Your boss is about to start production of her newest box-office smash-to-be, Inv

Question

Your boss is about to start production of her newest box-office smash-to-be, Invasion of the Economists, Part II, when she calls you in and asks you to build a model of the gross receipts of all the movies produced in the last five years. Your regression is (standard errors are in parentheses):

(60.0) (5.0) (800) (300) (1000)

                                                            N=25

Where G_i = the final gross receipts of the ith motion picture (in thousands of dollars)

            T_i = the number of screens (theaters) on which the ith film was shown in its first week

            F_i = the dummy variable equal to 1 if the star of the film is a female or 0 otherwise

            J_i = a dummy equal to 1 if the movie was released in June/July and 0 otherwise

            S_i = a dummy variable equal to 1 if the star of the film is a superstar (like Tom Cruise) and 0 otherwise.

Answer the following questions (show your work):

(1 point) Discuss the expected signs of the coefficients (Hint: positive, negative, or no expectations)

(8 points) Interpret coefficients

(12 points) Calculate appropriate t-scores and discuss statistical significance at =5%

(2 points) Tom Hanks will appear in this movie if your boss pays $4 million for this role. If your results are trustworthy, would you recommend your boss to hire Tom Hanks or John Smith (a nobody) for $500,000?

Explanation / Answer

T_i is the number of screens on which the ith film was screened. We can expect that as the number of screens increases, the final gross receipts will also increase. Therefore, the coefficient of T_i is expected to be positive.
     F_i is a dummy variable that equals 1 when the star of the movie is a female. Historically, it has been seen that movies with female leads tend to have lesser gross receipts in the box office. Therefore, the coefficient of F_i is expected to be negative.
     J_i is a dummy variable that equals 1 if the movie was released in June/July. The specific month in which the movie is released should not have any effect on the gross receipts. Therefore, there is no specific expectation about the coefficient of J_i.
     S_i is a dummy variable that equals 1 if the star of the film is a superstar. If a superstar stars in the film, it is expected that the gross receipts of the movie will be highly boosted. Therefore, the coefficient of S_i is expected to be positive.

The coefficient of T_i represents the increase in the gross receipts (in thousands of dollars) if the movie is shown on one additional screen.
     The coefficient of F_i represents the increase in the gross receipts (in thousands of dollars) if the star of the movie is a female.
     The coefficient of J_i represents the increase in the gross receipts (in thousands of dollars) if the movie is released in June/July.
     The coefficient of S_i represents the increase in the gross receipts (in thousands of dollars) if the star of the movie is a superstar.

The t-scores for the regression coefficients can be calculated as: t-score = coefficient/standard error.

Therefore, the t-scores for the coefficients in this regression are:
Intercept: 521.0/60.0 = 8.68
T_i: 10.4/5.0 = 2.08
F_i: -2000/800 = -2.5
J_i: 1120/300 = 3.73
S_i: 5027/1000 = 5.03

The number of degrees of freedom in this regression = n – k – 1 (where n = no. of observations, k = no. of regressors)
    = 25-4-1
     = 20

The critical value of the t-distribution for d.f. = 20 at the 5% level of significance (two-tailed test) = 2.086.
As the absolute value of all the above coefficients and the intercept term are greater than 2.086, we conclude that all the above coefficients and the intercept term are statistically significant.

The incremental cost of hiring Tom Hanks for the movie = $4 million - $500,000 = $3.5 million.
On the other hand, as shown by the coefficient of S_i, on hiring Tom Hanks, the gross receipts of the movie will increase by $5.027 million.
     Therefore, the producer stands to gain by $5.027mn - $3.5mn = $1.527mn on hiring Tom Hanks and the recommendation would be to hire Tom Hanks.

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