budget value is 150million and that the opening balance is half this value is estimated asd follows: 75 * 2.1946 =164.595 164.595 + 55.042 = 219.64 Therefore the estimated value is equal to 219.64 million. Q4: A. stacked charts There are more male participants who prefer science fiction and action movies than female, also more female prefer romance and fantasy movies compared to males. More generation Y prefer science fiction movies than any other group, the number is followed by generation X which has a higher number than baby boomers. More generation Y on the other hand prefer action movies compared to any other group, this group also has the majority that prefer fantasy movies. Baby boomers on the other hand have the least number of individuals in each movie category and therefore the phantom movie should target those aged between 13 and 49 years. B. individual prefers science fiction as their favorite movie This probability is determined by dividing the number that prefers science fiction by the total number of individuals, this value is = 0.086 C. probability values 1 . 18 divided by 220 = 0.082 2. 22 divided by 234 = 0.094 3. 8 divided by 106 = 0.075 D. 1. 54 divided by 220 = 0.245 2. 38 divided by 234 = 0.16 3. 14 divided by 106 = 0.13 E. 1 . 32 divided by 264 = 0.12 2. 16 divided by 296 = 0.054 F. 1 . 61 divided by 264 = 0.23 2. 41 divided by 296 = 0.15 Read More