Mastering Logistic Regression Step By Step Implementation In Python

Leo Migdal

-Dec 4, 2025, 1:24 PM

mastering logistic regression step by step implementation in python

Logistic regression is one of the common algorithms you can use for classification. Just the way linear regression predicts a continuous output, logistic regression predicts the probability of a binary outcome. In this step-by-step guide, we’ll look at how logistic regression works and how to build a logistic regression model using Python. We’ll use the Breast Cancer Wisconsin dataset to build a logistic regression model that predicts whether a tumor is malignant or benign based on certain features. Logistic regression works by modeling the probability of a binary outcome based on one or more predictor variables. Let’s take a linear combination of input features or predictor variables.

If x represents the input features and β represents the coefficients or parameters of the model: Where β0 is the intercept term and the βs are model coefficients. A basic machine learning approach that is frequently used for binary classification tasks is called logistic regression. Though its name suggests otherwise, it uses the sigmoid function to simulate the likelihood of an instance falling into a specific class, producing values between 0 and 1. Logistic regression, with its emphasis on interpretability, simplicity, and efficient computation, is widely applied in a variety of fields, such as marketing, finance, and healthcare, and it offers insightful forecasts and useful information for... A statistical model for binary classification is called logistic regression.

Using the sigmoid function, it forecasts the likelihood that an instance will belong to a particular class, guaranteeing results between 0 and 1. To minimize the log loss, the model computes a linear combination of input characteristics, transforms it using the sigmoid, and then optimizes its coefficients using methods like gradient descent. These coefficients establish the decision boundary that divides the classes. Because of its ease of use, interpretability, and versatility across multiple domains, Logistic Regression is widely used in machine learning for problems that involve binary outcomes. Overfitting can be avoided by implementing regularization. Logistic Regression models the likelihood that an instance will belong to a particular class.

It uses a linear equation to combine the input information and the sigmoid function to restrict predictions between 0 and 1. Gradient descent and other techniques are used to optimize the model's coefficients to minimize the log loss. These coefficients produce the resulting decision boundary, which divides instances into two classes. When it comes to binary classification, logistic regression is the best choice because it is easy to understand, straightforward, and useful in a variety of settings. Generalization can be improved by using regularization. Important key concepts in logistic regression include:

Prerequisite: Understanding Logistic Regression How can you implement logistic regression from scratch in Python? Provide detailed steps, code implementation, and a thorough explanation of how logistic regression works, including the cost function and gradient descent optimization. Logistic regression is a statistical model that predicts the probability that a given input belongs to a certain category. In this guide, we will implement logistic regression from scratch using Python. The main steps involved are defining the sigmoid function, cost function, gradient descent optimization, and making predictions based on our trained model.

We will be using NumPy for numerical calculations. You can install it via pip if you don’t have it already: The sigmoid function maps any real-valued number into the range of 0 and 1. It is defined as: Next, we need to define the cost function used to measure the performance of our model, which is based on the log-loss: binary classification, Data Science, logistic regression, machine learning, Machine Learning Algorithms, maximum likelihood estimation, Predictive analytics, Python for Data Analysis, python machine learning, Python statistics, Regression Analysis, statistical modeling

Logistic Regression stands as a cornerstone algorithm in machine learning and statistics, specifically designed for problems where the outcome, or dependent variable, is categorical and binary. This means the model aims to predict one of two possible states (e.g., success/failure, 0/1, or in our case, Default/No Default). Crucially, unlike linear regression which predicts a continuous numerical value, logistic regression estimates the probability of an event belonging to the positive class. The process of fitting a logistic regression model involves determining the optimal set of coefficients for the predictor variables. This optimization is typically achieved using a technique called Maximum Likelihood Estimation (MLE). MLE works by selecting the coefficients that maximize the likelihood of observing the actual outcome data given the input features.

