Least Squares

The best line through messy data

An interactive lesson with 6 steps, about 5 minutes: you predict, drag and solve, with instant feedback on every answer. It runs in your browser and needs JavaScript.

What you’ll learn

• Least squares finds the best approximate solution of an overdetermined system.
• Geometrically it’s a perpendicular projection, giving the normal equations AᵀAx = Aᵀb.
• The mean is the least-squares constant; the regression line passes through the mean point.

Steps

1. Too many equations
2. Fit the line
3. Least squares is a projection
4. A shadow
5. The simplest fit
6. Slope by formula