# 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.
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Logistic models were adjusted using the methodology of quantile regression at the quantiles [tau] = 0.25, [tau] = 0.5 and [tau] = 0.75, and a model was also adjusted using the ordinary least squares method for comparative ends (Figure 1).
Least squares method is a mathematical optimization technique that finds the best match for the data by minimizing the square of the error.
Then the model accuracy based on the UKF is better than those based on the nonlinear least squares method and trial-and-error method.
* Regression (Panel Least Squares method and Period random effects method)
Table 2 contains the results from the least squares method and [M.sub.split(q)] estimation.
This paper studies GRAPPA as a noisy input-output system, which has been addressed in various ways, including Koopmans-Levin (KL) method , logarithmic least squares frequency-domain method , combined instrumental variables and subspace fitting method , and bias-eliminated least squares methods .
Values of 2P-AEF parameters obtained by GA are denoted by GA 2P-AEF, whereas results obtained by least squares method for TRF  are denoted by LS TRF in Table 3.
For decades, much research has been performed on the multivariable systems [11,12], and some typical approaches for the parameter estimation of the multivariable systems have been reported , such as the canonical approach , the iterative methods [15, 16], and the least squares methods .
Least squares method is a seeking the best approximation point method, which consider the Euclidean distance as the error metric, which generated vector space by the variable coefficient matrix.
T hereafter, we modelled the mechanical behaviour of this slope by the use of linear regression by least squares method. In the final part of this paper, a review of confrontation between the estimated slope and the two key parameters; the indentation modulus and hardness of conventional, was held to identify the factors explaining the trend characteristic points by Vickers nanoindentation test.
Least squares method. In this section we consider the Legendre and Chebyshev pseudo-spectral least squares methods for the first order system of equations (3.1)-(3.2) of the Stokes-Darcy equations.
And the output weights are analytically calculated using regularized least squares method.

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