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 theater ($thousands) on the weekend a movie opened for ten movies:

a. Use the least-squares method to compute the regression coefficients b₀ and b₁.

b. Interpret the meaning of b₀ and b₁ 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, r², 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 results 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?

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Tomatometer Rating Movie Receipts The Mummy Zookeeper's Wife Beatriz at Dinner 16 7.8 61 6.1 80 28.4 The Hero 76 11.3 24.8 Wonder Woman 93 Baby Boss 52 13.3 The Circle 15 2.9 Dean 61 4.0 Baywatch 20 5.1 1.9 Churchill 38