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JWBK119-12
Logistic Regression Approach 183
Table 12.7 Characteristics of female horseshoe crabs.
Spine Carapace Spine Carapace
∗
Color condition width Weight Response Color condition width weight Response
(x C ) (x S ) (x Width ) (x Weight ) (y) (x C ) (x S ) (x Width ) (x Weight ) (y)
3 3 28.3 3050 1 3 3 28.7 3150 1
4 3 22.5 1550 0 3 1 26.8 2700 1
2 1 26 2300 1 5 3 27.5 2600 0
4 3 24.8 2100 0 3 3 24.9 2100 0
4 3 26 2600 1 2 1 29.3 3200 1
3 3 23.8 2100 0 2 3 25.8 2600 0
2 1 26.5 2350 0 3 2 25.7 2000 0
4 2 24.7 1900 0 3 1 25.7 2000 1
3 1 23.7 1950 0 3 1 26.7 2700 1
4 3 25.6 2150 0 5 3 23.7 1850 0
4 3 24.3 2150 0 3 3 26.8 2650 0
3 3 25.8 2650 0 3 3 27.5 3150 1
3 3 28.2 3050 1 5 3 23.4 1900 0
5 2 21 1850 0 3 3 27.9 2800 1
3 1 26 2300 1 4 3 27.5 3100 1
2 1 27.1 2950 1 2 1 26.1 2800 1
3 3 25.2 2000 1 2 1 27.7 2500 1
3 3 29 3000 1 3 1 30 3300 1
5 3 24.7 2200 0 4 1 28.5 3250 1
3 3 27.4 2700 1 4 3 28.9 2800 1
3 2 23.2 1950 1 3 3 28.2 2600 1
2 2 25 2300 1 3 3 25 2100 1
3 1 22.5 1600 1 3 3 28.5 3000 1
4 3 26.7 2600 1 3 1 30.3 3600 1
5 3 25.8 2000 1 5 3 26.2 1300 0
∗ 1, satellites present; 2, satellites absent.

objective of the analysis is to predict whether there are any satellites present, the
response, y, is assumed to be a binary variable of the following form:

0, if satellites present,
y =
1, if satellites absent.
Part of the original data set is reproduced in Table 12.7. The analysis in this example
is conducted based on this partial data set.
In an initial analysis, a single explanatory variable based on the carapace width
is assumed. Since the response is binary and can be assumed to follow a Bernoulli
distribution, a simple logistic regression model with a single explanatory variable of
the following form is postulated:

π Pres (x Width )

ln = α + βx Width (12.15)
1 − π Pres (x Width )