Linear Regression Calculator
Fit a least-squares line to paired data. Free linear regression calculator giving slope, intercept, r-squared, the equation and predictions.
About the Linear Regression Calculator
Linear regression fits the straight line that best predicts y from x by minimising the squared vertical distances to the data. This free linear regression calculator takes your paired x and y values and returns the slope, the intercept, the full equation y = mx + b, the correlation r and the coefficient of determination r-squared.
The slope is m = Σ((x − x̄)(y − ȳ)) ÷ Σ(x − x̄)², and the intercept is b = ȳ − m·x̄. Once you have the equation you can predict y for any new x. R-squared tells you how well the line fits: 1 is a perfect fit, 0 means the line explains none of the variation.
Students, data analysts and researchers use regression to model trends and make predictions — sales versus advertising, height versus weight, temperature versus energy use. Everything runs privately in your browser.
How to Use the Linear Regression Calculator
- 1Enter your x values and your y values as matched lists.
- 2Ensure both lists have the same count of numbers.
- 3Read the slope, intercept and the equation of the best-fit line.
- 4Enter a new x value to predict its y, and check r-squared for fit quality.
Frequently Asked Questions
How do I calculate the line of best fit?
Compute the slope m = Σ((x − x̄)(y − ȳ)) ÷ Σ(x − x̄)² and the intercept b = ȳ − m·x̄. For points (1,2), (2,4), (3,5), (4,4), (5,5) the best fit is y = 0.6x + 2.2. The calculator does the arithmetic for any dataset.
What does r-squared tell me?
R-squared is the fraction of the variation in y explained by the line. An r-squared of 0.85 means 85% of the variability in y is accounted for by x; the remaining 15% is unexplained scatter. Higher is a better fit, but always plot the data to check.
How do I use the regression equation to predict?
Substitute a new x into y = mx + b. With y = 0.7x + 1.5, predicting for x = 6 gives 0.7 × 6 + 1.5 = 5.7. Be cautious predicting far outside the range of your data — the linear pattern may not hold.
What is the difference between correlation and regression?
Correlation (r) measures the strength and direction of a linear relationship as a single number between −1 and 1. Regression produces the actual line — slope and intercept — so you can make predictions. They are related: r-squared is literally r multiplied by itself.
How many data points do I need for regression?
Technically two, but a line through two points always fits perfectly and tells you nothing about reliability. Aim for at least 10-30 pairs so the slope and r-squared are meaningful and less swayed by a single outlier.