★☆☆ Beginner

📈 Linear Regression — OLS Least Squares

Click the canvas to add data points. The least-squares regression line updates instantly. Drag points to see how outliers affect slope and R².

Datasets:

—

Slope (m)

—

Intercept (b)

—

R² (fit quality)

—

Pearson r

Points (n)

—

SSE (residuals²)

y = m·x + b (add at least 2 points)

Ordinary Least Squares (OLS)

OLS minimises the sum of squared vertical distances from each point to the line. The unique solution is:

m = Σ(xᵢ−x̄)(yᵢ−ȳ) / Σ(xᵢ−x̄)² · b = ȳ − m·x̄

R² (coefficient of determination) measures the fraction of total variance explained by the line: R² = 1 − SSE/SST. R² = 1 is a perfect fit; R² = 0 means the line explains nothing.