2. (30 points) Can you use movie critics opinions to forecast box office receipts on the opening weekend? The data stored in Tomatometer.csv include 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. (5 points) Use the least-squares method to get the regression coefficients b₀ and b₁. Interpret the meaning of b₀ and b₁ in this problem.

b. (5 points) Predict the mean receipts for a movie that has a Tomatometer rating of 55%.

c. (5 points) Determine the coefficient of determination, r², and explain its meaning in this problem.

d. (5 points) Perform a residual analysis and check the four assumptions of simple linear regression. Are they valid? Explain.

e. (5 points) At the 0.05 level of significance, is there evidence of a linear relationship between Tomatometer rating and receipts? Explain.

f. (5 points) Based on the results of part (a)-(e), do you think that Tomatometer rating is a useful predictor of receipts on the first weekend a movie opens? Explain.