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Linear Regression Calculator

Best fit line y = mx + b with slope, intercept and R².

Best for: Use it to model a trend, forecast, or quantify how one variable relates to another.

Complete guide

Input

How it's calculated & sources
The Linear Regression Calculator uses the standard, deterministic formula, so the same inputs always produce the same result. It runs entirely in your browser, so your inputs are never uploaded. Last reviewed June 2026.

Free & no sign-up · runs entirely in your browser. Results are estimates for general information, not professional advice — verify important decisions with a qualified expert. Last reviewed June 2026.

How it works

Slope m = Σ(xᵢ − x̄)(yᵢ − ȳ) / Σ(xᵢ − x̄)²

Intercept b = ȳ − m·x̄. Line: y = m·x + b. R² = 1 − SSres/SStot.

Example

x=1,2,3,4,5 y=2,4,5,4,5 → y = 0.6x + 2.2, R² ≈ 0.6

Frequently asked questions

What does R² mean?+

Proportion of variance in y explained by x. 1 = perfect fit, 0 = no linear relation.

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Complete guide

Quick answers

Short, sourced answers to the questions people (and AI assistants) ask most.

What is Linear Regression?
A linear regression calculator fits the best straight line through a set of (x, y) points using least squares.
Why does Linear Regression matter?
The slope m is the change in y per unit x; b is the value of y at x = 0. R-squared shows how much of y's variation the line explains.
How is Linear Regression calculated?
It finds the slope and intercept that minimise the sum of squared vertical distances from the points to the line. Formula: y = m x + b; m = sum((x - xbar)(y - ybar)) / sum((x - xbar)^2); b = ybar - m xbar.
What are common linear regression mistakes?
Extrapolating far beyond the data range.
When should you use the Linear Regression Calculator?
Use it to model a trend, forecast, or quantify how one variable relates to another.

What is the Linear Regression Calculator?

A linear regression calculator fits the best straight line through a set of (x, y) points using least squares.

How the Linear Regression Calculator works

It finds the slope and intercept that minimise the sum of squared vertical distances from the points to the line.

y = m x + b; m = sum((x - xbar)(y - ybar)) / sum((x - xbar)^2); b = ybar - m xbar

Common mistakes to avoid

  • Extrapolating far beyond the data range.
  • Fitting a line to clearly non-linear data.
  • Assuming correlation implies causation.

Keywords: regression, linear, ols.

Sources: NIST/SEMATECH e-Handbook of Statistical Methods

Reviewed by the Free Tools Galaxy editorial team · Updated June 2026 · Calculated privately in your browser.

Frequently asked questions

Is the Linear Regression Calculator free to use?+

Yes. Every tool on Free Tools Galaxy is 100% free, runs in your browser and requires no signup.

How accurate is the Linear Regression Calculator?+

Linear Regression Calculator uses the standard linear regression formula in double-precision arithmetic, so the same inputs always produce the same result and you can verify any figure by hand. It is an educational estimate — real-world outcomes depend on your actual rates, rules and assumptions.

Do you store my inputs?+

No. The Linear Regression Calculator runs entirely in your browser. Nothing is uploaded or saved to a server.

Can I use the Linear Regression Calculator on mobile?+

Yes — the interface is fully responsive and works on phones, tablets and desktops.

What are common mistakes to avoid?+

The most frequent mistake is mixing units. Double-check your inputs use a single, consistent unit before clicking Calculate.

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Best fit line y = mx + b with slope, intercept and R².

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