Linear regression is a method to model the relationship between a dependent variable and one or more independent variables by fitting a linear equation. It works by finding a line that best represents the data, minimizing the differences between observed and predicted values. This approach is great for predicting continuous outcomes, like temperature or stock prices, where we assume a linear relationship between variables.
Logistic regression, unlike linear regression, is designed for classification tasks. It models the probability of a binary outcome, like yes/no or true/false, by using a logistic function. Instead of continuous predictions, logistic regression estimates probabilities that fall between 0 and 1, allowing it to classify instances based on threshold values (often 0.5). This makes it ideal for scenarios like predicting whether it will rain or not.
Both linear and logistic regression aim to establish a relationship between input features and an outcome, and they use a linear equation as the foundation for this. However, while linear regression predicts continuous values (e.g., house prices), logistic regression predicts probabilities for categorical outcomes (e.g., default or no default on a loan). Logistic regression further stands out by using a logistic (sigmoid) function to scale predictions between 0 and 1, enabling binary classification.
The Sigmoid function is essential in logistic regression because it transforms the linear equation output into a probability between 0 and 1. This allows us to interpret the model’s output as a likelihood for each class, making it easier to decide between categories (like yes/no) by setting a threshold. Without the Sigmoid function, logistic regression would not be able to provide these probability-based classifications effectively.
Maximum Likelihood Estimation (MLE) is the optimization approach that logistic regression uses to find the best-fitting model parameters. By maximizing the likelihood, MLE adjusts the model’s coefficients so that the predicted probabilities align closely with the observed data. This makes the model’s predictions as accurate as possible for binary outcomes, helping logistic regression effectively classify data.