Answered: -27 -36 81 onstruct it in R. 37, 65, 0, | bartleby

Linear Algebra: A Modern Introduction

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter3: Matrices

Section3.7: Applications

Problem 14EQ

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Question

7

Suppose that random vector X E R' has mean u and variance-covariance matrix
42
-37
65
-37
178
-53
-27
Σ
65
-53
185
-36
-27
-36
81
For your convenience, you can construct it in R by running the following code:
Sigma <- matrix(c(42, -37, 65, 0, -37, 178, -53, -27, 65, -53, 185, -36, 0, -27, -36, 81), 4, 4)
(a)
Calculate the partial correlation of X1 and X, given X3 and X4. Store its value in variable ans_a.
(b)
Calculate the total correlation between X1 and the other elements of X. Store its value in variable ans b.

(c)
Now, consider a principal component analysis of these variables (without scaling them).
(i)
Obtain the coefficient vectors for the first two principal components of X. Store them in vectors ans c i 1 and ans c i 2, respectively.
(ii)
How many principal components do you need to explain at least 90% of the variation in the data? Store your answer in variable ans c ii.
(iii)
How many principal components should you keep according to the Kaiser's Rule? Store your answer in variable ans_c_iii.
(iv)
Now, perform the scaled principal component analysis. Store the proportions of variation explained by each principal component in a vector ans_c_iv.

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A cellphone provider classifies its customers as low users (less than 400 minutes per month) or high users (400 or more minutes per month). Studies have shown that 40% of people who were low users one month will be low users the next month and that 30% of the people who were high users one month will high users next month. a. Set up a 2x2 stochastic matrix with columns and rows labeled L and H that displays these transitions b. After many months, how many % of the customers are high users

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