Average
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Mean, median, mode, range and standard deviation from any list.
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Statistics — Regression
Linear Regression Calculator
Paste your paired X and Y values to get the least-squares line of best fit — slope, intercept, the y = mx + b equation and R-squared.
Line of best fit
—
Least-squares regression line.
| Slope b₁ | — |
|---|---|
| Intercept b₀ | — |
| R squared fit quality | — |
| Correlation r | — |
| Pairs n | — |
Show our math
Enter your figures above to see the step-by-step working.
Least-squares fit — be cautious predicting outside your data rangeEverything computed client-side — nothing leaves this page
How the Linear Regression Calculator Works
Linear regression finds the straight line that best predicts Y from X by minimising the sum of the squared vertical distances from each point to the line — the least-squares method. Paste your paired data and the desk returns the line’s equation, its slope and intercept, and how well it fits.
The slope is how much Y changes for each one-unit rise in X; the intercept is the predicted Y when X is zero. The R² value, from 0 to 1, is the share of the variation in Y explained by the line — the closer to 1, the tighter the fit.
slope = Σ(x − x̄)(y − ȳ) ÷ Σ(x − x̄)² · intercept = ȳ − slope · x̄
Frequently Asked Questions
What do the slope and intercept mean?
The slope is the predicted change in Y for each one-unit increase in X. The intercept is the predicted value of Y when X equals zero. Together they define the line y = slope·x + intercept.
What is a good R-squared value?
R² ranges from 0 to 1 and gives the fraction of the variation in Y explained by the line. What counts as “good” depends on the field — physical measurements may expect above 0.9, while noisy social data may treat 0.3 as meaningful.
Can I use this to predict new values?
Yes — plug an X into the equation to get a predicted Y. Be cautious predicting far outside the range of your data (extrapolation), where the linear pattern may no longer hold.
More From The Desk
Same plain method, different figuresAverage
Standard
Deviation
Sample and population spread, variance and mean from any list.
Open the standard deviation calculator →Correlation
Coefficient
Pearson’s r and r-squared from paired X and Y data.
Open the correlation calculator →Confidence
Interval
A z-interval for the mean, with margin of error.
Open the confidence interval calculator →Paycheck
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