Hat Matrix Symmetry Visualization

Interactive Linear Regression Example

Point 1 X: 1.0

Point 2 X: 2.0

Point 3 X: -1.0

Hat Matrix H

What Symmetry Means:

H_ij = H_ji means:

• How much point i influences point j’s fitted value = How much point j influences point i’s fitted value
  
• This reciprocal relationship holds for ALL pairs of points
• Reciprocal influence is a geometric consequence of orthogonal projection

Key Observations