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Suppose three tests are administered to a random sample of college students. Let X₁, ..., Xy be observation vectors in R³ that 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 S = 52 26 52 26 13 26 52 26 65 Let y = C₁x₁ + ₂x₂ + c3x3 be an "index" of student performance with c + c2 + constants C1, C2, C3 so that the variance of y over the data set is as large as possible. + cz = 1 and c₁ ≥ 0. Find the

Suppose three tests are administered to a random sample of college students. Let X₁, ..., Xy be observation vectors in R³ that 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 S = 52 26 52 26 13 26 52 26 65 Let y = C₁x₁ + ₂x₂ + c3x3 be an "index" of student performance with c + c2 + constants C1, C2, C3 so that the variance of y over the data set is as large as possible. + cz = 1 and c₁ ≥ 0. Find the

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Suppose three tests are administered to a random sample of college students. Let X₁, ... ; ,XN be observation vectors in R³ that 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 S = 52 26 52 26 52 13 26 26 65 Let y = C₁x1 + €2x2 + c3x3 be an "index" of student performance with c² + c3 + c3 = 1 and c₁ ≥ 0. Find the constants C₁, C2, C3 so that the variance of y over the data set is as large as possible.
Transcribed Image Text:Suppose three tests are administered to a random sample of college students. Let X₁, ... ; ,XN be observation vectors in R³ that 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 S = 52 26 52 26 52 13 26 26 65 Let y = C₁x1 + €2x2 + c3x3 be an "index" of student performance with c² + c3 + c3 = 1 and c₁ ≥ 0. Find the constants C₁, C2, C3 so that the variance of y over the data set is as large as possible.
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