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Let X₁, X₂ denote the variables for the two-dimensional data summarized by the covariance matrix, the eigenvalues, and the unit eigenvectors shown below. Find a new variable y, of the form y₁=c₁x₁ + C₂x₂, with c₁+c=1, such that y, has maximum possible variance over the given data. How much of the variance in the data is explained by y₁? 55.2 -10 -0.38 4-[ = -0.93 0.38 and A₂ = 30.603, u₂= -10 34.668 -0.93 S= Y₁ = A₁ = 59.265, u₁

Let X₁, X₂ denote the variables for the two-dimensional data summarized by the covariance matrix, the eigenvalues, and the unit eigenvectors shown below. Find a new variable y, of the form y₁=c₁x₁ + C₂x₂, with c₁+c=1, such that y, has maximum possible variance over the given data. How much of the variance in the data is explained by y₁? 55.2 -10 -0.38 4-[ = -0.93 0.38 and A₂ = 30.603, u₂= -10 34.668 -0.93 S= Y₁ = A₁ = 59.265, u₁

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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2 2 Let x₁, x₂ denote the variables for the two-dimensional data summarized by the covariance matrix, the eigenvalues, and the unit eigenvectors shown below. Find a new variable y₁ of the form y₁ = C₁X₁ + C₂x₂, with c₁+c=1, such that y, has maximum possible variance over the given data. How much of the variance in the data is explained by y₁? - 0.38 55.2 - 10 - 10 34.668 A₁ = 59.265, u₁ = -0.93 0.38 and ₂ = 30.603, u₂= -0.93 S= Y₁
Transcribed Image Text:2 2 Let x₁, x₂ denote the variables for the two-dimensional data summarized by the covariance matrix, the eigenvalues, and the unit eigenvectors shown below. Find a new variable y₁ of the form y₁ = C₁X₁ + C₂x₂, with c₁+c=1, such that y, has maximum possible variance over the given data. How much of the variance in the data is explained by y₁? - 0.38 55.2 - 10 - 10 34.668 A₁ = 59.265, u₁ = -0.93 0.38 and ₂ = 30.603, u₂= -0.93 S= Y₁
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