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Chapter 8: Yes, No, Maybe So: Making Predictions by Using Logistic Regression
the logistic regression model
The sign on the parameter β 1 tells you the direction of the S-curve. If β 1 is pos-
itive, the S-curve goes from low to high (see Figure 8-1a); if β 1 is negative, the
S-curve goes from high to low (Figure 8-1b).
β1 > 0
1.0
1.0
0.8
0.8
0.6
0.6
p
p
Figure 8-1:
0.4
0.4
Two basic
0.2
0.2
types of
S-curves. Interpreting the coefficients of β1 < 0 151
0.0
0.0
X X
The magnitude of β 1 (indicated by its absolute value) tells you how much cur-
vature is in the model. High values indicate a steep curvature and low values
indicate slow curvature. The parameter β 0 just shifts the S-curve to the
proper location to fit your data. It shows you the cutoff point where x-values
change from high to low probability and vice versa.
Estimating the chance a movie will be
a hit by using logistic regression
Often, the best way to figure something out is to see it in action. In this sec-
tion, I give you an example of a situation where you can use a logistic regres-
sion model to estimate a probability. (I expand on this example later in this
chapter; for now, I’m just setting up a scenario for logistic regression.)
Suppose movie marketers want to estimate the chance that someone will
enjoy a certain family movie, and you believe age may have something to do
with it. Translating this research question into x’s and y’s, the response vari-
able (y) is whether or not a person will enjoy the movie, and the explanatory
variable (x) is the person’s age. You want to estimate p, the chance of some-
one enjoying the movie. You collect data on a random sample of 40 people,
shown in Table 8-1. Based on your data, it appears that younger people
enjoyed the movie more than older people, and that at a certain age, the
trend switches from liking the movie to disliking it; so, you can build a logistic
regression model to estimate p.