In statistics

Statistics

Statistics is the study of the collection, organization, analysis, and interpretation of data. It deals with all aspects of this, including the planning of data collection in terms of the design of surveys and experiments....

, ordinary least squares (OLS) or linear least squares is a method for estimating the unknown parameters in a linear regression model. This method minimizes the sum of squared vertical distances between the observed responses in the dataset and the responses predicted by the linear approximation. The resulting estimator can be expressed by a simple formula, especially in the case of a single regressor

Simple linear regression

In statistics, simple linear regression is the least squares estimator of a linear regression model with a single explanatory variable. In other words, simple linear regression fits a straight line through the set of n points in such a way that makes the sum of squared residuals of the model as...

 on the right-hand side.

The OLS estimator is consistent

Consistent estimator

In statistics, a sequence of estimators for parameter θ0 is said to be consistent if this sequence converges in probability to θ0...

 when the regressors are exogenous

Exogenous

Exogenous refers to an action or object coming from outside a system. It is the opposite of endogenous, something generated from within the system....

 and there is no multicollinearity

Multicollinearity

Multicollinearity is a statistical phenomenon in which two or more predictor variables in a multiple regression model are highly correlated. In this situation the coefficient estimates may change erratically in response to small changes in the model or the data...

, and optimal in the class of linear unbiased estimators when the errors are homoscedastic and serially uncorrelated

Autocorrelation

Autocorrelation is the cross-correlation of a signal with itself. Informally, it is the similarity between observations as a function of the time separation between them...

.