Linear Regression Calculator: Line of Best Fit y = a + bx with r² and Prediction
Enter X and Y values in pairs. You get the line of best fit, how well it fits (r²) and a prediction for any x you type.
- Nothing you type is stored
- Free
- No signup
Line of best fit
ŷ = 0.7333 + 2.1714x
- Slope b
- 2.171429
- Intercept a
- 0.733333
- r² (coefficient of determination)
- 0.9902
- Predicted y
- 15.9333
This x is outside your data range (1 to 6), so the prediction is an extrapolation and may be unreliable.
Least-squares fit; r² shows how much of the variation in y the line explains.
Show working
- x̄ = 3.5, ȳ = 8.333333
- Sxx = Σ(x − x̄)² = 17.5, Sxy = Σ(x − x̄)(y − ȳ) = 38
- b = Sxy / Sxx = 38 / 17.5 = 2.171429
- a = ȳ − b·x̄ = 8.333333 − 2.171429 × 3.5 = 0.733333
- r² = 1 − SSE/SST = 1 − 0.819048 / 83.333333 = 0.990171
- ŷ(7) = 0.733333 + 2.171429 × 7 = 15.933333
How to use
- Enter the X values, then the matching Y values in the same order.
- Optionally type an x to predict y.
- Read the equation, slope, intercept and r².
Good to know
Least squares: slope b = Sxy/Sxx and intercept a = ȳ − b·x̄. This is the line that makes the sum of squared vertical distances from the points as small as possible.
r² is the share of the variation in y explained by the line (0 to 1). The standard error of the estimate √(SSE/(n − 2)) is the typical size of a prediction miss, in y units.
Predicting outside the range of your x data (extrapolation) is risky: the straight-line pattern may not continue. The calculator warns you when you do it.
Questions
What is the regression line for x = 1…6, y = 3, 5, 7, 10, 11, 14?
ŷ = 0.7333 + 2.1714x, with r² ≈ 0.990.
What does the slope mean?
How much y changes on average when x goes up by 1. A slope of 2.17 means y rises about 2.17 per unit of x.
Is regression the same as correlation?
They are linked: r² is the same in both. Correlation measures strength; regression gives the actual line for predictions.
Can I fit a curve?
This tool fits a straight line only. For curved patterns try transforming the data (e.g. log of y) first.
Is my data stored or sent anywhere?
No. The calculation runs entirely in your browser; nothing you type leaves your device.