# R_squared

Below is a demonstration of the features of the `R_squared` function

## Contents

```
clear; close all; clc;
```

## Syntax

`[R_sq]=R_squared(y,yf);`

## Description

This function calculates the coefficient of determination (R-Squared) for the (e.g. measurement) data `y` and the data `yf` (e.g. a model fit). NaN entries in either inputs are ignored.

## Examples

Plot settings

lineWidth=3; markerSize=50; fontSize=25;

Example data

t=linspace(0,2*pi,25); y=sin(t)+0.1*randn(size(t));

Example fit

yf=sin(t);

Compute R-squared

[R_sq]=R_squared(y,yf)

R_sq = 0.9885

Visualize

cFigure; hold on; title(['R^2=',sprintf('%.4f',R_sq)],'Interpreter','Tex'); plot(t,y,'k.','MarkerSize',markerSize); plot(t,yf,'g-','LineWidth',lineWidth); set(gca,'FontSize',fontSize); axis tight; axis square; box on; grid on; drawnow;

* GIBBON* www.gibboncode.org

*Kevin Mattheus Moerman*, gibbon.toolbox@gmail.com

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License: https://github.com/gibbonCode/GIBBON/blob/master/LICENSE

GIBBON: The Geometry and Image-based Bioengineering add-On. A toolbox for image segmentation, image-based modeling, meshing, and finite element analysis.

Copyright (C) 2019 Kevin Mattheus Moerman

This program is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version.

This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.

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