The successful application of MLE ensures the model parameters are statistically robust and accurately reflect the relationship between the predictors and the outcome probability. Mathematically, logistic regression transforms the continuous linear combination of predictors into a probability through the use of the sigmoid function. Before this transformation, the model relates the input variables to the log odds of the outcome (P(X)) via a standard linear equation. This intermediate step, known as the logit transformation, provides the foundation for the model’s structure: log[p(X) / (1-p(X))] = β0 + β1X1 + β2X2 + … + βpXp Before going to dive deep , we need to understand some related terminologies , these are following :

Sigmoid Function:A mathematical function that maps any real number input value to a value between 0 and 1 — used to convert outputs into probabilities. The given formula is to calculate Sigmoid function. Where x = input feature vector .w = weight vector.w^T .x= dot product of weights and inputs.Eg. consider Input vector x=[1,75]x = [1, 75]x=[1,75]Weight vector w=[0.5,0.01]w = [0.5, 0.01]w=[0.5,0.01]wTx=(0.5×1)+(0.01×75)=0.5+0.75=1.25Now apply to Sigmoid: Here we get output as 0.77 for our input 75. 2.

Decision Boundary :In logistic regression, the decision boundary is the point where the model changes its prediction from one class to another (like from class 0 to class 1). It divides the feature space into two areas: one where the model predicts class 0, and the other where it predicts class 1. As the amount of available data, the strength of computing power, and the number of algorithmic improvements continue to rise, so does the importance of data science and machine learning. Classification is among the most important areas of machine learning, and logistic regression is one of its basic methods. By the end of this tutorial, you’ll have learned about classification in general and the fundamentals of logistic regression in particular, as well as how to implement logistic regression in Python. Free Bonus: Click here to get access to a free NumPy Resources Guide that points you to the best tutorials, videos, and books for improving your NumPy skills.

Classification is a very important area of supervised machine learning. A large number of important machine learning problems fall within this area. There are many classification methods, and logistic regression is one of them. Supervised machine learning algorithms define models that capture relationships among data. Classification is an area of supervised machine learning that tries to predict which class or category some entity belongs to, based on its features. For example, you might analyze the employees of some company and try to establish a dependence on the features or variables, such as the level of education, number of years in a current position,...

The set of data related to a single employee is one observation. The features or variables can take one of two forms: When you’re dealing with outcomes that are binary – like “yes” or “no,” “churn” or “not churn,” “pass” or “fail” – traditional linear regression won’t quite cut it. That’s where logistic regression comes into play, a powerful statistical method for modeling the probability of a binary outcome. While scikit-learn is fantastic for predictive modeling, Statsmodels offers a deep dive into statistical inference, providing comprehensive summaries that are invaluable for understanding your model’s underlying structure and the significance of its predictors. In this comprehensive tutorial, we’ll walk you through performing python statsmodels logistic regression.

You’ll learn how to set up your data, build the model, interpret its detailed output, and make predictions, all with a focus on statistical rigor. At its core, logistic regression models the probability of a binary event occurring. Instead of directly predicting a 0 or 1, it predicts a probability value between 0 and 1 using the logistic (sigmoid) function. This “S-shaped” curve transforms the linear combination of predictors into a probability. While often used for classification (by setting a threshold, e.g., probability > 0.5 means “yes”), its real strength lies in understanding how each predictor influences the odds of the outcome. It’s a fundamental tool in fields ranging from medical research to marketing analytics.

You might be familiar with scikit-learn for machine learning tasks. So, why opt for Statsmodels? The key difference lies in their primary focus: Logistic regression is a statistical method used for binary classification tasks where we need to categorize data into one of two classes. The algorithm differs in its approach as it uses curved S-shaped function (sigmoid function) for plotting any real-valued input to a value between 0 and 1. To understand it better we will implement logistic regression from scratch in this article.

We will import required libraries from python: We define a class LogisticRegressionScratch that implements logistic regression using gradient descent. We’ll generate a random dataset and standardize it:

Mastering Logistic Regression Step By Step Implementation In Python

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