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 ?
Application of the method of least squares for subordinating the solution to non-homogeneous boundary conditions prescribed on the part of the boundary reduces the problems to corresponding problems of nonconstrained optimization.
Rektorys and V Zahradnik, "Solution of the first biharmonic problem by the method of least squares on the boundary," Aplikace Matematiky, vol.
assigning to parameter b acceptable values such as b = 1/2, b = 2 or b = -1); this makes it possible to create variants of the model, transformable into linear representations, for which the method of least squares can be useful for estimation (Griffiths, Carter and Judge, 1993).
A note on the variational method (Rayleigh-Ritz), Galerkin's method and the method of least squares," Radio Science, Vol.
Above all, the steps of the improved AHP based on the method of least squares can be summarized as follows:
Step 4: Determine the final group decision making comparison matrix by the method of least squares.
2) Determine the final group decision making comparison matrix revised by the method of Least squares according to the step 4.
Normal equations The equations resulting from application of the method of least squares.
The method of least squares gives the linear fits: Detection altitude = 1.
The equations used for extrapolation were obtained by the method of least squares.
at 0[degrees], 25[degrees], and 60[degrees] C and fitted to a linear equation by the method of least squares.
Where by: [DELTA]U(t)-linear visco-elastic deflection (m); F-force (N); l--reference lenghth (m); I--moment of inertia of the beam's cross section (m4), E-modulus of elasticity (MPa) Parameters of the three-parameter and four-parameter models, which describe visco-elastic behaviour of LVL elements, may be determined by application of the method of least squares.

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