A movie production company in interested in predicting the first year box office
ID: 3154066 • Letter: A
Question
A movie production company in interested in predicting the first year box office sales of a movie. They think the total production cost, total promotional costs and total book sales affect the first year box office sales. Using the BoxOffice data below.
A) What are the values of b0, b1, b2, and b3 ? Interpret their meaning.
B) What is the least squares prediction equation?
C) What is the 95% prediction interval for the first year box office of a movie with total production cost of 10 million, total promotional costs of 7 million, and total book sales of 6 million?
D) Find the multiple correlation coefficient and interpret your results. (What is the relationship between each independent variable and the dependent variable?)
E) What percentage of the variation in first year box office sales is explained by the independent variables?
F) Test the significance of the regression model.
G) Test the significance of each independent variable and the intercept.
First yr box
office
First yr box
office
Total Prod Cost Total PromotionalCosts Total Book
Sales 85.09999847 8.5 5.099999905 4.699999809 106.3000031 12.89999962 5.800000191 8.800000191 50.20000076 5.199999809 2.099999905 15.10000038 130.6000061 10.69999981 8.4 12.19999981 54.79999924 3.099999905 2.900000095 10.60000038 30.29999924 3.5 1.200000048 3.5 79.40000153 9.199999809 3.700000048 9.699999809 91 9 7.599999905 5.900000095 135.3999939 15.10000038 7.699999809 20.79999924 89.30000305 10.19999981 4.5 7.900000095
Explanation / Answer
The regression output for the given data is
Regression Analysis: First yr box versus Total Prod C, Total Promot, ...
The regression equation is
First yr box office = 7.68 + 3.66 Total Prod Cost + 7.62 Total Promotional Costs
+ 0.828 Total Book
Predictor Coef SE Coef T P
Constant 7.676 6.760 1.14 0.299
Total Prod Cost 3.662 1.118 3.28 0.017
Total Promotional Costs 7.621 1.657 4.60 0.004
Total Book 0.8285 0.5394 1.54 0.175
S = 7.54101 R-Sq = 96.7% R-Sq(adj) = 95.0%
Analysis of Variance
Source DF SS MS F P
Regression 3 9932.5 3310.8 58.22 0.000
Residual Error 6 341.2 56.9
Total 9 10273.7
Source DF Seq SS
Total Prod Cost 1 8647.4
Total Promotional Costs 1 1150.9
Total Book 1 134.2
Unusual Observations
Total First
Prod yr box
Obs Cost office Fit SE Fit Residual St Resid
8 9.0 91.00 103.44 5.24 -12.44 -2.30R
R denotes an observation with a large standardized residual.
Predicted Values for New Observations
New Obs Fit SE Fit 95% CI 95% PI
1 102.61 4.20 (92.34, 112.88) (81.49, 123.73)
A) The values of b0, b1, b2, and b3 are 7.676, 3.662, 7.621, 0.8285.
The regression coefficeint of a constant b0 is 7.676
the regression of b1 is 3.662 , this means for every unit increase of total production cost there is 3.662 times increase in first year box office.
the regression of b2 is 7.621 , this means for every unit increase of total promational cost there is 7.621 times increase in first year box office.
the regression of b3 is 0.8285 , this means for every unit increase of total book cost there is 0.8285 times increase in first year box office.
b) Least square prediction equation is
First yr box office = 7.68 + 3.66 Total Prod Cost + 7.62 Total Promotional Costs
+ 0.828 Total Book
C) The 95% prediction interval for the first year box office of a movie with total production cost of 10 million, total promotional costs of 7 million, and total book sales of 6 million is (81.49, 123.73)
D) Find the multiple correlation coefficient and interpret your results. (What is the relationship between each independent variable and the dependent variable?)
the multiple correlation coefficient is 0.983; This is high postive correlaiton between dependent variable and independent variables. This means increase in independent variables coresponding increase in dependent variable.
correlation between first year box office and total production cost = 0.917
it is high positive correlation.
correlation between first year box office and total promotional cost = 0.93
it is high positive correlation.
correlation between first year box office and total book cost = 0.4747
it is moderate positive correlation.
E) What percentage of the variation in first year box office sales is explained by the independent variables?
R-square value is 0.967 which means 96.7% of the variation in first year box office sales is explained by the independent variables.
F) Test the significance of the regression model.
The F-statistic of the model is 58.22 and the corresponding p-value is less than 0.0005
since p-value is very less so the model is significant at 0.05% level
G) Test the significance of each independent variable and the intercept.
From the above output p-value corresponding total production cost is 0.0169, this is significant at 1% level (since 0.0169 greater than 0.01)
From the above output p-value corresponding total promotional cost is 0.0037, this is not significant at 1% level (since 0.0169 less than 0.01)
From the above output p-value corresponding total book is 0.1754, this is significant at 1% level (since 0.1754 greater than 0.01)
The intercept is p-value is 0.2995 , so this is significant.
Regression output confidence interval variables coefficients std. error t (df=6) p-value 95% lower 95% upper Intercept 7.6760 6.7602 1.135 .2995 -8.8656 24.2177 Total Prod Cost 3.6616 1.1178 3.276 .0169 0.9266 6.3966 Total Promotional Costs 7.6211 1.6573 4.598 .0037 3.5657 11.6764 Total Book 0.8285 0.5394 1.536 .1754 -0.4913 2.1482Related Questions
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