Editing Mathematical statistics (section)

===Regression===
{{main|Regression analysis}}

In [[statistics]], '''regression analysis''' is a statistical process for estimating the relationships among variables. It includes many ways for modeling and analyzing several variables, when the focus is on the relationship between a [[dependent variable]] and one or more [[independent variable]]s. More specifically, regression analysis helps one understand how the typical value of the dependent variable (or 'criterion variable') changes when any one of the independent variables is varied, while the other independent variables are held fixed. Most commonly, regression analysis estimates the [[conditional expectation]] of the dependent variable given the independent variables – that is, the [[average value]] of the dependent variable when the independent variables are fixed. Less commonly, the focus is on a [[quantile]], or other [[location parameter]] of the conditional distribution of the dependent variable given the independent variables. In all cases, the estimation target is a [[function (mathematics)|function]] of the independent variables called the '''regression function'''. In regression analysis, it is also of interest to characterize the variation of the dependent variable around the regression function which can be described by a [[probability distribution]].

Many techniques for carrying out regression analysis have been developed. Familiar methods, such as [[linear regression]], are [[parametric statistics|parametric]], in that the regression function is defined in terms of a finite number of unknown [[parameter]]s that are estimated from the [[data]] (e.g. using [[ordinary least squares]]). [[Nonparametric regression]] refers to techniques that allow the regression function to lie in a specified set of [[function (mathematics)|functions]], which may be [[dimension|infinite-dimensional]].