Data Analysis

Non-Linear Curve Fitter

Paste your raw X/Y coordinates to instantly perform least-squares regression modeling. Extract optimal coefficients and R² values securely in your browser.

100% client-side

1. Input Data

Column Mapping

X Y

2. Regression Model

How this model is fitted and scored

Examples:

Mathematical Model

R² = ,

Awaiting data...

How-To Guide

How to fit a curve to your data

Paste columns of numbers, choose a model, and read off the fitted equation, R² and RMSE, all computed locally in your browser.

Paste Data

Enter your data columns separated by spaces, tabs or commas | one point per line. Or click Load example data.

Map Columns

Tell the tool which columns represent your X (independent) and Y (dependent) variables.

Choose a model

Pick linear, polynomial, exponential, power or logarithmic from the dropdown, based on the shape you expect.

Check the fit

Click Compute Fit. Read R² and RMSE, watch for the overfitting warning, then use Copy Eq to grab the equation.

How the fitting works

Least-squares regression

Linear and polynomial models are fitted by ordinary least squares. R² (coefficient of determination) reports the fraction of variance explained; RMSE is the typical residual size in the units of Y. Both are computed on your original data.

Linearised non-linear models

Exponential, power and logarithmic fits are obtained by transforming the data (fitting a straight line in log-space). This is fast and standard, but it minimises error on the transformed data, so parameters can differ from a true non-linear least-squares fit when values span several orders of magnitude.

Watch out for overfitting. A model with as many parameters as data points will pass through every point and report R² = 1, even if the underlying relationship is different. A cubic needs several points beyond its 4 parameters before R² becomes meaningful; the tool warns you when your sample is too small for the chosen model.

Method & Equations

The math behind the fit

Fits are computed by least-squares regression and assessed with R² and RMSE, all in your browser.

Parameters are chosen by ordinary least squares, minimising the residual sum of squares:

\min_{θ} \sum_{i = 1}^{n} {(y_{i} - f (x_{i}; θ))}^{2}

Goodness of fit is reported with the coefficient of determination and the root-mean-square error:

R^{2} = 1 - \frac{\sum_{i}^{} {(y_{i} - {\hat{y}}_{i})}^{2}}{\sum_{i}^{} {(y_{i} - \bar{y})}^{2}}

RMSE = \sqrt{\frac{1}{n} \sum_{i = 1}^{n} {(y_{i} - {\hat{y}}_{i})}^{2}}

where $y_{i}$ are the observed values, ${\hat{y}}_{i}$ the fitted values, $\bar{y}$ the mean of y, and n the number of points. $R^{2}$ and RMSE are computed on the original data.

Model forms available:

Linear $y = m x + c$
Polynomial $y = \sum_{k = 0}^{d} a_{k} x^{k}$ (degree $d$ = 2 or 3)
Exponential $y = a e^{b x}$ → fitted as $\ln y = \ln a + b x$
Power $y = a x^{b}$ → fitted as $\ln y = \ln a + b \ln x$
Logarithmic $y = a + b \ln x$

The exponential, power and logarithmic models are fitted by linearisation (least squares on the transformed variables), which minimises error in log-space rather than in the original space.

References & documentation

Draper, N. R., & Smith, H. (1998). Applied Regression Analysis (3rd ed.). Wiley.
Heckert, N. A., Filliben, J. J., Croarkin, C., et al. (2002). NIST/SEMATECH e-Handbook of Statistical Methods, Ch. 4 “Process Modeling”. itl.nist.gov/div898/handbook.
Wikipedia: Least squares · Coefficient of determination.
Regression library: regression.js (Tom Alexander).

Frequently asked questions

Is my data sent to a server?

No. Parsing, fitting and plotting all happen in your browser using regression.js and Plotly.

Why does my exponential fit look slightly off?

Exponential/power/logarithmic models are fitted by linearisation (least squares in log-space), not true non-linear least squares, so the curve can look biased when data spans many orders of magnitude.

What do R² and RMSE mean?

R² is the fraction of variance the model explains (1 is perfect). RMSE is the root-mean-square residual, in the same units as Y, smaller is better.

Why did I get a warning about too few points?

If you have as many (or fewer) points as the model has parameters, the fit is exact or under-determined and R² is not informative. Add more data.

Which model should I pick?

Match the expected shape: straight line → linear; growth/decay → exponential; curves through the origin → power; diminishing returns → logarithmic; one/two bends → polynomial 2/3.

What R² (R-squared) means Least-squares fitting regression.js library

Runs entirely in your browser, no data leaves your device.