Least Squares Line Calculator

Work out least squares line instantly with clear inputs, formula shown and shareable results.

About Least Squares Line Calculator

The least squares line minimises the sum of squared vertical residuals. Its slope is Σ(x−x̄)(y−ȳ)/Σ(x−x̄)², and it always passes through the point of means (x̄, ȳ).

Formulas

Least squares slope

b = Σ(x − x̄)(y − ȳ) / Σ(x − x̄)²

Intercept

a = ȳ − b·x̄

Worked example

With the default values below, Least Squares Line Calculator returns Regression line of y = 0.6x + 2.2. Change any input above and every figure here is recalculated in your browser.

Inputs used

x values: 1, 2, 3, 4, 5
y values: 2, 4, 5, 4, 5
Predict y at x =: 6

Results

Regression line: y = 0.6x + 2.2
Slope b: 0.60000000
Intercept a: 2.20000000
Predicted y: 5.80000000

Step by step

1Values used
2Least squares slope
3Intercept
4Regression line= y = 0.6x + 2.2
5Slope b= 0.60000000
6Intercept a= 2.20000000
7Predicted y= 5.80000000

Assumptions and limits

The result is derived only from the 3 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
Figures are rounded for display to 8 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

For x = 1..5 and y = 2, 4, 5, 4, 5?

The slope is 0.6 and the intercept 2.2, giving y = 0.6x + 2.2 and a prediction of 5.8 at x = 6.

Why squared residuals?

Squaring makes the problem differentiable with a unique closed-form solution, and it penalises large misses more heavily.