Explanation
In statistics, linear regression is an approach for modeling the relationship between a scalar dependent variable y and one or more explanatory variables (or independent variable) denoted X.
The case of one explanatory variable is called simple linear regression. For more than one explanatory variable, the process is called multiple linear regression. (This term should be distinguished from multivariate linear regression^ where multiple correlated dependent variables are predicted, rather than a single scalar variable.) In linear regression data are modeled using linear predictor functions, and unknown model parameters are estimated from the data.
Such models are called linear models. Most commonly, linear regression refers to a model in which the conditional mean of y given the value of X is an affine function of X.
Less commonly: linear regression could refer to a model in which the median, or some other quantile of the conditional distribution of y given X is expressed as a linear function of X.
Like all forms of regression analysis, linear regression focuses on the conditional probability distribution of y given X, rather than on the joint probability distribution of y and X:
which is the domain of multivariate analysis.