Polynomial<T>.LeastSquaresFit Method

public static Polynomial<T> LeastSquaresFit(
	Vector<T> xValues,
	Vector<T> yValues,
	int degree
)

Public Shared Function LeastSquaresFit ( 
	xValues As Vector(Of T),
	yValues As Vector(Of T),
	degree As Integer
) As Polynomial(Of T)

public:
static Polynomial<T>^ LeastSquaresFit(
	Vector<T>^ xValues, 
	Vector<T>^ yValues, 
	int degree
)

static member LeastSquaresFit : 
        xValues : Vector<'T> * 
        yValues : Vector<'T> * 
        degree : int -> Polynomial<'T> 

Parameters

xValues  Vector<T>

An array of numbers containing the X-coordinates of the points.

yValues  Vector<T>

An array of numbers containing the Y-coordinates of the points.

degree  Int32

The degree of the least squares polynomial. Must be smaller than the number of data points.

Return Value

The least squares fit of a polynomial through a set of points is the polynomial that minimizes the sum of the squares of the residuals. The residuals are the differences between the predicted and the actual values.

The coordinates of the points are provided in two T arrays. These must have the same number of elements, or an exception is thrown.

In rare cases, the least squares polynomial is a vertical line. In this case, a DivideByZeroException exception is thrown.

public static Polynomial<T> LeastSquaresFit(
	Vector<T> xValues,
	Vector<T> yValues,
	int degree,
	Vector<T>? weights
)

Public Shared Function LeastSquaresFit ( 
	xValues As Vector(Of T),
	yValues As Vector(Of T),
	degree As Integer,
	weights As Vector(Of T)
) As Polynomial(Of T)

public:
static Polynomial<T>^ LeastSquaresFit(
	Vector<T>^ xValues, 
	Vector<T>^ yValues, 
	int degree, 
	Vector<T>^ weights
)

static member LeastSquaresFit : 
        xValues : Vector<'T> * 
        yValues : Vector<'T> * 
        degree : int * 
        weights : Vector<'T> -> Polynomial<'T> 

Parameters

xValues  Vector<T>

A vector containing the X-coordinates of the points.

yValues  Vector<T>

A vector containing the Y-coordinates of the points.

degree  Int32

The degree of the least squares polynomial. Must be smaller than the number of data points.

weights  Vector<T>

A vector containing the weights of the observations.

Return Value

The least squares fit of a polynomial through a set of points is the polynomial that minimizes the sum of the squares of the residuals. The residuals are the differences between the predicted and the actual values.

The coordinates of the points are provided in two arrays. These must have the same number of elements, or an exception is thrown.

In rare cases, the least squares polynomial is a vertical line. In this case, a DivideByZeroException exception is thrown.

Reference