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Descriptive statistics of Gross Revenue:
Column1  
Mean  65.92714286 
Standard Error  12.74835205 
Median  26.82 
Mode  #N/A 
Standard Deviation  111.8663352 
Sample Variance  12514.07696 
Kurtosis  11.76090225 
Skewness  3.24359001 
Range  651.6 
Minimum  0.67 
Maximum  652.27 
Sum  5076.39 
Count  77 
This analysis tells that average gross revenue is 65.92. the standard deviation of this distribution is large so we can say that there is more fluctuation in the data.
Column1  
Mean  2460.052 
Standard Error  117.8053 
Median  2720 
Mode  3003 
Standard Deviation  1033.737 
Sample Variance  1068613 
Kurtosis  0.87365 
Skewness  0.23422 
Range  3658 
Minimum  653 
Maximum  4311 
Sum  189424 
Count  77 
The data of theatres shows that the average value is 3003 and the standard deviation is 1033. It is negatively skewed data from skewness measure which is 0.234.
Column1  
Mean  54.71429 
Standard Error  2.049445 
Median  56 
Mode  81 
Standard Deviation  17.98381 
Sample Variance  323.4173 
Kurtosis  0.99233 
Skewness  0.061818 
Range  67 
Minimum  22 
Maximum  89 
Sum  4213 
Count  77 
The mean of a meteoritic score is 54.71. it is positively skewed data. Only 16 movies are of the category in a robot. Their average metacritique ranking is 54.66667 which shows that it is very close to the on an average metacritique ranking.
C. Ans
Boxandwhisker plot for the distribution of the gross revenue:
D. Ans
Correlation between a rating of a film and the revenue
0.160167647
They are positively correlated so we can say that both the data is in the same direction. If one is increasing then another will also increase.
Column1  
Largest(1)  4311 
Smallest(1)  653 
Confidence Level(90.0%)  196.16365 
No of action films analyses: = 13
Mean of their gross income = 228.38 millions
P value for the liklyhood test = 0.003102892 . so it is very less probable that film earn this much amount.
Regression output of Y
SUMMARY OUTPUT  
Regression Statistics  
Multiple R  0.781191  
R Square  0.61026  
Adjusted R Square  0.555433  
Standard Error  58.77616  
Observations  76  
ANOVA  
 df  SS  MS  F  Significance F  
Regression  8  367832.9  45979.11  15.21073  1.81E12  
Residual  68  234915.3  3454.637  
Total  76  602748.2 


 
 Coefficients  Standard Error  t Stat  Pvalue  Lower 95%  Upper 95%  Lower 95.0%  Upper 95.0% 
Intercept  159.867  32.93921  4.85339  7.42E06  225.596  94.1376  225.596  94.1376 
4291  0.047216  0.00852  5.541532  5.27E07  0.030214  0.064218  0.030214  0.064218 
59  1.354561  0.418749  3.234777  0.001881  0.518959  2.190162  0.518959  2.190162 
1  65.2928  20.40998  3.199063  0.002095  24.56532  106.0203  24.56532  106.0203 
1  46.23357  26.21074  1.763917  0.082238  6.06914  98.53627  6.06914  98.53627 
0  13.34658  31.99987  0.417082  0.677932  50.5082  77.20133  50.5082  77.20133 
0  12.27422  25.26018  0.485912  0.628592  38.1317  62.68012  38.1317  62.68012 
0  13.32961  23.82147  0.559563  0.577616  34.2054  60.86461  34.2054  60.86461 
0  0  0  65535  #NUM!  0  0  0  0 
The regression line found In the previous examples tells the relationship between Y Gross Revenue in Millions of US$ and X Number of theatres. P value in this test is equal to 5.71E11. This less than 0.05 so we can say that we need to accept the null hypothesis. The intercept of the coefficient is 93.6278 and the standard error in this 75.2322.
The regression line in above case can be written as
Y = 159.867 + 0.047216 X_{1} + 1.354561 X_{2}+ 65.2928 X_{3} + 46.23357 X_{4} + 13.34658 X_{5} + 12.27422 X_{6} + 13.32961 X_{7} + 0 X_{8}
It is a relationship between Gross Revenue in Millions of US$ and other variables. The gross revenue can be predicted from the number of theaters and other variables. The intercept part is 159.867. it is negative so we can say that in the case where all variables are 0 then it shows the negative gross income so there is a loss in this business. The coefficient of last variable is 0 , it means that it does not affect the gross income.
R Square  0.61026 
Adjusted R Square  0.555433 
The adjusted R squire is a modified version of R squire. In the prediction of the output we modified the relation and it shows that the updated r squire. If the adjusted R squire is larger than it means that the expected value is larger than the actual one.
K. Ans
Since p value is less than 0.05 in all cases except X_{3}, X_{4}, X_{5} so we can say that overall modal satisfying the required significance except these variables.
L. Ans
There are eight independent variables which effect the gross revenue in this regression modal but since the coefficient of X_{8} is 0 so we can say that except thriller all other factors effects the gross profit.
It is given that
Y gross profit
X1 Metacritique score of 30
X2 Shows in 4,000 theatres
X3 Not a sequel or a reboot
Regression analysis result
SUMMARY OUTPUT  
Regression Statistics  
Multiple R  0.767026  
R Square  0.588329  
Adjusted R Square  0.571176  
Standard Error  58.70521  
Observations  76  
ANOVA  
 df  SS  MS  F  Significance F  
Regression  3  354614.5  118204.8  34.29904  7.04E14  
Residual  72  248133.7  3446.302  
Total  75  602748.2 


 
 Coefficients  Standard Error  t Stat  Pvalue  Lower 95%  Upper 95%  Lower 95.0%  Upper 95.0% 
Intercept  158.8  30.8676  5.14457  2.23E06  220.334  97.267  220.334  97.267 
4291  0.051576  0.007616  6.771887  2.9E09  0.036393  0.066759  0.036393  0.066759 
59  1.447145  0.385132  3.757532  0.000346  0.679399  2.214892  0.679399  2.214892 
1  66.64747  19.42855  3.430388  0.001001  27.91736  105.3776  27.91736  105.3776 
Regression line is Y = 158.8 + 0.051 X_{1}+1.447 X_{2}+ 66.64 X_{3}
Predicted Y =158.8 + 0.051 x 30+1.447 x 4000+ 66.64 x 0
Y = 5601.65
Following graph shows the connection among these three variables. The curves shows that the nonlinear distribution of Gross profit, the theatres. The graph of metacritique shows the linear distribution or we can say that it is closed to linear distribution.
The above analysis tells very much information about the movies interest Australia. We can see that only 16 movies are of category reboot. On other side 15 movies are of comedy category their average metacritique ranking is 51.66667. it is very less in the case of metacritique ranking of the movies which are under reboot category. So it directly tells that most of the people taking interest in the movies of reboot category. This interest is larger than the movies of action categories. There are 14 movies are of categories in action so we can see that the average of the metacritique ranking of these movies is 52.71429. it is less than the average ranking. The average gross income of action movies is 156.37. it is larger than the average income of all type of the movies so we can try to analyze this interest also.