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 = C₁ X₁ + ₂x₂, with c² + c²₂² = = 1, such that y, has maximum possible variance over the given data. How much of the variance in the data is explained by y₁? 31.6 16.6 -0.73 S= A₁ =47.121, u₁= 16,94₁ = [1 and λ₂ 13.847, U₂ = -0.68 -0.73 29.368 0.68 Y₁ = - 16.6 SCELE

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