Module 6 · Regression & Correlation · Topic 5
Least Squares. The least squares method finds the line that minimizes the sum of the squared residuals (SSE = Σ(yᵢ − ŷᵢ)²). This produces the best-fitting line in terms of vertical distances from data points.
Why Squared?. Squaring the residuals ensures positive and negative errors don’t cancel, penalizes larger errors more, and yields a unique, mathematically tractable solution.
b = Σ[(xᵢ − x̄)(yᵢ − ȳ)] / Σ[(xᵢ − x̄)²]
yhat = a + bx - Line that minimizes the sum of squared residuals.r = sum((x_i-xbar)(y_i-ybar)) / sqrt(sum((x_i-xbar)^2)sum((y_i-ybar)^2)) - Measures direction and strength of a linear association.Imagine pinning a thread to a scatter plot so it passes through (̄x, ȳ). Rotating it until the sum of squared vertical residuals is minimized gives the least squares line.
Go interactive
This module opens on its first lesson free; the rest of it unlocks with Premium. Every calculator and simulation below is free.
Keep reading