python中的正交距离回归：返回值的含义

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.