What is linear regression?

Linear regression is a statistical modeling method used to predict the value of a dependent variable based on one or more independent variables. The model assumes a linear relationship between the input features and the target variable.

Formally, the model looks like this:

[ y = \beta_0 + \beta_1 x_1 + \beta_2 x_2 + \dots + \beta_n x_n + \varepsilon ]

where:

• (y) is the target variable,
• (x_i) are the features,
• (\beta_i) are the model coefficients,
• (\varepsilon) is the error (noise).

The goal of training is to find the coefficients (\beta_i) that minimize the prediction error, usually using the least squares method.

Linear regression is often used for forecasting, assessing the influence of factors, and as a baseline model in machine learning. Regularization (e.g., L1 or L2) is applied to combat overfitting and improve the model's generalization ability.