Example 17.6

EXAMPLE 17.6 Will a Movie Be Profitable?

movprof

The MOVIES data set (described on page 550) includes both the movie's budget and the total U.S. revenue. For this example, we classify each movie as “profitable” () if U.S. revenue is larger than the budget and nonprofitable () otherwise. This is our response variable.

Figure 17.2: FIGURE 17.2 Scatterplot of the movie profit data with a scatterplot smoother, Example 17.6. The smoother suggests the upper half of an S-shape similar to those shown in Figure 17.1.

17-8

The data set contains several explanatory variables, but we focus here on the natural logarithm of the opening-weekend revenue, LOpening. Figure 17.2 is a scatterplot of the data with a scatterplot smoother (page 68). The probability that a movie is profitable increases with the log opening weekend revenue. Because an S-shaped curve like those in Figure 17.1 is suggested by the smoother, we fit the logistic regression model

where is the probability that the movie is profitable and is the log opening-weekend revenue. The model for estimated log odds fitted by software is

The estimated odds ratio is . This means that if opening-weekend revenue were roughly times larger (for example, $18.1 million to $49.2 million), the odds that the movie will be profitable increase by 2.2 times.