ODR Fit with Uncertainties

This Python script performs Orthogonal Distance Regression (ODR) on data with uncertainties in both the x and y variables. It reads data from a CSV file, performs the ODR analysis, and creates plots for the data, fit, residuals, and parameter correlation ellipses.

Features

• Reads data from a CSV file with columns for x, y, and their uncertainties (dx and dy)
• Performs ODR analysis using the scipy.odr module
• Calculates chi-square, reduced chi-square, and p-value for the fit
• Creates a figure with subplots for:
  • Data points with error bars and the best-fit line
  • Residuals plot with error bars
  • Parameter correlation ellipses (2D confidence regions) for the slope and intercept
• Prints the regression results, including the best-fit parameters, their uncertainties, correlation coefficient, chi-square, reduced chi-square, and p-value

Dependencies

• Python 3.x
• NumPy
• Pandas
• SciPy
• Matplotlib

Installation

Clone this repository, and install the dependencies. Detailed installation guide for beginners here: https://github.com/hezy/ODR-example/blob/main/Installation_Guide.md

Usage

1. Prepare a CSV file with the following columns: x, dx, y, dy

   • x: x-values of the data points
   • dx: uncertainties in the x-values
   • y: y-values of the data points
   • dy: uncertainties in the y-values

2. Run the script:

   python odr-fit.py data.csv
   

(change to your file name)

3. The script will read the data from the CSV file, perform the ODR analysis, and save the regression results in a file fit_results.txt

4. Three figures will be saved as files:

• fit_plot.png - the data points with best-fit line
• residuals_plots.png - the differences between observed y's to fitted y's
• correlation_ellipses.png - fitted parameters correlation ellipsesi

Example

An example CSV file (data.csv) is provided with the script that produced it (generate-fake-data.py). The data represents measurements with uncertainties in both x and y variables.

Running the script with the provided example data will produce the following output:

Regression Results:
-----------------
Slope: 2.162649 ± 0.018603
Intercept: -0.521548 ± 0.147845

Covariance matrix:
 2.222766e-04 -1.474776e-03
-1.474776e-03  1.403852e-02
Pearson's Correlation coefficient: -0.536201

Chi-square: 20.241101
Degrees of freedom: 13
Reduced chi-square: 1.557008
P-value: 0.089359

These results will be saved as a text file. Three figures will also be saved, showing the data points with error bars and the best-fit line, residuals plot, and parameter correlation ellipses for the 1σ, 2σ, and 3σ confidence levels.