Polynomial least squares

In mathematical statistics, polynomial least squares comprises a broad range of statistical methods for estimating an underlying polynomial that describes observations.wikipedia
31 Related Articles

Least squares

least-squaresmethod of least squaresleast squares method
These methods include polynomial regression, curve fitting, linear regression, least squares, ordinary least squares, simple linear regression, linear least squares, approximation theory and method of moments.
Polynomial least squares describes the variance in a prediction of the dependent variable as a function of the independent variable and the deviations from the fitted curve.

Ordinary least squares

OLSleast squaresOrdinary least squares regression
These methods include polynomial regression, curve fitting, linear regression, least squares, ordinary least squares, simple linear regression, linear least squares, approximation theory and method of moments.
The variance in the prediction of the independent variable as a function of the dependent variable is given in the article Polynomial least squares.

Econometrics

econometriceconometricianeconometric analysis
Polynomial least squares has applications in radar trackers, estimation theory, signal processing, statistics, and econometrics. The former is commonly used in statistics and econometrics to fit a scatter plot with a first degree polynomial (that is, a linear expression).
The variance in a prediction of the dependent variable (unemployment) as a function of the independent variable (GDP growth) is given in polynomial least squares.

Statistics

statisticalstatistical analysisstatistician
Polynomial least squares has applications in radar trackers, estimation theory, signal processing, statistics, and econometrics.
Both linear regression and non-linear regression are addressed in polynomial least squares, which also describes the variance in a prediction of the dependent variable (y axis) as a function of the independent variable (x axis) and the deviations (errors, noise, disturbances) from the estimated (fitted) curve.

Mathematical statistics

mathematical statisticianstatistics mathematical statistics
In mathematical statistics, polynomial least squares comprises a broad range of statistical methods for estimating an underlying polynomial that describes observations.

Polynomial regression

cubic regressionPolynomial fittingregression
These methods include polynomial regression, curve fitting, linear regression, least squares, ordinary least squares, simple linear regression, linear least squares, approximation theory and method of moments.

Curve fitting

nominalbest-fitbest fit
These methods include polynomial regression, curve fitting, linear regression, least squares, ordinary least squares, simple linear regression, linear least squares, approximation theory and method of moments.

Linear regression

regression coefficientmultiple linear regressionregression
These methods include polynomial regression, curve fitting, linear regression, least squares, ordinary least squares, simple linear regression, linear least squares, approximation theory and method of moments.

Simple linear regression

simple regressioni.e. regression linelinear least squares regression with an intercept term and a single explanator
These methods include polynomial regression, curve fitting, linear regression, least squares, ordinary least squares, simple linear regression, linear least squares, approximation theory and method of moments.

Approximation theory

approximationChebyshev approximationapproximate
These methods include polynomial regression, curve fitting, linear regression, least squares, ordinary least squares, simple linear regression, linear least squares, approximation theory and method of moments.

Method of moments (statistics)

method of momentsmethod of matching momentsmethod of moment matching
These methods include polynomial regression, curve fitting, linear regression, least squares, ordinary least squares, simple linear regression, linear least squares, approximation theory and method of moments.

Radar tracker

trackingplot associationtracked
Polynomial least squares has applications in radar trackers, estimation theory, signal processing, statistics, and econometrics.

Estimation theory

parameter estimationestimationestimated
Polynomial least squares has applications in radar trackers, estimation theory, signal processing, statistics, and econometrics.

Signal processing

signal analysissignalsignal processor
Polynomial least squares has applications in radar trackers, estimation theory, signal processing, statistics, and econometrics.

Scatter plot

scatterplotscatter plotsscatter diagram
The former is commonly used in statistics and econometrics to fit a scatter plot with a first degree polynomial (that is, a linear expression).

Kalman filter

Kalman filteringunscented Kalman filterInformation Filter
The latter is commonly used in target tracking in the form of Kalman filtering, which is effectively a recursive implementation of polynomial least squares.

Average

Rushing averageReceiving averagemean
In effect, both applications produce average curves as generalizations of the common average of a set of numbers, which is equivalent to zero degree polynomial least squares.

Polynomial

polynomial functionpolynomialsmultivariate polynomial
In effect, both applications produce average curves as generalizations of the common average of a set of numbers, which is equivalent to zero degree polynomial least squares.

Sample (statistics)

samplesamplesstatistical sample
Given observations z_n from a sample, where the subscript n is the observation index, the problem is to apply polynomial least squares to estimate y(t), and to determine its variance along with its expected value.

Variance

sample variancepopulation variancevariability
Given observations z_n from a sample, where the subscript n is the observation index, the problem is to apply polynomial least squares to estimate y(t), and to determine its variance along with its expected value.

Expected value

expectationexpectedmean
Given observations z_n from a sample, where the subscript n is the observation index, the problem is to apply polynomial least squares to estimate y(t), and to determine its variance along with its expected value.

Linearity

linearlinearlycomplex linear
(1) The term linearity in mathematics may be considered to take two forms that are sometimes confusing: a linear system or transformation (sometimes called an operator) and a linear equation.

Mean

mean valueaveragepopulation mean
(2) The error \varepsilon is modeled as a zero mean stochastic process, sample points of which are random variables that are uncorrelated and assumed to have identical probability distributions (specifically same mean and variance), but not necessarily Gaussian, treated as inputs to polynomial least squares.

Random variable

random variablesrandom variationrandom
(2) The error \varepsilon is modeled as a zero mean stochastic process, sample points of which are random variables that are uncorrelated and assumed to have identical probability distributions (specifically same mean and variance), but not necessarily Gaussian, treated as inputs to polynomial least squares.

Probability distribution

distributioncontinuous probability distributiondiscrete probability distribution
(2) The error \varepsilon is modeled as a zero mean stochastic process, sample points of which are random variables that are uncorrelated and assumed to have identical probability distributions (specifically same mean and variance), but not necessarily Gaussian, treated as inputs to polynomial least squares.