Linear regression#

https://www.mihaileric.com/static/linear_regression_joke-9400ea8c70e0500f1934f7a22c86bc68-b75a8.png

Linear regression is a fundamental statistical and machine learning technique used for modeling the relationship between a dependent variable (target) and one or more independent variables (features). If we have \(n\) training samples an \(d\) features, they form a numeric dataset

(4)#\[\mathcal D = \{(\boldsymbol x_i, y_i)\}_{i=1}^n, \quad \boldsymbol x_i \in \mathbb R^d.\]

More precisely, the linear regression is called

  • simple linear regression if \(d=1\);

  • multiple linear regresion if \(d>1\);

  • multivariate linear regression if the labels are vectors: \(\boldsymbol y_i \in \mathbb R^m\), \(m>1\).