(adsbygoogle = window.adsbygoogle || []).push({}); [SOLVED] Multivariate Linear Regression With Coefficient Constraint

I'm attempting a multivariate linear regression (mvlr) by method of least squares. Basically, I'm solving a matrix of the following form for [tex]\beta_p,[/tex][tex]

$ \begin{bmatrix} \sum y \\ \sum x_1 y \\ \sum x_2 y \\ \sum x_3 y \end{bmatrix} = \begin{bmatrix} n & \sum x_1 & \sum x_2 & \sum x_3 \\ \sum x_1 & \sum x_1^2 & \sum x_1 x_2 & \sum x_1 x_3 \\ \sum x_2 & \sum x_2 x_1 & \sum x_2^2 & \sum x_2 x_3 \\ \sum x_3 & \sum x_3 x_1 & \sum x_3 x_2 & \sum x_3^2 & \end{bmatrix}\begin{bmatrix} \beta_0 \\ \beta_1 \\ \beta_2 \\ \beta_3 \end{bmatrix} $\end{text}[/tex]

x are sets of data, y is the data I want to fit, and [tex]\beta[/tex] are the coefficients.

My problem is that I want to set a constraint such that [tex]\beta[/tex] remains positive. What would be a good way to achieve this?

**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!

# Multivariate Linear Regression With Coefficient Constraint

Loading...

Similar Threads - Multivariate Linear Regression | Date |
---|---|

A Multivariate Regression vs Stratification for confounding | Apr 11, 2017 |

A Adding Multivariate Normal Distributions | Apr 2, 2017 |

About the linear combination of multivariate normal distributions. | Mar 24, 2011 |

Multivariate linear regression | May 22, 2010 |

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