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Tuesday, February 17, 2015

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 bQ(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

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