Table of contents
Upskilling Made Easy.
Understanding Logistic Regression
Published 13 May 2025
2.0K+
5 sec read
Logistic regression is a statistical method used for binary classification tasks, where the output is either 0 or 1 (i.e., true or false). Unlike linear regression, which predicts continuous values, logistic regression estimates the probability that a given input point belongs to a certain class. It’s a fundamental algorithm used across various fields, including medicine, finance, and social sciences, particularly when the goal is to understand the impact of several independent variables on a binary outcome.
At the heart of logistic regression lies the sigmoid function, which is used to transform the output of the linear combination of the inputs into a probability score. The sigmoid function takes any real-valued number and squashes it to a value between 0 and 1, making it suitable for probability estimation.
The sigmoid function is defined mathematically as:
sigma(z) = 1/(1 + e^-z )
Where:
In logistic regression, we model the probability that the dependent variable ( Y ) (the output) equals 1 for a given input ( X ) (the independent variables). The relationship can be represented as:
P(Y = 1 | X) = sigma(c + m1 X_1 + m2 X_2 + ... + mn X_n)
Where:
The coefficients (( beta ) values) are estimated using the maximum likelihood estimation (MLE) method, which finds the parameter values that maximize the likelihood of observing the given sample data.
Imagine you’re working with a dataset that contains information about students applying for university admission. You want to predict whether a student will be admitted based on their exam scores.
Here’s a simplified dataset representing exam scores and admission results:
Exam Score | Admitted (0 = No, 1 = Yes) |
---|---|
45 | 0 |
60 | 1 |
55 | 0 |
95 | 1 |
80 | 1 |
Defining the Input and Output:
Using Sigmoid Function:
Making Predictions:
P(textAdmitted = 1 | textScore = 75) = sigma(0.2 + 0.05 times 75) approx 0.82
This means there’s an approximately 82% chance that a student scoring 75 will be admitted.
Logistic regression is a key technique for binary classification problems, leveraging the power of the sigmoid function to make predictions based on input features. Understanding the basics of logistic regression, the role of the sigmoid function, and the methodology behind coefficient estimation is crucial for effective data analysis and predictive modeling in various applications. Whether you're predicting outcomes in health care, marketing, or education, mastering logistic regression lays a solid foundation for further exploration in the field of machine learning.
Happy predicting!