A security analyst specializing in the stocks of the motion picture industry 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:
DEPENDENT VARIABLE: E
R-SQUARE
F-RATIO
P-VALUE ON F
OBSERVATIONS: 15
0.8311
63.96
0.0001
VARIABLE
PARAMETER ESTIMATE
STANDARD ERROR
T-RATIO
P-VALUE
INTERCEPT
25042000.00
20131000.00
1.24
0.2369
N
32.31
8.54
3.78
0.0023
How well do movie ticket sales in December explain the level of earnings for the entire year? Present statistical evidence to support your answer. Also, 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? Prior to this analysis, the estimates for earnings in December are $48 million. Is this evidence strong enough for you to consider a improving the current recommendation for the motion picture industry? Explain.
To evaluate how well movie ticket sales in December explain the level of earnings for the entire year, we can look at the R-Square value. The R-Square value is a measure of how well the regression model (the relationship between earnings and ticket sales) fits the actual data. In this case, the R-Square value is 0.8311, which means that approximately 83.11% of the variation in earnings can be explained by the number of movie tickets sold in December.
Additionally, we can consider the F-Ratio and its associated p-value. The F-Ratio is a test of the overall significance of the regression model, and the p-value on the F-Ratio indicates the probability of observing such a large F-Ratio by chance if the regression model was not significant. In this case, the F-Ratio is 63.96, with a p-value of 0.0001. This suggests that the regression model is statistically significant, meaning that the relationship between movie ticket sales in December and annual earnings in the motion picture industry is not likely due to random chance.
Based on this regression analysis, if movie ticket sales in December are expected to be approximately 950,000, we can use the estimated regression equation, E = a + bN, to predict earnings for the year. From the regression output, we can see that the estimated intercept (a) is 25,042,000 and the estimated coefficient for N (b) is 32.31. Therefore, the expected earnings for the year would be: E = 25,042,000 + 32.31 * 950,000 = $54,937,700.
In terms of evaluating the strength of the evidence to consider improving the current recommendation for the motion picture industry, it depends on the context and the specific goals of the analyst. A few factors to consider are the size of the estimated coefficient for N, the p-value associated with the coefficient, and the magnitude of the prior estimates for earnings in December.
In this case, the estimated coefficient for N is 32.31, with a p-value of 0.0023. This indicates a positive relationship between ticket sales in December and annual earnings, and the coefficient suggests that for every one unit increase in ticket sales in December, earnings increase by approximately $32.31 million. The prior estimates for earnings in December were $48 million.
Based on these factors, the evidence suggests that movie ticket sales in December have a statistically significant and positive impact on annual earnings in the motion picture industry. However, the magnitude of the coefficient might not be large enough to consider a significant improvement in the current recommendation for the industry. Further analysis and consideration of other factors is necessary to make a more informed decision.