Page 160 - Statistics II for Dummies

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Part II: Using Different Types of Regression to Make Predictions
Finding the coefficients

and making the model

After you have Minitab run a logistic regression analysis on your data, you
can find the coefficients b and b and put them together to form the best-
0 1
fitting logistic regression model for your data.
Figure 8-2 shows part of the Minitab output for the movie enjoyment and age
data. (I discuss the remaining output in the section “Checking the fit of the
model.”) The first column of numbers is labeled Coef, which stands for the
coefficients in the model. The first coefficient, b , is labeled Constant. The
0
second coefficient is in the row labeled by your explanatory variable, x. (In
the movie and age data, the explanatory variable is age. This age coefficient
represents the value of b in the model.)
1
According to the Minitab output in Figure 8-2, the value of b is 4.87 and the
0
value of b is –0.18. After you’ve determined the coefficients b and b from
1 0 1
the Minitab output to find the best-fitting S-curve for your data, you put these
two coefficients into the general logistic regression model: .

For the movie and age data, you get , which is the best-fitting
logistic regression model for this data set.

The graph of the best-fitting logistic regression model for the movie and
age data is shown in Figure 8-3. Note that the graph is a downward-sloping
S-curve because higher probabilities of liking the movie are affiliated with
lower ages and lower probabilities are affiliated with higher ages.

The movie marketers now have the answer to their question. This movie has
a higher chance of being well liked by kids (and the younger, the better) and
a lower chance of being well liked by adults (and the older they are, the lower
the chance of liking the movie).

The point where the probability changes from high to low (that is, at the
= 0.50 mark) is between ages 25 and 30. That means that the tide of prob-
ability of liking the movie appears to turn from higher to lower in that age
range. Using calculus terms, this point is called the saddle point of the S-curve,
which is the point where the graph changes from concave up to concave
down, or vice versa.

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