Chapter 13, Problem 73PS

Can you use movie critics’ opinions to forecast box office receipts on the opening weekend? The following data, stored in Tomatometer, indicate the Tomatometer rating, the percentage of professional critic reviews that are positive, and the receipts per theatre $\text{(\$thousands)}$ on the weekend a movie opened for ten movies:

a. Use the least -squares method to compute the regression coefficients $b_0$ and $b_1.$

b. Interpret the meaning of $b_0$ and $b_1$ in this problem.

c. Predict the mean receipts for a movie that has a Tomatometer rating of $55\%.$

d. Should you use the model to predict the receipts for a movie that has a Tomatometer rating of $5\%?$ 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

Tomatometer rating and receipts?

h. Construct a $95\%$ confidence interval estimate of the mean receipts for a movie that has a Tomatometer rating of $55\%$ and a $95\%$ prediction interval of the receipts for a single movie that has a Tomatometer rating of $55\%.$

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