Geometry of Least Squares

Workspace

Example and controls

Example

Step 1 of 5

The three vertical measurements are the coordinates of one point in observation space.

Input

Drag or type

Changing a response moves y. The design matrix stays fixed.

Design values

Data space

Drag points vertically

least-squares line vertical residuals candidate line

Observation space

rank(X) = 2 · plane

Drag freely · edge drag rolls · wheel zooms

data y projection ŷ residual r other fit Xβ

Live mathematics

projected

Inputs

Model space

Closest point

Normal equations

Compare another fit

h₀ h₁

Distance decomposition

candidate error²

minimum error²

extra distance²