Logistic regression is a foundational algorithm in statistics and machine learning, primarily used for binary classification problems—predicting one of two possible outcomes. Unlike linear regression, which outputs continuous values, logistic regression predicts the probability that a data point belongs to a particular class.
The logistic (or sigmoid) function maps any real-valued number into a range between 0 and 1, which makes it suitable for probability prediction.
The mathematical formula for logistic regression is:
\[ P(y = 1 \mid x) = \frac{1}{1 + e^{-(\beta_0 + \beta_1 x_1 + \beta_2 x_2 + \cdots + \beta_n x_n)}} \]
Here, \( \beta_0 \) is the intercept and \( \beta_1, \beta_2, \ldots, \beta_n \) are the coefficients of the features \( x_1, x_2, \ldots, x_n \). The result is a probability between 0 and 1, which can be converted to a class label using a threshold (commonly 0.5).
Logistic regression is widely appreciated for its simplicity, efficiency, and interpretability. It's commonly used in applications like spam detection, medical diagnosis, and customer churn prediction.