Linear Regression
Best-fit line y = mx + b with R²
Need to best? Linear Regression gives you an exact answer in seconds. Fill in X values (comma separated) and Y values (comma separated) and read your answer immediately. Every answer includes a transparent breakdown you can repeat by hand. Use it whenever you need a reliable number without opening a spreadsheet. Everything runs in your browser — your inputs are not sent to our servers, and it works offline after the first visit (currency conversion needs a live connection). Searching for linear regression calculator least squares slope intercept r squared or a quick estimate? This tool covers it — free, fast, and private. Open Linear Regression, enter your numbers, and you will have a trustworthy answer before you know it.
What does the page calculator do?
Linear Regression works out the best-fit line mx from the X values and Y values, following standard Math conventions — the page defaults produce a best-fit line mx of y = 2.0000x + 0.0000.
- Inputs: X values and Y values.
- Output: the best-fit line mx, plus the intermediate steps behind it.
- Method: the standard Math formula, evaluated entirely in your browser.
Quick answer
With the default inputs (x values of 1,2,3,4, y values of 2,4,6,8), linear regression returns a best-fit line mx of y = 2.0000x + 0.0000. Assumptions and limits are summarized below.
How does it work?
Linear Regression computes the best-fit line mx directly from your inputs — the X values and Y values feed the formula. Nothing is uploaded: the math runs locally in your browser and the result appears as you type.
How the Linear Regression works
This page is a working linear regression: enter your values, read the output, and follow the step list to see exactly how the answer was derived.
Using the Linear Regression
- X values — one of the values the calculation builds from; the result reflects exactly what you type here.
- Y values — used in the first stage of the calculation, so entering it accurately matters more than any later refinement.
- The output panel in linear regression leads with the headline result and follows with the steps behind it, so the value can be checked rather than assumed.
- Iterate. Vary the inputs one at a time; the movement in the output shows which lever matters most for your linear regression question.
The formula behind the result
The calculation in Linear Regression applies the standard Math method, keeping full precision internally and rounding only the final display.
Worked example: with x values of 1,2,3,4, y values of 2,4,6,8, this linear regression calculation returns y = 2.0000x + 0.0000. The same run reports R² = 1.0000 | Slope: 2.0000 | Intercept: 0.0000.
The steps it follows:
- x̄ = 2.50 | ȳ = 5.00
- Sxx = Σ(x−x̄)² = 5.00 | Sxy = Σ(x−x̄)(y−ȳ) = 10.00
- Slope m = Sxy/Sxx = 2.0000
- Intercept b = ȳ − m·x̄ = 0.0000
Substitute your own values and the same steps produce your answer — that is the point of a calculator that shows its working.
Understanding the result
The best-fit line mx is the headline answer; the supporting figures beneath it and the step list give the surrounding context needed to judge it.
Where it helps
Linear Regression fits planning and checking: short-term planning, comparing scenarios side by side, and double-checking the best-fit line mx, or any moment when the figure needs to be right the first time.
Common mistakes
The most common error with Linear Regression is a unit mismatch — one value entered in different units than its label assumes quietly skews the figure. Check each label before typing.
Tip: Run Linear Regression twice with deliberately low and high inputs; the spread tells you how sensitive the output is, which a single run never shows.
Assumptions and limitations
The model behind Linear Regression covers the standard case; special cases, edge values, or jurisdiction-specific rules may need manual adjustment.
Why use this calculator
Because it is fast and private — Linear Regression runs entirely in your browser, nothing is uploaded, and no account is needed.
From Our Guides Library
Frequently Asked Questions
What does the tool calculate?
Linear Regression turns the values you enter into a verified best-fit line mx — the formula, every intermediate step, and the assumptions sit beside the result instead of hidden behind it. Because the page doubles as documentation: Linear Regression puts the formula, a worked example, and the assumptions right beside the calculator.
How is the best-fit line mx calculated?
The first steps are x̄ = 2.50 | ȳ = 5.00, then sxx = σ(x−x̄)² = 5.00 | sxy = σ(x−x̄)(y−ȳ) = 10.00. Linear Regression substitutes the X values and Y values into the formula, evaluates it in the order shown in the steps panel, and reports the result rounded for readability.
What do I need to use the Linear Regression?
The X values and Y values it asks for, or the page defaults if you just want to see the calculation work. Each input maps directly to the formula, and changing any one of them recalculates the best-fit line mx instantly.
What does the result from the tool mean?
The main number the linear regression returns is the best-fit line mx for your exact inputs, and the supporting figures and step list give it context. Results from Linear Regression are estimates computed from the values entered; real-world outcomes can differ when fees, taxes, or conditions not modeled here apply.
When is the page most useful?
Typical uses for Linear Regression include short-term planning, comparing scenarios side by side, and double-checking the best-fit line mx — anywhere the figure needs to be defensible rather than guessed. Run Linear Regression twice with deliberately low and high inputs; the spread tells you how sensitive the figure is, which a single run never shows.