Question

A dataset for 10 recent movies based on novels contains the variables shown. Units for all variables is millions of USD.Production: Total production cost of the movie Promotion: Total promotion cost of the movie Book: Total book sales revenue Box: First-year movie theater revenue

1. Using the summary, write the sample regression equation. (Define your variables)
2. Is there evidence book sales are useful for predicting box office revenue? Use α = .05. (Write clear hypotheses, give a p-value for the test, and state a conclusion in context)
3. An advertising executive claims that every dollar spent promoting the movie generates $14 at the box office. Conduct a hypothesis test at the α = .05 significance level to test whether the executive’s claim is too high.

Answer 1

(a) The sample regression equation is:

Revenue = 14.0654 + 1.4361*Production + 10.3702*Promotion + 0.9030*Book

(b) The hypothesis being tested is:

H₀: β₃ = 0

H₁: β₃ ≠ 0

The p-value is 0.34143.

Since the p-value (0.34143) is greater than the significance level (0.05), we fail to reject the null hypothesis.

Therefore, we cannot conclude that book sales are useful for predicting box office revenue.

(c) The hypothesis being tested is:

H₀: β₂ = 0

H₁: β₂ ≠ 0

The p-value is 0.00197.

Since the p-value (0.00197) is less than the significance level (0.05), we can reject the null hypothesis.

Therefore, we can conclude that every dollar spent promoting the movie generates $14 at the box office.