john nash is credited with developing the method of least squares for regression.
who is credited with developing the method of least squares for regression?
john nash
polynomial regression models are usually fit using the method of least squares. the least-squares method minimizes the variance of the unbiased estimators of the coefficients, under the conditions of the gauss–markov theorem. the least-squares method was published in 1805 by legendre and in 1809 by gauss. the first design of an experiment for polynomial regression appeared in an 1815 paper of gergonne. in the twentieth century, polynomial regression played an important role in the development of regression analysis, with a greater emphasis on issues of design and inference. more recently, the use of polynomial models has been complemented by other methods, with non-polynomial models having advantages for some classes of problems.
polynomial regression
many statistical methods seek to minimize the residual sum of squares, and these are called "methods of least squares" in contrast to least absolute deviations. the latter gives equal weight to small and big errors, while the former gives more weight to large errors. residual sum of squares is also differentiable, which provides a handy property for doing regression. least squares applied to linear regression is called ordinary least squares method and least squares applied to nonlinear regression is called non-linear least squares. also in a linear regression model the non deterministic part of the model is called error term, disturbance or more simply noise. both linear regression and non-linear regression are addressed in polynomial least squares, which also describes the variance in a prediction of the dependent variable (y axis) as a function of the independent variable (x axis) and the deviations (errors, noise, disturbances) from the estimated (fitted) curve.
statistics