Let x₁, x₂ denote the variables for the two-dimensional data in Exercise 1. Find a new variable y of the form y₁ = c₁x₁ + c₂x₂, with c²₁ + c²₂ = 1, such that y, has maxi- mum possible variance over the given data. How much of the variance in the data is explained by y₁?

Data From Exercise 1

Convert the matrix of observations to mean deviation form, and construct the sample covariance matrix.

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