9781118041581

Forecasting 167

Top management of the movie chain seeks to use demand analysis to produce the best-

possible prediction of the film’s weekly gross revenue per screen. The chain’s profit

directly depends on this prediction. For instance, a contract having the chain pay the stu-

dio $4,500 per screen per week (for a four-week guaranteed run) will be a bargain if the

film turns out to be a megahit and earns gross revenue of $8,000 per screen per week. The

same contract is a losing proposition if the film bombs and brings in only $1,500 per

screen per week.

The theater chain’s staff economists have used data from 204 major film releases

during the preceding calendar year to estimate a demand equation to predict average

revenues for a typical film. The best regression equation fitting the data is found to be

AR 12,697N.197(1.31)S(1.27)H(1.22)C(1.15)A [4.16]

The dependent variable is the average revenue per screen per week (during the first four

weeks of the film’s release). In turn, N denotes the number of nationwide screens on

which the film is playing. The other explanatory variables are dummy variables: S 1 for

a summer release, H 1 for a holiday release, C 1 if the cast contains one or more

proven blockbuster stars, and A 1 if the film is a large-budget action film. (If a film

does not fall into a given category, the dummy variable is assigned the value of 0.)

According to Equation 4.16, a nondescript film (S H C A 0) released in

2,000 theaters nationwide would generate revenue per screen per week of AR 

12,697(2,000).197$2,841. Consider the effect of varying the number of screens. The

negative exponent .197 means that average revenue per screenfalls with the number of

screens playing the film. A film in narrow release (for instance, in an exclusive engage-

ment on single screens in major cities) earns much more revenue per screenthan a film in

the widest release (3,500 screens nationwide), which inevitably leaves many seats empty.

Thus, the same nondescript film released on only 100 screens nationwide would earn

AR 12,697(100).197$5,125 per screen per week. Next, note the effect of each

dummy variable. The multiplicative factor associated with S (1.31) means that, other

things equal, a summer release (S 1) will increase AR by a factor of (1.31)^1 , or 31 per-

cent. Similarly, a starry cast will increase predicted AR by 22 percent, and an action film

will raise AR by 15 percent. It is easy to check that releasing a summer action film with a

starry cast increases revenue by a factor of (1.31)(1.22)(1.15) 1.84, or 84 percent.

The data used to estimate Equation 4.16 (average revenues, numbers of screens,

and so on) were collected from the weekly entertainment magazine Variety, which reports

on all major U.S. film releases. The theater chain collected these data for 204 films.

Equation 4.16’s multiplicative form was estimated (via ordinary least squares) in the

equivalent log-linear form. Thus, the actual regression equation (from which Equation 4.16

is derived) is

log(AR) 9.45  .197log(N)  .27S  .23H  .20C  .14A [4.17]

To go from Equation 4.17 to Equation 4.16, we took the antilog of Equation 4.18’s coef-

ficients. Thus, antilog(9.45) 12,697, antilog(.27) 1.31, antilog(.23) 1.27, and so on.

Estimating Movie

Demand

Revisited

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