LinearFitEx

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Updated2023-02-21
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Advanced Analysis Library Only

AnalysisLibErrType LinearFitEx (double arrayX[], double arrayY[], double weight[], ssize_t numberOfElements, int fitMethod, double tolerance, double fittedData[], double *slope, double *intercept, double *residue);

Purpose

Fits the data set (x, y) to the linear model using the Least Square, Least Absolute Residual, or Bisquare method. The following equation represents the linear model:

where	f represents the fittedData
	a is the slope
	x represents the input sequence arrayX
	b is the intercept

If fitMethod is LEAST_SQUARE, the function finds the slope and intercept of the linear model by minimizing the residue as follows:

where	n is numberOfElements
	w_i is the i-th element of weight
	f_i is the i-th element of fittedData
	y_i is the i-th element of arrayY

If fitMethod is LEAST_ABSOLUTE_RESIDUAL, the function finds the slope and intercept of the linear model by minimizing the residue as follows:

If fitMethod is BISQUARE, the function finds slope and intercept of the linear model by using reweighted least square fitting iteratively, as shown in the following flowchart:

Parameters

Input
Name	Type	Description
arrayX	double []	The x value of the data set (x, y).
arrayY	double []	The y value of the data set (x, y). If fittedData is NULL, arrayY is overwritten by the best fitted array.
weight	double []	The weight of each data point. If weight is NULL, the function sets all the elements of weight to 1.
numberOfElements	ssize_t	The length of arrayX, arrayY, and weight.
fitMethod	int	The fitting method. fitMethod must be one of the following values: LEAST_SQUARE (0) LEAST_ABSOLUTE_RESIDUAL (1) BISQUARE (2) The Least Square method is preferable if the noise in arrayY is Gaussian distributed. The Least Absolute Residual and Bisquare method are robust fitting methods. Therefore, they are preferable if there are outliers in the observations. In most cases, the Bisquare method is less sensitive to outliers than the Least Absolute Residual method.
tolerance	double	The stop criteria used in the Least Absolute Residual method or Bisquare method. In these two methods, the function adjusts the slope and intercept iteratively. If the relative difference of residue in two successive iterations is less than tolerance, the function returns the resulting slope and intercept. If tolerance is less than or equal to 0, the function sets tolerance to 0.0001.
Output
Name	Type	Description
fittedData	double []	The y values calculated using the fitted linear model. If fittedData is NULL, the best fit array overwrites arrayY.
slope	double	The slope of the fitted linear model.
intercept	double	The intercept of the fitted linear model.
residue	double	The weighted mean error of the linear fit. If fitMethod is LEAST_ABSOLUTE_RESIDUAL, residue is the weighted mean absolute error, as follows: If fitMethod is LEAST_SQUARE or BISQUARE, residue is the weighted mean square error, as follows:

Return Value

Name	Type	Description
status	AnalysisLibErrType	A value that specifies the type of error that occurred. Refer to analysis.h for definitions of these constants.

Additional Information

Library: Advanced Analysis Library

Include file: analysis.h

LabWindows/CVI compatibility: LabWindows/CVI 8.0 and later

LabWindows/CVI

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