Linear regression calculator

Enter your values. The answer and the full worked solution update as you type.

Result

Slope b1.99

Intercept a0.05

Correlation r0.9987

r²0.9973

Step-by-step solution

Means

x̄ = 3, ȳ = 6.02

Sums of squares

Sxy = 19.9, Sxx = 10, Syy = 39.71

Line and correlation

b = Sxy/Sxx = 1.99, a = ȳ − b·x̄ = 0.05

ŷ = 0.05 + 1.99·x

r = Sxy/√(Sxx·Syy) = 0.9987

Key formulas

Sums of squares: S_xx = Σ(x − x̄)² = Σx² − (Σx)²/n, S_xy = Σxy − ΣxΣy/n
Slope: b = S_xy/S_xx
Intercept: a = ȳ − b·x̄
Correlation: r = S_xy/√(S_xxS_yy)
Residual: e = y − ŷ

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