I have a function [tex]y = \sqrt{ax^2 + bx +c}[/tex], and 2 sets of points [tex]{x_i},{y_i}[/tex] that need to be fit on this curve. First in this problem, I need to somehow convert this nonlinear function into linear and then apply least square methods to determine a,b,c.(adsbygoogle = window.adsbygoogle || []).push({});

What I came up is ofcouse squaring both sides, removing root. Now I have: [tex] y^2 = ax^2 + bx + c[/tex]. I tried factoring this into [tex]a(x-x_1)(x-x_2)[/tex] but don't think this is better form. I'm not sure how is this even possible, there are 3 numbers to be determined as I can find only 2 equations from least square method (slope & intercept). How to determine a,b,c ? I know how to do it in eg. Mathematica, but I'm writing this as a FORTRAN program, so I need to write exact procedure. I don't know how to do nonlinear fits "by hand".

Thanks.

P.S. Simpler example of what is supposed to be done (at least I think) is function y = ax^n. Here you just take log of both sides to get: log(y) = nlog(x) + log(a), then calculate log(y_i) and log(x_i) and slope of the line with log(x) and log(y) as variables is n, with intercept log(a).

**Physics Forums - The Fusion of Science and Community**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Quadratic to Linear Fit

Loading...

Similar Threads for Quadratic Linear | Date |
---|---|

A Error estimation in linear regression | Mar 12, 2018 |

Tri-quadratic equation setup? | Jun 19, 2014 |

Confidence Interval for Coefficient of Quadratic Fit | Jan 13, 2014 |

Quadratic form and degrees of freedom- fixed title | Jan 15, 2013 |

Quadratic Regression calculation | Sep 24, 2012 |

**Physics Forums - The Fusion of Science and Community**