In statistics, ordinary least squares (OLS) is a type of linear least squares method for choosing the unknown parameters in a linear regression model (with...

of that for least squares. Least squares problems fall into two categories: linear or ordinary least squares and nonlinear least squares, depending on...

Weighted least squares (WLS), also known as weighted linear regression, is a generalization of ordinary least squares and linear regression in which knowledge...

including variants for ordinary (unweighted), weighted, and generalized (correlated) residuals. Numerical methods for linear least squares include inverting...

In statistics, generalized least squares (GLS) is a method used to estimate the unknown parameters in a linear regression model. It is used when there...

{\boldsymbol {\beta }}=\mathbf {d} } (see Ordinary least squares). Stochastic (linearly) constrained least squares: the elements of β {\displaystyle {\boldsymbol...

purpose of this page is to provide supplementary materials for the ordinary least squares article, reducing the load of the main article with mathematics...

system exceeds the number of observations. In such settings, the ordinary least-squares problem is ill-posed and is therefore impossible to fit because...

interest is correlated with the error term (endogenous), in which case ordinary least squares and ANOVA give biased results. A valid instrument induces changes...

theorem (or simply Gauss theorem for some authors) states that the ordinary least squares (OLS) estimator has the lowest sampling variance within the class...

provide the most efficient, linear and unbiased estimators. In ordinary least squares, the relevant assumption of the classical linear regression model...

and a dependent variable. Standard types of regression, such as ordinary least squares, have favourable properties if their underlying assumptions are...

Least-squares adjustment is a model for the solution of an overdetermined system of equations based on the principle of least squares of observation residuals...

{T}}} . Suppose that we wish to estimate a linear model using linear least squares. The model can be written as y = X β + ε , {\displaystyle \mathbf {y}...

often assumed to be that which minimizes the sum of squared residuals. This is the ordinary least squares (OLS) approach. However, in cases where the dependent...

For example, the method of ordinary least squares computes the unique line (or hyperplane) that minimizes the sum of squared differences between the true...

simple general linear model, and it can be estimated for example by ordinary least squares. Unfortunately, the task of decomposing the estimated matrix Π ^...

Heteroscedasticity does not cause ordinary least squares coefficient estimates to be biased, although it can cause ordinary least squares estimates of the variance...

total sum of squares = explained sum of squares + residual sum of squares. For a proof of this in the multivariate ordinary least squares (OLS) case, see...

the "ordinary" least squares approach in the sense that the James–Stein estimator has a lower mean squared error than the "ordinary" least squares estimator...

In applied statistics, total least squares is a type of errors-in-variables regression, a least squares data modeling technique in which observational...

The vector of estimated polynomial regression coefficients (using ordinary least squares estimation) is β → ^ = ( X T X ) − 1 X T y → , {\displaystyle {\widehat...

values. It is analogous to the least squares technique, except that it is based on absolute values instead of squared values. It attempts to find a function...

stipulation that the ordinary least squares (OLS) method should be used: the accuracy of each predicted value is measured by its squared residual (vertical...

different sizes and A {\displaystyle A} may be non-square. The standard approach is ordinary least squares linear regression.[clarification needed] However...

Partial least squares (PLS) regression is a statistical method that bears some relation to principal components regression and is a reduced rank regression;...

assumed that the variances are proportional to the squared distances. The ordinary and weighted least squares methods described above assume independent distance...

be measured with two sums of squares formulas: The sum of squares of residuals, also called the residual sum of squares: S S res = ∑ i ( y i − f i ) 2...

correlation coefficient. Theil–Sen regression has several advantages over Ordinary least squares regression. It is insensitive to outliers. It can be used for significance...

least squares. Its square root is called regression standard error, standard error of the regression, or standard error of the equation (see Ordinary...