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Linear Algebra: A Modern Introduction

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter3: Matrices

Section3.7: Applications

Problem 13EQ

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3. Let X = (X1,..., Xm)', m > 2, be random vector with covariance matrix
Σ
Ở11
O 12
O 21 222
The multivariate correlation coefficient between X1 and X2, ..., Xm, denoted R1-2.m;
the maximum correlation between X1 and any linear function W2X2 + ... + Wm Xm.
(i) Show that
ן1 ך
21
-1
O 1222
R1-2,.m
σ1
(ii) Suppose that random vector X has multivariate normal distribution. Show that
R1.2.m is equal to the correlation between X1 and E[X1|X2,.., Xm].

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