A researcher was interested in how a movie’s box office revenue is affected by the audience suitability rating assigned by the Motion Picture Association of America

(MPAA) and the quality of the film as judged by Entertainment Weekly’s survey of ten prominent film critics. Data for 105 films were used to estimate the following equation by least squares:

where R = domestic revenue, in dollars; S = MPAA suitability rating (0 if rated G, PG, or PG-13, 1 if rated R); Q = Entertainment Weekly quality rating (12 = A, 11 = A−, 10 = B+, …); and the t values are in brackets. Explain the errors in each of these critiques of the results:

a. “The R² value of 0.214 is close enough to 0 that it can be assumed that the null hypothesis can be rejected.”

b. “The coefficient of S has the wrong sign and is also much too large.”

c. “The estimated coefficient of Q is biased downward because S and Q are negatively correlated.”

Transcribed Image Text:

R = 6,800,024-25,232,790S+6,453,431Q, R2 = 0.214 [0.61] [4.36] [3.74]