Orthogonal distance regression in python: meaning of returned values

Question

I am following the Orthogonal distance regression method to fit data with errors on both the dependent and independent variables.

I am fitting the data with a simple straight line, my model is y = ax + b.

Now, I am able to write the code and plot the line fitting the data, but I am NOT able to read the results:

Beta: [ 2.08346947  0.0024333 ]
Beta Std Error: [ 0.03654482  0.00279946]
Beta Covariance: [[  2.06089823e-03  -9.99220260e-05]
[ -9.99220260e-05   1.20935366e-05]]
Residual Variance: 0.648029925546
Inverse Condition #: 0.011825289654
Reason(s) for Halting:
   Sum of squares convergence

The Beta is just the array containing the values of the parameters of my model (a, b), and Beta Std Error, the associated errors.

Regarding the other values, I don't know their meaning.

Especially, I would like to know which one is indicative of a goodness-of-fit, something like the chi-square when one fits with the errors only on the dependent variable.

Answer 1

Beta Covariance is the covariance matrix of your fitted parameters. It can be thought of as a matrix describing out inter-connected your two parameters are with respect to both themselves and each other.

Residual Variance I believe is a measure of the goodness-of-fit where the smaller the value, the better the fit to your data.

Inverse Condition is the inverse (1/x) of the condition number. The condition number defines how sensitive your fitted function is to changes in the input.

scipy.odr is a wrapper around a much older FORTRAN77 package known as ODRPACK. The documentation for ODRPACK can actually be found on on the scipy website. This may help you in understanding what you need to know as it contains the mathematical descriptions of the parameters.