Let p=3 and m = 1 and suppose the random variables X₁, X, and X₂ have the positivedefinite covariance matrix:21Σ= 0.40.30.410.2Write its factor model.0.30.21

Here p=3 and m=1 and suppose the random variables X1,X2 and X3 have the positive definite covariance…

Answered: Let p=3 and m=1 and suppose the random…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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a. Give the design matrix, the observation vector, and the unknown parameter vector. Choose the correct design matrix X below. b. Find the associated least-squares curve for the data
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Let X Є pxn denote a zero mean observation matrix matrix of obser- vations, P be a pxp orthogonal matrix, and Y = PTX. (a) Show that if C is the covariance matrix of X then PTCP is the co- variance matrix of Y = PT CP. (b) It can be verified that tr (FG) = tr (GF) for any two n x n matrices F and G. Use this fact to show that the total variance of the data in Y is equal to the total variance of the data in X.
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Let p=3 and m=1 and suppose the random variables X₁, X, and X, have the positive definite covariance matrix: 1 Σ= 0.4 0.4 0.3 1 0.2 1 0.3 0.2 Write its factor model.