Fit Plots (Least Squares & ODR)

This tutorial presents the available post-fit plots when using least squares (lmfit) or orthogonal distance regression (odr). These diagnostics are not available when using MCMC (emcee), which has its own visualizations.

We will load a sample dataset consisting of two Gaussian peaks and a linear background, restrict the fit range using Xmin/Xmax, and explore:

  • 99% confidence bands
  • Residuals
  • Model decomposition
  • 2D parameter correlation contours (not avaible with odr)

1. Load the Data

Use the menu File > Load Data and select:

examples/data/double_gaussian_with_slope.csv

The data will be automatically plotted, and the table will be filled.

data

2. Apply Xmin/Xmax Selection

Click the Xmin/Xmax button in the toolbar.

  • Click twice on the plot to define the domain to fit
  • The shaded area will indicate the active region

This allows excluding noisy or irrelevant parts of the dataset.

x selection

3. Define the Formula

In the Fit Formula dock, enter:

y = p0 * exp(-0.5 * ((x - p1)/p2)**2) + p3 * x + p4

All parameters are initialized to 0 by default. You can manually set initial values or use the Fit Options panel to configure them.

4. Run the Fit

In the Fit Control dock:

  • Select General Options tab
  • Select a method (except emcee)
  • Click Run Fit

This will produce the main fit curve and open the Fit Results dock.

5. Visualize the Fit

Once the fit is complete, you can activate various diagnostics via the toolbar:

fit

a. 99% Confidence Band

Enable the Confidence Interval icon.

  • A shaded region appears around the fit
  • Indicates uncertainty based on parameter covariance

99

b. Residuals Plot

Click the Residuals icon.

  • Opens a Data–Fit residuals tab below the main plot
  • Displays the deviation between experimental data and fitted curve, helping detect systematic errors or poor model agreement

residual

c. Decomposition Plot

Click the Fit decomposition icon.

  • Displays individual model terms (Gaussian + slope)
  • Useful for understanding each contribution

decomposition

d. 2D Parameter Contours

Enable the 2D Contour icon.

  • Shows contour plots of parameter correlations
  • Especially useful to detect strong dependencies

2d