# 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

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### 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**

### Linear regression

**regression coefficientmultiple linear regressionregression**

### Simple linear regression

**simple regressioni.e. regression linelinear least squares regression with an intercept term and a single explanator**

### Approximation theory

**approximationChebyshev approximationapproximate**

### Method of moments (statistics)

**method of momentsmethod of matching momentsmethod of moment matching**

### 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**

### 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.