This regression calculator hub brings together free, interactive tools for fitting a model to your data — linear, quadratic, exponential, and polynomial — each with a live plot of your points and the fitted curve, the R² goodness-of-fit, step-by-step working, and the matching NumPy code. Pick the shape that matches your data and start fitting.
What is regression?
Regression finds the curve that best describes the relationship between an input x and an output y. “Best” almost always means least squares: the curve that minimises the sum of the squared vertical gaps between your data points and the curve. The only thing that changes between regression types is the shape of the curve you allow — a straight line, a parabola, an exponential, or a higher-degree polynomial. Every calculator here shows those gaps (the residuals) on the plot so you can see exactly what is being minimised.
Choose your regression calculator
- Linear regression calculator — fits a straight line
y = mx + b. Use it when the data trends up or down at a roughly constant rate. Reports slope, intercept, R² and correlation, and predicts new values. - Quadratic regression calculator — fits a parabola
y = ax² + bx + c. Use it when the data rises then falls (or vice versa) with a single bend. - Exponential regression calculator — fits
y = a·e^(bx). Use it for growth or decay that speeds up over time, like populations, compound interest, or radioactive decay. - Polynomial regression calculator — fits a curve of any degree you choose. Use it for data with several bends that a line or parabola cannot capture.
How to pick the right model
Start with the simplest model that fits. Plot your data first (every calculator here does that automatically) and look at the shape. A roughly straight cloud of points calls for linear regression; a single hump or valley calls for quadratic; ever-steepening growth calls for exponential; multiple wiggles call for a higher-degree polynomial. Resist the temptation to crank the polynomial degree up until R² hits 1 — a model flexible enough to pass through every point usually overfits and predicts new data badly. The best model is the simplest one that captures the real trend.
Reading R²
Every regression calculator on this site reports R², the coefficient of determination, from 0 to 1. It is the fraction of the variation in y that the fitted curve explains: 0.95 means the model accounts for 95% of the variation. It is the quickest single number for comparing how well different models fit the same data — but always read it alongside the plot, because a high R² from an over-flexible model can be misleading.
Regression in machine learning
Regression is where supervised machine learning begins. The pattern is always the same: choose a model shape, define a loss (squared error), and find the parameters that minimise it. Linear and polynomial regression have exact closed-form solutions; more complex models swap the closed form for gradient descent, but the underlying idea — fit a function by minimising error — is identical. Master these calculators and the leap to logistic regression and neural networks is far smaller.
Frequently asked questions
Which regression should I use?
Match the curve to your data’s shape: straight trend → linear, single bend → quadratic, accelerating growth or decay → exponential, several bends → polynomial. Plot first, then choose.
Are these regression calculators free?
Yes — every tool is free, needs no account, and runs entirely in your browser, including the charts. Your data never leaves your device.
Do they match Excel and NumPy?
They do. All of them use the same least-squares mathematics as Excel’s trendlines and NumPy’s polyfit, so you can prototype here and reproduce the result in code.