TrendLinePolynomial(Series,Int32,Double,Int32,Int32) 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.

[Visual Basic]
Overloads Public 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

[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 Type

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.

See Also

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