least squares

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least squares

(lēst skwārz),
A principle of estimation invented by Gauss in which the estimates of a set of parameters in a statistical model are the quantities that minimize the sum of squared differences between the observed values of the dependent variable and the values predicted by the model.

least squares

a method of regression analysis. The line on a graph that best summarizes the relationship between two variables is the one that ensures that there is the least value of the sum of the squares of the deviation between the fitted curve and each of the original data points.
References in periodicals archive ?
Lawson and Hanson (1995) proved that the problem (11) is equivalent to the least-squares problem
If the primal problem (19) has an unbounded optimal solution, then the least-squares problem (23) has for every [z.
If the LP problem is degenerate, ill-conditioned or we have any initial basis, then it is expedient to start the solution process with the least-squares problem (23).
Definition 3: The Structured Total Least-Squares problem seeks to minimize the error vector [e.
2] as bound-constrained linear least-squares problems by ADM.
CHAN, A reduced Newton method for constrained linear least-squares problems, J.
We now have a true least-squares problem, which again can be solved with the SVD.
4) is equal to the smallest singular value and thus minimal, and we have solved the linearized least-squares problem.
To achieve this, our strategy in cases with [tau] [greater than or equal to] 2 is to reduce the denominator degree from n to n - ([tau] - 1) and start the approximation process again, now inevitably as a least-squares problem rather than interpolation since N is unchanged (line 42).
Also, rank revealing factorization can be used to solve least-squares problems using the method proposed by Bjorck [1, 2].
1) This is a formal derivation and it is worth noting that one should not form generalized inverses as a method for computing solutions to linear least-squares problems.
The efficient algorithms developed in this work were used to solve large-scale least-squares problems involving millions of observations from the National Geodetic Survey.