﻿ TrendLinePolynomial(Series,Int32,Double,Int32,Int32) Method
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 dotnetCHARTING Namespace > ForecastEngine Class > TrendLinePolynomial Method : TrendLinePolynomial(Series,Int32,Double,Int32,Int32) Method

s
A statistical series.
degree
The degree of the polynomial which is fitted to the data set given (i.e. if degree is 2, then a quadratic is fitted).
step
The distance in the x-coordinate between two adjacent extended points. Please note that this also corresponds to the distance in the x-coordinate between the highest and lowest original data point and the first (above or below) additional evaluation point.
forward
The number of additional evaluation points which are evaluated above the x-coordinates of the original given data set.
backward
The number of additional evaluation points which are evaluated below the x-coordinates of the original given data set.
Fits a polynomial of a given degree to a data set in accordance with the least squares approach and returns the value of the fitted function over an extended (i.e. above, below or both) range of the x-coordinate values of the given data set.

# Syntax

Visual Basic (Declaration)
```Public Overloads Shared Function TrendLinePolynomial( _
ByVal s As Series, _
ByVal degree As Integer, _
ByVal step As Double, _
ByVal forward As Integer, _
ByVal backward As Integer _
) As Series```
Visual Basic (Usage)Copy Code
``````Dim s As Series
Dim degree As Integer
Dim step As Double
Dim forward As Integer
Dim backward As Integer
Dim value As Series

value = ForecastEngine.TrendLinePolynomial(s, degree, step, forward, backward)``````
C#
```public static Series TrendLinePolynomial(
Series s,
int degree,
double step,
int forward,
int backward
)```

#### Parameters

s
A statistical series.
degree
The degree of the polynomial which is fitted to the data set given (i.e. if degree is 2, then a quadratic is fitted).
step
The distance in the x-coordinate between two adjacent extended points. Please note that this also corresponds to the distance in the x-coordinate between the highest and lowest original data point and the first (above or below) additional evaluation point.
forward
The number of additional evaluation points which are evaluated above the x-coordinates of the original given data set.
backward
The number of additional evaluation points which are evaluated below the x-coordinates of the original given data set.

#### Return Value

A series where the k-th element of the array represents of k-th point (i.e. { x_k, y_k }) of the total set over which the fitted function is evaluated. The total set over which the fitted function is evaluated consists of the `backward' points, original data set points and the `forward' points.

Remark: This methods corresponds in functionality to the method of the same name within Microsoft Excel.

# Remarks

For example, if we fit a polynomial of degree 2, then we fit the quadratic polynomial (i.e. f(x) = a_0 + a_1 x + a_2 x^2); similarly if we fit a polynomial of degree 3, then we fit the cubic polynomial (i.e. f(x) = a_0 + a_1 x + a_2 x^2 + a_3 x^3).

Remark: The difference between this method and TrendLinePolynomial, is that it allows the values of the fitted function to be evaluated over an extended range. That is, a range in the x-coordinate greater than the original given data set.

### Where the extended values are evaluated?

The parameters `step`, `forward`, `backward` allows the position and number of additional points above and/or below the range of the values in the x-coordinate of the original data set to be given. The `forward` parameter specifies the number of the additional evaluation points of the fitted function which are greater than the values of the x-coordinates of the original data set. Similarly, the `backward` parameter specifies the number of the additional evaluation points of the fitted function which are lower than the values of the x-coordinates of the original data set. The `step` specifies the distance in the x-coordinate between each of the additional data points, where the first additional data point either above or below is exactly a distance of `step` from the points of the original data set which the highest and lowest values in the x-coordinate.

For example, consider the data set `x = 1, 2, 3`; `y = 1, 2, 3`. Now if `step = 1`, `forward = 2`, and `backward = 3`, then this method when applied will return a two dimensional array. This two dimensional array will have the following structure: `{ { -2, f(-2) } { -1, f(-1) } { 0, f(0) }{ 1, 1 } { 2, 2 }{ 3, 3 } { 4, f(4) } { 5, f(5) } }`, where `f(-2), f(-1), f(0), f(4), f(5)` correspond to the value of the fitted functions at the points `x = -2, -1, 0, 4, 5`, respectively.