Question: Let x 1 , x 2 denote the variables for the two-dimensional data in Exercise 1. Find a new variable y of the form y

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.

19 22 6 12 6 9 3 15 2 13 20 5

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