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Logistic Regression

Logistic regression aims to solve classification problems. It does this by predicting categorical outcomes, unlike linear regression that predicts a continuous outcome.

In the simplest case there are two outcomes, which is called binomial, an example of which is predicting if a tumor is malignant or benign. Other cases have more than two outcomes to classify, in this case it is called multinomial. A common example for multinomial logistic regression would be predicting the class of an iris flower between 3 different species.

Here we will be using basic logistic regression to predict a binomial variable. This means it has only two possible outcomes.

How does it work?

In Python we have modules that will do the work for us. Start by importing the NumPy module.

import numpy

Store the independent variables in X.

Store the dependent variable in y.

Below is a sample dataset:

#X represents the size of a tumor in centimeters.
X = numpy.array([3.78, 2.44, 2.09, 0.14, 1.72, 1.65, 4.92, 4.37, 4.96, 4.52, 3.69, 5.88]).reshape(-1,1)

#Note: X has to be reshaped into a column from a row for the LogisticRegression() function to work.
#y represents whether or not the tumor is cancerous (0 for "No", 1 for "Yes").
y = numpy.array([0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1])

We will use a method from the sklearn module, so we will have to import that module as well:

from sklearn import linear_model

From the sklearn module we will use the LogisticRegression() method to create a logistic regression object.

This object has a method called fit() that takes the independent and dependent values as parameters and fills the regression object with data that describes the relationship:

logr = linear_model.LogisticRegression()
logr.fit(X,y)

Now we have a logistic regression object that is ready to whether a tumor is cancerous based on the tumor size:

#predict if tumor is cancerous where the size is 3.46mm:
predicted = logr.predict(numpy.array([3.46]).reshape(-1,1))

Example

See the whole example in action:

import numpy
from sklearn import linear_model

#Reshaped for Logistic function.
X = numpy.array([3.78, 2.44, 2.09, 0.14, 1.72, 1.65, 4.92, 4.37, 4.96, 4.52, 3.69, 5.88]).reshape(-1,1)
y = numpy.array([0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1])

logr = linear_model.LogisticRegression()
logr.fit(X,y)

#predict if tumor is cancerous where the size is 3.46mm:
predicted = logr.predict(numpy.array([3.46]).reshape(-1,1))
print(predicted)

Result


 [0]

We have predicted that a tumor with a size of 3.46mm will not be cancerous.

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