Question

A researcher was interested in the revenue figures for the opening weekend of films released in the last calendar year January to December 2016. The following model is estimated by OLS, from a sample of 1,200 films:

ln(R_i) = β₀ + β₁ ln(B_i) + β₂ S_i + β₃ R15_i + u_i

where R = Revenue, B = Budget for film production, S = Critics’ average score for the film, R15=1 if the film rating is for 15 year olds and above and ln is the natural log.

Variable          Coefficient     Standard error

CONSTANT 15.473             5.3559

ln(B)                1.6652             1.0283

S                      0.2745             0.1449

R15                 -0.0834            0.0232

a)  Interpret the estimated slope coefficients. Do they have the expected signs? Explain.

b)  Is the coefficient of S significant at 5%?

c)  What model would you estimate (what additional variables would you need to define, if any) to answer the question is the return to revenue different in terms of an additional increase in the budget for films rated for under 15 year olds and 15 years old and above?

Answer 1

a)

Variable	Coefficient	Interpretation
ln(B)	1.6652	For a 1 % increase in the budget for film production, the revenue increases by 1.6652%.
S	0.2745	For one unit increase in the critic's average score, the revenue increases by 100*0.2745=27.45%.
R15	-0.0834	If the film rating is for 15 years olds and above, the revenue decreases by 100*0.0834=8.34%.

The sign for variable ln(B) is +ve which obvious, as the budget for film production increase, the revenue increase, the critics rating also helps in the increase of revenue, and if the film is age restricted to 15, there is a loss of a group of the entire population which means -ve sign is expected. All the sign is consistent with what is expected.

b)

The significance of the variable S is determined by calculating the t statistic and the corresponding p-value.

The t statistic is obtained using the following formula,

The p-value is obtained from the t distribution table for the degree of freedom = n - 4 = 1196.

Conclusion: Since the p-value is less than 0.05 at a 5% significant level, the null hypothesis is rejected hence we there is sufficient evidence to conclude that the variable S is statistically significant in the model.

c)

The variables that could affect the revenue of a film may be a foreign language dubbing (Y/N), marketing cost, number of screens.