.netCHARTING v10.5 Documentation


dotnetCHARTING Namespace > ForecastEngine Class > TrendLinePolynomial Method : TrendLinePolynomial(String,Series,Int32,DateTime,DateTime) Method
The name of the series which will be displayed on the chart, i.e. its label.
A statistical series.
The degree of the polynomial which is fitted to the data set given (i.e. if degree is 2, then a quadratic is fitted).
The start date of the trend line
The end date of the trend line
TrendLinePolynomial(String,Series,Int32,DateTime,DateTime) Method
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
'Declaration
 
Public Overloads Shared Function TrendLinePolynomial( _
   ByVal seriesName As String, _
   ByVal s As Series, _
   ByVal degree As Integer, _
   ByVal startDate As Date, _
   ByVal endDate As Date _
) As Series
'Usage
 
Dim seriesName As String
Dim s As Series
Dim degree As Integer
Dim startDate As Date
Dim endDate As Date
Dim value As Series
 
value = ForecastEngine.TrendLinePolynomial(seriesName, s, degree, startDate, endDate)
public static Series TrendLinePolynomial( 
   string seriesName,
   Series s,
   int degree,
   DateTime startDate,
   DateTime endDate
)

Parameters

seriesName
The name of the series which will be displayed on the chart, i.e. its label.
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).
startDate
The start date of the trend line
endDate
The end date of the trend line

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(String,Series,Int32), 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.

Requirements

Target Platforms: Windows 7, Windows Vista SP1 or later, Windows XP SP3, Windows Server 2008 (Server Core not supported), Windows Server 2008 R2 (Server Core supported with SP1 or later), Windows Server 2003 SP2

See Also