Search results
Results from the WOW.Com Content Network
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 fixed level-one [clarification needed] effects of a linear function of a set of explanatory variables) by the principle of least squares: minimizing the sum of the squares of the differences between the observed dependent variable (values ...
The result of fitting a set of data points with a quadratic function Conic fitting a set of points using least-squares approximation. In regression analysis, least squares is a parameter estimation method based on minimizing the sum of the squares of the residuals (a residual being the difference between an observed value and the fitted value provided by a model) made in the results of each ...
The normal equations can be derived directly from a matrix representation of the problem as follows. The objective is to minimize = ‖ ‖ = () = +.Here () = has the dimension 1x1 (the number of columns of ), so it is a scalar and equal to its own transpose, hence = and the quantity to minimize becomes
Linear least squares (LLS) is the least squares approximation of linear functions to data. It is a set of formulations for solving statistical problems involved in linear regression , including variants for ordinary (unweighted), weighted , and generalized (correlated) residuals .
As described in ordinary least squares, least squares is widely used because the estimated function (, ^) approximates the conditional expectation (|). [7] However, alternative variants (e.g., least absolute deviations or quantile regression ) are useful when researchers want to model other functions f ( X i , β ) {\displaystyle f(X_{i},\beta )} .
Weighted least squares (WLS), also known as weighted linear regression, [1] [2] is a generalization of ordinary least squares and linear regression in which knowledge of the unequal variance of observations (heteroscedasticity) is incorporated into the regression.
The numerical methods for linear least squares are important because linear regression models are among the most important types of model, both as formal statistical models and for exploration of data-sets. The majority of statistical computer packages contain
Isaac Newton is credited with inventing "a certain technique known today as linear regression analysis" in his work on equinoxes in 1700, and wrote down the first of the two normal equations of the ordinary least squares method.