Data Regression Tool
Paste your data points and find the best-fit model automatically: linear, polynomial, exponential, logarithmic and power regression, scored by R² (and adjusted R² to avoid overfitting), with a scatter+fit chart, residual chart and prediction table. For science, tuning, testing and business.
How to Use
- Paste your data — either two lines <code>x: 1, 2, 3, …</code> and <code>y: 2, 4.1, …</code>, or two columns / <code>x y</code> pairs (one per line). A header row is fine.
- Leave it on <strong>Auto</strong> and the tool fits every applicable model and picks the best by adjusted R² — so it won't overfit a wiggly polynomial to a straight line. The example fits to <strong>y ≈ 2.06x − 0.04</strong>.
- Or force a specific model: linear, quadratic, cubic, exponential, logarithmic or power. The comparison table shows R² and adjusted R² for all of them.
- The <strong>scatter chart</strong> draws your points with the fitted curve, and the <strong>residual chart</strong> shows the errors (y − ŷ) — a good fit has residuals scattered randomly around zero.
- Type x-values into the <strong>predict</strong> box (comma separated) to extend the model, or leave it blank for an automatic prediction table around and beyond your data.
Data & best-fit curve
Residuals
Models it fits
About the Data Regression Tool
Whether you are at a desk or on your phone, the Data Regression Tool makes everyday maths and number work easy — and it is completely free. Paste your data points and find the best-fit model automatically: linear, polynomial, exponential, logarithmic and power regression, scored by R² (and adjusted R² to avoid overfitting), with a scatter+fit chart, residual chart and prediction table. For science, tuning, testing and business.
How it works
Type your numbers into the boxes. The answer shows up right away — you do not have to press a button. If you change a number, the answer changes too. So you can try different numbers and watch what happens, or check an answer you worked out yourself. Just make sure each box has the right kind of number in it.
Want the deeper story? The Knowledge Base explains the ideas behind the tools in more detail.
Frequently Asked Questions
How does it choose the best model?
It fits each model by least squares, computes R² (the fraction of variance explained) and the <strong>adjusted R²</strong>, then picks the highest adjusted R². Adjusted R² penalises extra parameters, so a cubic that barely fits better than a line won't win — that keeps the tool from overfitting. You can always override the choice and pick a specific model.
What is R²?
The coefficient of determination — how much of the variation in y the model explains, from 0 (no better than the mean) to 1 (perfect fit). R² = 0.99 means the model accounts for 99% of the variance. It's the standard goodness-of-fit measure for regression. Adjusted R² is the same idea but corrected for the number of parameters, so models of different complexity compare fairly.
How are the nonlinear models fitted?
Exponential (y = a·e^{bx}), power (y = a·x^b) and logarithmic (y = a + b·ln x) are fitted by transforming to a straight line — taking logs of y and/or x — running ordinary least squares, then transforming back. The reported R² is computed on the <em>original</em> data, so it's directly comparable to the other models.
When should I use each model?
<strong>Linear</strong> for a constant rate of change; <strong>polynomial</strong> for curves with turning points; <strong>exponential</strong> for growth/decay that compounds (populations, interest, cooling); <strong>logarithmic</strong> for fast-then-flattening trends (diminishing returns); <strong>power</strong> for scaling laws (area vs length, allometry). If you're unsure, Auto will rank them for you.
What do the residuals tell me?
A residual is the gap between a data point and the fitted curve (y − ŷ). If the right model is chosen, residuals scatter randomly around zero with no pattern. A clear curve or funnel shape in the residual chart means the model is wrong (e.g. fitting a line to exponential data) — switch models and watch the residuals flatten out.
Is my data sent anywhere?
No — parsing, every fit, the charts and predictions run entirely in your browser. Paste freely; nothing is uploaded and it works offline.
How do I use the Data Regression Tool?
Just type your numbers. The answer shows up right away — there is no button to press. Change anything and it updates by itself.
Is it free? Does it work without internet?
Yes to both. It is free with no sign-up, and once the page has loaded it keeps working even with no internet.
Where does my data go?
Nowhere — every calculation runs on your own device. Nothing you enter is uploaded, logged, or stored.
Common Use Cases
Science & lab work
Fit a calibration curve or rate law to measurements and read off the parameters.
Tuning & testing
Model how a metric responds to a setting and predict the sweet spot.
Business & forecasting
Trend sales or costs and project forward with a prediction table.
Engineering
Characterise sensors and components; spot the right physical model from residuals.
Education
See how R² and adjusted R² compare across model types on the same data.
Quick trendlines
Drop in points and get an equation you can paste anywhere.
Last updated: