Version:

Last Modified: January 9, 2017

Finds the line that best represents an input signal or input data set using a specific fitting method.

An array of dependent values representing the *y*-values of the data set.

This input changes to **signal** when the data type is a waveform or an array of waveforms.

An array of independent values representing the *x*-values of the data set.

This input is available only if you wire an array of double-precision floating-point numbers to **y** or **signal**.

An array of weights for the data set.

Value that determines when to stop the iterative adjustment of the slope and intercept when you use the Least Absolute Residual or Bisquare methods.

If **tolerance** is less than or equal to 0, this node sets **tolerance** to 0.0001.

How tolerance Affects the Outputs with Different Fitting Methods

For the Least Absolute Residual method, if the relative difference between **residue** in two successive iterations is less than **tolerance**, this node returns the resulting **residue**. For the Bisquare method, if any relative difference between **slope** and **intercept** in two successive iterations is less than **tolerance**, this node returns the resulting **slope** and **intercept**.

**Default: **0.0001

Error conditions that occur before this node runs. The node responds to this input according to standard error behavior.

**Default: **No error

Upper and lower constraints for the slope and intercept of the calculated best linear fit.

Lower bound for the slope.

**Default: **-Infinity

Upper bound for the slope.

**Default: **Infinity

Lower bound for the intercept.

**Default: **-Infinity

Upper bound for the intercept.

**Default: **Infinity

Method of fitting data to a line.

Name | Value | Description |
---|---|---|

Least Square | 0 | Uses the least square method. |

Least Absolute Residual | 1 | Uses the least absolute residual method. |

Bisquare | 2 | Uses the bisquare method. |

Algorithm for the Least Square Method

The least square method of fitting finds the slope and intercept of the linear model by minimizing residue according to the following equation:

$\frac{1}{N}\underset{i=0}{\overset{N-1}{\sum}}{w}_{i}{({f}_{i}-{y}_{i})}^{2}$

where

*N*is the length of**y**or the number of data values in a waveform*w*_{i}is the*i*^{th}element of**weight***f*_{i}is the*i*^{th}element of**best linear fit***y*_{i}is the*i*^{th}element of**y**or the*i*^{th}data value in a waveform

Algorithm for the Least Absolute Residual Method

The least absolute residual method finds the slope and intercept of the linear model by minimizing residue according to the following equation:

$\frac{1}{N}\underset{i=0}{\overset{N-1}{\sum}}{w}_{i}|{f}_{i}-{y}_{i}|$

where

*N*is the length of**y**or the number of data values in a waveform*w*_{i}is the*i*^{th}element of**weight***f*_{i}is the*i*^{th}element of**best linear fit***y*_{i}is the*i*^{th}element of**y**or the*i*^{th}data value in a waveform

Algorithm for the Bisquare Method

The bisquare method of fitting finds the slope and intercept using an iterative process, as shown in the following illustration.

The node calculates residue according to the following equation:

$\frac{1}{N}\underset{i=0}{\overset{N-1}{\sum}}{w}_{i}{({f}_{i}-{y}_{i})}^{2}$

where

*N*is the length of**y**or the number of data values in a waveform*w*_{i}is the*i*^{th}element of**weight***f*_{i}is the*i*^{th}element of**best linear fit***y*_{i}is the*i*^{th}element of**y**or the*i*^{th}data value in a waveform.

**Default: **Least Square

A waveform or array representing the line that best fits the input signal.

Slope of the calculated best linear fit.

Intercept of the calculated best linear fit.

Weighted mean error of the fitted model.

This node uses the general least squares method to fit the data points in an input signal to a straight line of the general form described by the following equation:

$f=ax+b$

where *x* is an input sequence, *a* is the slope of **best linear fit**, and *b* is the intercept of **best linear fit**.

This node finds the values of *a* and *b* that best fit the observations (X, Y). When the input signal is an array of double-precision, floating-point numbers, X is the **x** component of the input signal and Y is **y** component of the input signal. When the input signal is a waveform or an array of waveforms, X is the input sequence calculated from the start time of the waveform and Y is the data values in the waveform.

The following equation describes the linear curve resulting from the linear fit algorithm:

$y[i]=ax[i]+b$

**Where This Node Can Run: **

Desktop OS: Windows

FPGA: Not supported