**Table of Contents**

Sake is a PHP implementation of Polynomial Least Squares Regression. The algorithm takes data points as input and returns the resulting polynomial.

Graphs can be made using any plotting package. Sake provides the polynomial and will compute as many points as desired.

Polynomial regression is a model in the form of a polynomial
function. The model is typically used to understand trends in a collection
data points. It is often used in the analysis of behaviors in graphs. A
simple linear example is shown bellow where the
`c`

are coefficients,
_{i}`x`

is the input and `y`

the
output.

The coefficients are determined based on the input data set. The general equasion for the coefficients is shown below.

n |
Ʃ
^{n}x |
- |
Ʃ
^{n}x^{k} |

Ʃ
^{n}x |
Ʃ
^{n}x^{2} |
- |
Ʃ
^{n}x^{k+1} |

- |
- |
- |
- |

Ʃ
^{n}x^{k} |
Ʃ
^{n}x^{k+1} |
- |
Ʃ
^{n}x^{2k} |

c _{1} |

c _{2} |

- |

c _{k+1} |

Ʃ
^{n}y |

Ʃ
^{n}yt |

- |

Ʃ
^{n}yt^{k} |

**Sake Home Page**: http://sake.sourceforge.net/**Source Forge Project:**https://sourceforge.net/projects/sake/**Developer Guide**:http://sake.sourceforge.net/devGuide/**API Documentation**: http://sake.sourceforge.net/sakeApi/**Source Repository**: http://sake.svn.sourceforge.net/svnroot/sake/trunk/**Downloads**: https://sourceforge.net/project/showfiles.php?group_id=243341

**The MIT License**

```
Copyright (c) 2008 Thomas Davis
(sunsetbrew)
```

```
Permission is hereby granted, free of charge, to any person
obtaining a copy of this software and associated documentation files (the
"Software"), to deal in the Software without restriction, including
without limitation the rights to use, copy, modify, merge, publish,
distribute, sublicense, and/or sell copies of the Software, and to permit
persons to whom the Software is furnished to do so, subject to the
following conditions:
```

```
The above copyright notice and this permission notice shall
be included in all copies or substantial portions of the
Software.
```

```
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY
KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN
NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM,
DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR
OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE
USE OR OTHER DEALINGS IN THE SOFTWARE.
```

Please report bugs, request features or support using the tracker at http://sourceforge.net/tracker/?group_id=243341. Using this interface will help others who may see the issue and help the project team prioritize and remember it.

As it says in the license, this software is "AS IS". While the project team wants to provide the best software, it does not constitute a waver in the license.