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-27 -36 81 onstruct it in R. 37, 65, 0,

-27 -36 81 onstruct it in R. 37, 65, 0,

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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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.
Transcribed Image Text: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.
Transcribed Image Text:(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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