Chapter 13, Problem 73PS

Can you use Twitter activity to forecast box office receipts on the opening weekend? The following data (stored in Twitter Movies) indicate the Twitter activity (“want to see�) and the receipts $\left(\text{\$}\right)$ per theater on the weekend a movie opened for seven movies:

a. Use the least-squares method to compute the regression coefficients $b_{\text{0}}\text{ and }{b}_1.$

b. Interpret the meaning of $b_{\text{0}}\text{ and }{b}_1$ in this problem.

c. Predict the mean receipts for a movie that has a Twitter activity of 100,000.

d. Should you use the model to predict the receipts for a movie that has a Twitter activity of 1,000,000? Why or why not?

e. Determine the coefficient of determination, $r^2,$ and explain its meaning in this problem.

f. Perform a residual analysis. Is there any evidence of a pattern in the residuals? Explain.

g. At the 0.05 level of significance, is there evidence of a linear relationship between Twitter activity and receipts?

h. Construct a 95% confidence interval estimate of the mean receipts for a movie that has a Twitter activity of 100,000 and a 95% prediction interval of the receipts for a single movie that has a Twitter activity of 100,000.

i. Based on the results of (a)-(h), do you think that Twitter activity is a useful predictor of receipts on the first weekend a movie opens? What issues about these data might make you hesitant to use Twitter activity to predict receipts?