# least squares

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## least squares

pl.n. Statistics
A method of determining the curve that best describes the relationship between expected and observed sets of data by minimizing the sums of the squares of deviation between observed and expected values.
American Heritage® Dictionary of the English Language, Fifth Edition. Copyright © 2016 by Houghton Mifflin Harcourt Publishing Company. Published by Houghton Mifflin Harcourt Publishing Company. All rights reserved.

## least squares

n
(Mathematics) a method for determining the best value of an unknown quantity relating one or more sets of observations or measurements, esp to find a curve that best fits a set of data. It states that the sum of the squares of the deviations of the experimentally determined value from its optimum value should be a minimum
Collins English Dictionary – Complete and Unabridged, 12th Edition 2014 © HarperCollins Publishers 1991, 1994, 1998, 2000, 2003, 2006, 2007, 2009, 2011, 2014

## least′ squares′

n.
a statistical method of estimating values from a set of observations by minimizing the sum of the squares of the differences between the observations and the values to be found.
Also called least′-squares′ meth`od.
[1860–65]
Random House Kernerman Webster's College Dictionary, © 2010 K Dictionaries Ltd. Copyright 2005, 1997, 1991 by Random House, Inc. All rights reserved.
ThesaurusAntonymsRelated WordsSynonymsLegend:
 Noun 1 least squares - a method of fitting a curve to data points so as to minimize the sum of the squares of the distances of the points from the curvemethod of least squaresstatistics - a branch of applied mathematics concerned with the collection and interpretation of quantitative data and the use of probability theory to estimate population parametersstatistical method, statistical procedure - a method of analyzing or representing statistical data; a procedure for calculating a statistic
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References in periodicals archive ?
Next ordinary least squares regression model was developed by using the aspatial diagnostics to compare different models i.e.
Multicollinearity, Ridge, Principal components, Least squares, Japanese quail.
The recursion least squares method is applied to the load inertia estimation during AMT startup.
The mathematics underpinning the calculation of the equation of the straight line of best fit in the least squares sense (or regression line) is not explained in the text.
The least squares solution to the matrix equation Av = b with A [member of] [C.sup.mxn] and b [member of] [C.sup.m] is given by x = [A.sup.[dagger]] + (I - [A.sup.[dagger]] A)y, where y [member of] [C.sub.n] is an arbitrary vector.
Many iterative algorithms for system identification are based on the gradient method [31]and the least squares method [32-35].
In order to reduce noise level caused by EIV problems, some methods have been proposed, including total least squares (TLS) and instrumental variables [16].
In order to study the statistical relationship between dependent variables Y = [[y.sub.1], [y.sub.2], ..., [y.sub.q]] and the independent variables X = [[x.sub.1], [x.sub.2], ..., [x.sub.p]], partial least squares regression (PLS) analysis using principal component analysis tools, it first in the independent variable system X, extraction of a principal component of t, while the dependent variable Y system in the extraction of a principal component of u.
Recursive least squares provides a method so that the previous solution is utilized while only requiring the computation of an inverse whose square size is equal to the number of coefficients being estimated.
Partial least squares calibration models showed correlation coefficients of greater than 0.8 and standard errors of cross-validation for pH of 0.086, for Brix of 0.11, for serum viscosity of 89.2 cSt, for Bostwick consistency of 1.2 cm, for reducing sugars of 1.8 mg per mL, for ascorbic acid of 0.9 mg per 100 g and for lycopene of 11.7 ppm.
The term [N.sub.[DELTA]g] can be calculated using the Fast Fourier Transform or the least squares collocation method (Lyszkowicz, 2012; Krynski, 2007).
This paper develops least squares Legendre and Chebyshev spectral methods for the first order system of Stokes-Darcy equations.

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