Calculate linear regression

Fit an ordinary least-squares straight line to paired x and y observations.

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ToolLinear Regression Calculator
Input
Output
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Preview

How it works

The slope is Σ(x−x̄)(y−ȳ) ÷ Σ(x−x̄)² and the intercept is ȳ minus slope × x̄. Predictions lie on that line, residuals are observed minus predicted, and R² is the squared Pearson correlation for this intercept model.

  • At least two paired observations are required.
  • No weights, robust loss, polynomial terms, uncertainty interval, or causal claim are added.

Worked example

Five paired points
The same points used in the correlation calculator
Input
											X values: [1,2,3,4,5]
Y values: [2,4,5,4,5]
Output
												Slope: 0.6
Intercept: 2.2
R squared: 0.6
Equation: y = 0.6x + 2.2

When to use this

Calibration exercises fit response against concentration, trend charts overlay a straight line, and classroom datasets inspect residuals.

Edge cases

  • Identical x values make the slope denominator zero and are rejected.
  • A constant y series receives the implementation’s zero-variance R² convention, so that number is not evidence of predictive information.
  • One extreme point can pull an unweighted least-squares line sharply toward itself.

References