Repeat Exercise 9 with Data From Exercise 9 Suppose three tests are administered to a random sample

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Repeat Exercise 9 withimage



Data From Exercise 9


Suppose three tests are administered to a random sample of college students. Let X1,..., Xbe observation vectors in Rthat list the three scores of each student, and for j = 1, 2, 3, let xj denote a student's score on the jth exam. Suppose the covariance matrix of the data is


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Let y be an "index" of student performance, with y = cx1x+ c2x+ c3xand c1+ c2+ c32 = 1. Choose c1, c2, cso that the variance of y over the data set is as large as possible. The eigenvalues of the sample covariance matrix are λ = 3, 6, and 9.

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Linear Algebra And Its Applications

ISBN: 9781292351216

6th Global Edition

Authors: David Lay, Steven Lay, Judi McDonald

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