Please show step-by-step solution and do not skip steps. Explain your entire process in great detail. Problem #5: Suppose three tests are administered to a random sample of college students. Let X₁,..., Xy be observationvectors in R³ that list the three scores of each student, and for j = 1, 2, 3, let x; denote a student's score on the thexam. Suppose the covariance matrix of the data isProblem #5:S =10 20 232080 442344 53Let y = 01x1 + 02x2 + c3x3 be an "index" of student performance with c + c3 + c3 = 1 and c₁ ≥ 0. Find theconstants 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

As per the question we have to find the values of the constants so that is maximum.Which is…

blem #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: 10 20 23 80 44 53 S = 20 23 44 Let y = C₁x₁ + ₂x2 + Cc3x3 be an "index" of student performance with c² + c3 + c3 = 1 and c₁0. 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

blem #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: 10 20 23 80 44 53 S = 20 23 44 Let y = C₁x₁ + ₂x2 + Cc3x3 be an "index" of student performance with c² + c3 + c3 = 1 and c₁0. 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

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter1: Functions

Section1.2: The Least Square Line

Problem 5E

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