This linear regression calculator fits the least-squares line y = ax + b through paired data and reports the fit quality.
Statistics
Linear Regression Calculator
Fit a simple linear regression with least squares and report R².
Calculator
About this calculator
Formula notes
slope a = Σ((xᵢ−x̄)(yᵢ−ȳ)) / Σ(xᵢ−x̄)²; intercept b = ȳ − a·x̄; r² measures fit.
Worked examples
- Example: x = 1,2,3,4,5 and y = 2,4,5,4,5 give y = 0.6x + 2.2 with r² = 0.6.
- For points (1,2), (2,3), (3,5), and (4,6), least squares gives a positive slope near 1.4 and an intercept near 0.5.
How to use it
- Enter paired x and y lists of equal length.
- Read the fitted equation.
- Use r² to judge how well the line explains the data.
Frequently asked questions
What does the slope 0.6 mean here?
Each one-unit increase in x is associated with a 0.6-unit increase in predicted y.
Can I use the equation to predict new x values?
Yes, within the observed range; extrapolating far beyond the data is unreliable.
Limits and interpretation
- Simple linear regression assumes a linear mean relationship and requires residual diagnostics for variance, independence, and unusual observations.
- Extrapolating beyond the observed x range can be unreliable, and a high R2 does not prove causation or model correctness.