Answered: Consider a data set with 15 variables.…

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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Consider a data set with 15 variables. We know that the eigenvalues of the correlation matrix of these variables are:

4.3, 3.3, 2.1.2, 1, 0.6, 0.5, 0.5, 0.4, 0.35, 0.25, 0.2, 0.2, 0.11, 0.09.

A) How many principal components exists for this data set? Explain the relation between the variances of the principal components and the variances of the principal components and the eigenvalues of the correlation matrix.

B) Sketch a scree plot of these eigenvalues. Use the scree plot to decide how many principal components to keep for the dataset and calculate how much of the variability in the data is explained by this choice.

C) Assuming that we want to account for at least 70% of the variability in the data, explain which principal components should be selected.

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