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Statistics

Linear Regression Calculator

Linear regression finds the straight line that best fits a set of data points. This calculator computes the least-squares slope and intercept, plus the correlation coefficient r and r², from your paired x and y values.

Linear Regression Calculator

Least-squares line and correlation for paired data.

Try:
Answery = 0.8x + 1.8 (r = 0.852803)
  1. Meansx̄ = 3, ȳ = 4.2
  2. Sums of squaresSxx = 10, Sxy = 8
  3. Slopeb = Sxy / Sxx = 0.8
  4. Intercepta = ȳ − b·x̄ = 1.8
  5. Correlationr = 0.852803, r² = 0.727273
  6. Regression liney = 0.8x + 1.8
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Worked examples

Linear regression for (1, 2), (2, 4), (3, 5), (4, 4), (5, 6) Fit the least-squares line and report the correlation coefficient r.

Key terms

Slope The steepness of a line — its rise over its run. Y-intercept The y-coordinate where a curve crosses the y-axis. Mean The arithmetic average of a set of numbers — their sum divided by the count. Correlation coefficient A number between −1 and 1 measuring the strength and direction of a linear relationship.

Frequently asked questions

What is the least-squares line?

It is the line that minimizes the total squared vertical distance between the data points and the line.

What does the correlation coefficient r mean?

r ranges from −1 to 1: values near ±1 indicate a strong linear relationship, values near 0 indicate a weak one.

What is r²?

r² is the fraction of the variation in y explained by the regression line — a measure of fit quality.

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