How does the cost of a movie depend on its length? Data on the cost and running

Question

How does the cost of a movie depend on its length? Data on the cost and running time for major release firms of 2005 are summarized below: 2. Dependent variable is Budget (Smillion) R-squared =27.3% s-32.95 with 120-2-118 degrees of freedom Variable Coefficient SE(Coeff) Intercept 63.9981 Run time 1.02648 17.12 0.154 Is there evidence of an association between run time and cost? What's the value of the standard error of the slope of the regression line? Explain what that means in this context. Find a 95% confidence interval for the slope and interpret it in this context. Explain what the R-squared means in this context. a. b. c. d.

Explanation / Answer

a. The t stat of the slope coefficient is given by 6.6 (1.02/0.154). This shows that its significant at the 5% level of significance. Thus run time does significantly influence cost of the movie.

b. The standard error of the slope of the regression in this univariate case is 0.154.This means that the lower the standard error the more reliable the estimate of the slope coefficient and the t stat will be higher and hence the slope coefficient more significant.

c. The 95% confidence interval is given by 1.02648 +/ t(0.05)*32.95/sqrt(118). Here the t value needs to be obtained from the t table at 5% level of significance and at 118 degrees of freedom. So we have 1.02648 +/ 1.644*32.95/sqrt(118) = Thus the confidence interval lies between 6.01 and -3.96.

d. The R squared shows the proportion of the total variation in cost made up by the run time of the film. Here the R squared is given by 27.3% which means that 27.3% of the variation in cost is accounted for by run time. Thus there are other variables which are missing from the regression.

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