Logistic Regression: The Tutorial That Starts Where Others End

Last Updated on July 23, 2026 by Editorial Team Author(s): Felix Pappe Originally published on Towards AI. Go inside the training loop and watch the model learn If you’ve ever wondered what statistics packages and programs are doing when calculating logistic regression, this is for you. The logistic (sigmoid) function transforms a linear input into a probability, separating binary data points into class 0 and class 1.The article walks through how logistic regression turns inputs into probabilities using the sigmoid function, framing the learning problem as maximizing likelihood (and minimizing the resulting cross-entropy/binary log-loss). It then derives the gradient needed for optimization, explains how gradient descent updates model parameters iteratively using a learning rate, and connects each math step to an example “online shop” dataset. Finally, it illustrates the first parameter update and how repeating updates over many iterations makes the learned sigmoid curve better match the data, including why input standardisation improves training stability and how to convert learned parameters back to the original feature scale for interpretation. Read the full blog for free on Medium. Join thousands of data leaders on the AI newsletter. Join over 80,000 subscribers and keep up to date with the latest developments in AI. From research to projects and ideas. If you are building an AI startup, an AI-related product, or a service, we invite you to consider becoming a sponsor. Published via Towards AI