A Beginner's Guide to Curve Fitting Without Coding

In experimental science, raw data points rarely fall perfectly on a smooth line. Noise, instrumental limits, and statistical fluctuations create scatter. Curve fitting is the mathematical technique used to find the best-fit function that describes your physical system.

Traditionally, running non-linear regression required writing Python scripts with scipy.optimize.curve_fit or using complex mathematical software. In this guide, you'll learn how to fit equations to your data in just 3 clicks with AltaiPlot.

Step 1: Understand Common Fitting Models

• Linear (y = mx + c): Calibration curves, Ohm's law, and constant-rate kinetics.
• Exponential Decay: Radioactive decay, capacitor discharge, chemical reaction rates, and luminescence lifetime.
• Gaussian Peak: Spectroscopy bands, chromatography elution peaks, and thermal distribution profiles.
• Polynomial: Empirical non-linear calibration curves.

Step 2: Curve Fitting in 3 Simple Clicks

AltaiPlot bundles 101 SciPy-verified fitting algorithms into an intuitive visual workflow:

1. Highlight Your Region: Use the range selector cursors to limit the fit to your region of interest (e.g., a specific spectral peak).
2. Choose Model: Select your model from the fitting sidebar (Linear, Exponential, Gaussian, Lorentzian, etc.).
3. Click "Fit": AltaiPlot calculates optimal initial guesses and solves the Levenberg-Marquardt non-linear least squares problem instantly.

Step 3: Evaluating Goodness of Fit ($R^2$ and RMSE)

Once the fit converges, AltaiPlot presents the fit statistics directly below the graph:

• R² (Coefficient of Determination): Closer to 1.0 means a stronger correlation (e.g., R² = 0.998 indicates an excellent fit).
• Residuals Plot: Displays the point-by-point difference between raw data and your fitted curve. Evenly distributed noise around zero confirms a valid model.
• Parameter Uncertainties: Every estimated parameter (such as peak center or decay time) comes with its corresponding standard error (± SE).