Linear regression is a fundamental statistical learning method for modeling the relationship between a scalar dependent variable Y and one or more explanatory (independent) variables X. In simple linear regression (one X), the model is Y = wX + b + ε, where ε is the error term. In multiple regression (vector X), Y = w·X + b + ε. The model assumes Y is approximately a linear combination of the features. Training a linear regression model typically means estimating parameters w, b that minimize a loss function, usually the sum of squared errors (least squares) between predictions and true values. The closed-form solution (Normal Equation) or iterative methods like gradient descent can be used to find the optimum w. Linear regression is easy to interpret (each feature’s weight indicates its influence on the outcome) and fast to train, but obviously cannot capture complex relationships if the true relationship is non-linear (unless features are preprocessed/non-linear transformations are included). Regularized versions include Ridge (L2) and Lasso (L1) regression.