Linear Regression Calculator

How to use

1. Paste pairs of numbers, one pair per line — the first number on each line is x, the second is y. Comma, tab, space, and semicolon all work as separators.
2. Read the headline equation y = mx + b for the best-fit line, then check R² to see how much of the variation in y the line explains.
3. Look at the Pearson r sign — positive means y rises with x, negative means y falls. The magnitude (0 to 1) describes how tightly the points hug the line.
4. Type any x into the prediction box to get a forecast ŷ — useful for extrapolating one step beyond your data (don't extrapolate too far).

Frequently asked questions

What's the difference between r and R²?

Pearson r ranges from −1 to +1 and tells you the direction and strength of the linear relationship. R² is just r squared and is always between 0 and 1 — it's the share of the variation in y that the regression line explains. An r of −0.9 and an r of +0.9 give the same R² of 0.81 (the line explains 81% of the variance), but the relationships go in opposite directions.

Is correlation causation?

No. A strong fit means y moves with x in your sample, not that x causes y. Classic example: ice-cream sales correlate with shark attacks (both rise in summer); ice cream doesn't cause attacks. Use regression to describe a relationship, not to prove one variable drives the other.

When does linear regression NOT work?

When the relationship is curved (use polynomial fit instead), when a few extreme points pull the line off (look at the scatter plot — outliers wildly change m and b), when variance grows with x (heteroscedasticity), or when the y values aren't independent of each other. A high R² with an obviously curved scatter is a sign you need a different model.

What does the standard error of the slope tell me?

It's the typical uncertainty in m given the scatter around the line. A rough 95% confidence interval for the slope is m ± 2 × SE(m). If that interval crosses zero, you can't confidently say x and y are related — the data is consistent with no relationship.

What sample size do I need?

Two points give an exact line with R² = 1 but tell you nothing about reliability. Three is the minimum for a meaningful R² and a standard error. For trustworthy slope estimates, aim for at least 10 — and for inference (p-values, confidence intervals), 20–30 is a comfortable floor.

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