Asecurity analyst specializing in the stocks of the motion picture industry wish

Question

Asecurity analyst specializing in the stocks of the motion picture industry wishes to examine
the relation between the number of movie theater tickets sold in December and
the annual level of earnings in the motion picture industry. Time-series data for the last
15 years are used to estimate the regression model
E a bN
where E is total earnings of the motion picture industry measured in dollars per year
and N is the number of tickets sold in December. The regression output is as follows:
a. How well do movie ticket sales in December explain the level of earnings for the entire
year? Present statistical evidence to support your answer.
b. On average, what effect does a 100,000-ticket increase in December sales have on the
annual earnings in the movie industry?
c. Sales of movie tickets in December are expected to be approximately 950,000. According
to this regression analysis, what do you expect earnings for the year to be?

Explanation / Answer

Here the regression equation for predicting total earnings of the motion picture industry per year (E) using the independent variable number of tickets sold in December (N) is     E = 25042000.00 + 32.31 N Here the coefficient of N in the regression equation is +32.31. This indicates that the total earnings (E) and the number of tickets sold in December (N) are positively correlated and a unit increase in the sale of tickets in December results in an increase of $32.31 in total earnings. Also the R-SQUARE value of the regression model is 0.8311. This indicates that 83.11% of the variation in the total earnings can be explained by the independent variable number of tickets sold in December (N). If the sales of movie tickets in December are expected to be approximately 950,000, the expected earnings for the year is obtained by substituting N = 950,000 in the regression equation E = 25042000.00 + 32.31 N and is given by          E = 25042000.00 + 32.31*950,000 = 55,736,500 Thus if the sales of movie tickets in December are expected to be approximately 950,000, the expected earnings for the year is $55.7365 million. If the estimates for earnings in December are $48 million, then the percentage of total earning in December will be $48 million/$55.7365 million = 86.12%. Thus the month December has 86.12% earnings of the whole year. Only 13.88% of total earnings is obtained from the remaining 11 months. Therefore we should try to increase earnings in other months.

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