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Problem #5: 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 Problem #5: S= 130 55 68 55 25 26 68 26 40 Let y = C₁x1 + ₂x2 + c3x3 be an "index" of student performance with c2 + c2 + c = 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. 4 Enter the values of c₁, c2, C3 into the answer box below, separated by commas. numbers correct to 2 decimals

Problem #5: 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 Problem #5: S= 130 55 68 55 25 26 68 26 40 Let y = C₁x1 + ₂x2 + c3x3 be an "index" of student performance with c2 + c2 + c = 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. 4 Enter the values of c₁, c2, C3 into the answer box below, separated by commas. numbers correct to 2 decimals

MATLAB: An Introduction with Applications
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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Problem #5: 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 Problem #5: S. = 130 55 68 55 68 25 26 26 40 Let y = C₁x1 + ₂x2 + c3x3 be an "index" of student performance with c + 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. Enter the values of C₁, C2, C3 into the answer box below, separated by commas. numbers correct to 2 decimals
Transcribed Image Text:Problem #5: 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 Problem #5: S. = 130 55 68 55 68 25 26 26 40 Let y = C₁x1 + ₂x2 + c3x3 be an "index" of student performance with c + 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. Enter the values of C₁, C2, C3 into the answer box below, separated by commas. numbers correct to 2 decimals
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