8-10. The National Association of Theatre Owners is the largest exhibition trade

Question

8-10. The National Association of Theatre Owners is the largest exhibition trade organization in the world, representing more than 26,000 movie screens in all 50 states and in more than 20 countries worldwide. Its membership includes the largest cinema chains and hundreds of independent theater owners. It publishes statistics concerning the movie sector of the economy. The file titled Flicks contains data on total U.S. box office grosses (Sbillion), total number of admissions (billion), average U.S. ticket price ($), and number of movie screens for the years 1987-2015 (source: National Association of Theatre Owners, www.natoonline.org/data, Feb. 2016). a. Construct a regression equation that uses the other variables to predict total U.S. box office grosses. b. Determine if the overall model is significant. Use a significance level of 0.05. c. Determine the range of plausible values for the change in box office grosses if the average ticket price were increased by $1. Use a confidence level of 95%

Explanation / Answer

a)

By using regression output

From the above we see that Admission and Avg ticket prices are the significant variables

Hence the equation is

Grosses=5.471*Admission +1.4369*Average ticket prices

b)

Overall the model is significant this can be seen by looking at the F significance value

2.99965E-35 <0.05

Hence the given model is highly significant

c)

If Average Ticket prices increases by 1 dollar then by looking at the confidence interval from the anova output the confidence interval of Grosses will increase by a factor which has a range as below:

1.55517

SUMMARY OUTPUT Regression Statistics Multiple R 0.999463731 R Square 0.998927749 Adjusted R Square 0.998749041 Standard Error 0.084810467 Observations 29 ANOVA df SS MS F Significance F Regression 4 160.8228764 40.20572 5589.705 2.99965E-35 Residual 24 0.172627567 0.007193 Total 28 160.995504 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept 43.08121482 27.74968858 1.552494 0.133633 -14.19132753 100.3538 Admission 5.471969935 0.241155386 22.69064 1E-17 4.974249681 5.96969 Avg Ticket Prices 1.436949025 0.057280552 25.08616 9.91E-19 1.318727777 1.55517 Screens -5.90577E-06 1.22434E-05 -0.48236 0.633919 -3.1175E-05 1.94E-05 Year -0.025329939 0.014124204 -1.79337 0.085526 -0.054480863 0.003821

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