Linear Regression Calculator
Fit a least-squares line to paired data and calculate slope, intercept, R² and an optional prediction
Regression equation
How we calculated it
About the Linear Regression Calculator
Linear Regression Calculator fits a straight line that predicts one variable from another by minimizing squared residuals. It is useful for trend estimation, calibration and simple predictive models when a linear relationship is reasonable.
A fitted line can summarize association, but it should not be extrapolated far beyond the observed data without strong justification.
How to Use the Linear Regression Calculator
- Enter paired x and y observations.
- Calculate slope and intercept.
- Review fit statistics such as correlation or R² when available.
- Inspect residuals or a scatter plot before using the line for prediction.
How the Calculation Works
Simple least-squares regression fits y = b0 + b1x. Slope b1 = covariance(x,y)/variance(x), and intercept b0 = ȳ − b1x̄.
The fitted coefficients minimize the sum of squared vertical residuals between observed y values and predicted values.
Worked example
Linear Regression Calculator Worked Example
Points (1,3), (2,5), (3,7)
These points lie exactly on y=2x+1, so the fitted slope is 2 and intercept is 1.
Result guide
Understanding Your Linear Regression Calculator Result
Slope estimates the average change in predicted y for a one-unit increase in x. The intercept is the predicted y at x=0, which may or may not be meaningful in context.
Before you rely on the answer
Assumptions and Limitations
- A linear model is appropriate for the relationship.
- Observations are paired and measured consistently.
- Statistical inference from the regression requires additional assumptions about residuals and sampling.
Practical tip
Using This Result in Practice
Do not judge a regression only by R². A high R² can still accompany biased residual patterns or meaningless extrapolation.
Related calculations
Useful Calculations to Continue With
If you only need the strength and direction of linear association, use the Correlation Coefficient Calculator.
If you are analyzing uncertainty around an estimated regression quantity, the Standard Error Calculator may support the next step.
Common questions
Linear Regression Calculator FAQ
What does regression slope mean?
The expected change in predicted y for a one-unit increase in x under the fitted linear model.
Is regression the same as correlation?
No. Correlation summarizes association symmetrically; regression fits a directional prediction equation.
Can I predict outside the observed x range?
You can mathematically, but extrapolation can be unreliable if the relationship changes beyond the data.