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**Problem**- Given the following table

x y

15 50

26 46

32 44

48 43

57 40

a) Find the sample mean

b) Find the covarince matrix

c) Perform principal component analysis and find a size index which explains the greatest variation.

**My attempt**

a) n = 5

xbar = Sum(x)/n = 35.6

ybar = Sum(y)/n = 44.6

Sample mean = [35.6 44.6]

b) I calculated Var(X) = 1/n * Sum(X-Xbar)^2 = 228.24

Var(Y) = 1/n * Sum(Y-Ybar)^2 = 11.04

COV(X,Y) = 1/n * Sum[(X-Xbar)(Y-Ybar)] = -48.16

I made a 2x2 matrix in which principal diagonal elements are Var(X) and Var(Y). Each of the other two elements equals COV(X, Y)

Please see if there is any mistake in my solutions to parts a and b.

I have no idea how to answer part c. Could you help?

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