<Li> The combination of different observations taken under different conditions . The method came to be known as the method of least absolute deviation . It was notably performed by Roger Joseph Boscovich in his work on the shape of the earth in 1757 and by Pierre - Simon Laplace for the same problem in 1799 . </Li> <Li> The development of a criterion that can be evaluated to determine when the solution with the minimum error has been achieved . Laplace tried to specify a mathematical form of the probability density for the errors and define a method of estimation that minimizes the error of estimation . For this purpose, Laplace used a symmetric two - sided exponential distribution we now call Laplace distribution to model the error distribution, and used the sum of absolute deviation as error of estimation . He felt these to be the simplest assumptions he could make, and he had hoped to obtain the arithmetic mean as the best estimate . Instead, his estimator was the posterior median . </Li> <P> The first clear and concise exposition of the method of least squares was published by Legendre in 1805 . The technique is described as an algebraic procedure for fitting linear equations to data and Legendre demonstrates the new method by analyzing the same data as Laplace for the shape of the earth . The value of Legendre's method of least squares was immediately recognized by leading astronomers and geodesists of the time . </P> <P> In 1809 Carl Friedrich Gauss published his method of calculating the orbits of celestial bodies . In that work he claimed to have been in possession of the method of least squares since 1795 . This naturally led to a priority dispute with Legendre . However, to Gauss's credit, he went beyond Legendre and succeeded in connecting the method of least squares with the principles of probability and to the normal distribution . He had managed to complete Laplace's program of specifying a mathematical form of the probability density for the observations, depending on a finite number of unknown parameters, and define a method of estimation that minimizes the error of estimation . Gauss showed that arithmetic mean is indeed the best estimate of the location parameter by changing both the probability density and the method of estimation . He then turned the problem around by asking what form the density should have and what method of estimation should be used to get the arithmetic mean as estimate of the location parameter . In this attempt, he invented the normal distribution . </P>

Who is credited with developing the method of least squares for regression