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Logistic Regression is a statistical method used for binary classification tasks, where the outcome variable (dependent variable) is categorical with two possible classes.

Logistic Regression is a statistical method used for binary classification tasks, where the outcome variable (dependent variable) is categorical with two possible classes. Despite its name, logistic regression is a classification algorithm rather than a regression algorithm.

It works by modeling the probability that a given input belongs to a particular class. Logistic regression estimates the probability using the logistic function (also known as the sigmoid function), which maps any real-valued input to a value between 0 and 1.

The logistic function ( f(z) = \frac{1}{1 + e^{-z}} ) transforms the linear combination of input features into a probability score, where ( z ) is the linear combination of the input features and their corresponding coefficients. The coefficients are estimated using the maximum likelihood estimation method.

During training, logistic regression learns the optimal coefficients that best fit the training data and minimize the error between the predicted probabilities and the actual class labels. Once trained, the model can predict the probability of an input belonging to a particular class and make binary classification decisions based on a chosen threshold (usually 0.5).

Logistic regression is widely used in various fields, including healthcare, finance, marketing, and social sciences, due to its simplicity, interpretability, and effectiveness for binary classification tasks. Additionally, logistic regression can be extended to handle multiclass classification tasks through techniques such as one-vs-rest or multinomial logistic regression.