Linear regression

In statistics, linear regression is a model that estimates the relationship between a scalar response (dependent variable) and one or more explanatory variables (regressor or independent variable) related via a linear combination. A linear model with exactly one explanatory variable is a simple linear regression; a model with two or more explanatory variables is a multiple linear regression. In linear regression, the relationships are modeled using linear predictor functions whose unknown model parameters are estimated from the data. Most commonly, the conditional mean of the response given the values of the explanatory variables (or predictors) is assumed to be an affine function of those values; less commonly, the conditional median or some other quantile is used. Like all forms of regression analysis, linear regression focuses on the conditional probability distribution of the response given the values of the predictors, rather than on the joint probability distribution of all of these variables, which is the domain of multivariate analysis. A generalization of linear regression is found in nonlinear regression. Linear regression is also a type of machine learning algorithm, more specifically a supervised algorithm, that learns from the labelled datasets and maps the data points to the most optimized linear functions that can be used for prediction on new datasets. Linear regression was the first type of regression analysis to be studied rigorously, and to be used extensively in practical applications. This is because models which depend linearly on their unknown parameters are easier to fit than models which are non-linearly related to their parameters and because the statistical properties of the resulting estimators are easier to determine. Linear regression has many practical uses. Most applications fall into one of the following two broad categories: If the goal is prediction or forecasting using the data, linear regression can be used to...