A Primer on Linear Models (chapter 2)

Chapter 2 The Linear Least Squares Problem

2.0 contents

2.1 The Normal Equations

2.2 The Geometry of Least Squares

2.3 Reparameterization

2.4 Gram-Schmidt Orthonormalization

2.5 Summary of Important Results

---

2.1 The Normal Equations

One mathematical view of the linear model \(y = Xb + e\) is the best approximation \(Xb\) to the observed vector y.
Euclidean 방법으로 근사치를 구한다면 \[Q(b)= (y-Xb)^T(y-Xb) = \|y-Xb\|^2\] 를 최소화하는 \(b\) 를 \(Q(b)\) 의 least squares solution이라 한다.

2.2 The Geometry of Least Squares

2.3 Reparameterization

2.4 Gram-Schmidt Orthonormalization

2.5 Summary of Important Results