1. In this problem you will use Principal Components Analysis (PCA) toanalyze a simple data set. Do not use a PCA software but only theinformation provided below. You are free to use a calculator to aid yourcomputations.Consider the following data set, X:Name Feature 1 Feature 2 Feature 341367A4385BD81E87F72G33852H74J82The covariance matrix of X (and of centered X) is given by:2.32 1.61 -0.431.61 2.50 -1.28|-0.43 -1.28 7.88The eigen vectors and the corresponding eigen values of the covariancematrix are given by:|-0.70 0.70 -0.140.71 0.66 -0.250.08 0.27 0.96and0.753.688.27respectively.Apply PCA to the centered version of the data set showed above, usingonly the top principal component to embed data into a 1-D latent space.Answer the following questions about the location of the data points(A,B.C.D) in the latent space (rounded the second decimal):a) I: 0.28, J: -2.09b) I: -0.23, J: -2.75c) E: 0.45, F: -0.80d) G: 0.80, H: -0.17

We have been provided with all the data that is required to compute principle components. To obtain…

1. In this problem you will use Principal Components Analysis (PCA) to analyze a simple data set. Do not use a PCA software but only the information provided below. You are free to use a calculator to aid your computations. Consider the following data set, X:

1. In this problem you will use Principal Components Analysis (PCA) to analyze a simple data set. Do not use a PCA software but only the information provided below. You are free to use a calculator to aid your computations. Consider the following data set, X:

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Question

1. In this problem you will use Principal Components Analysis (PCA) to
analyze a simple data set. Do not use a PCA software but only the
information provided below. You are free to use a calculator to aid your
computations.
Consider the following data set, X:
Name Feature 1 Feature 2 Feature 3
4
1
3
6
7
A
4
3
8
5
B
D
8
1
E
8
7
F
7
2
G
3
3
8
5
2
H
7
4
J
8
2
The covariance matrix of X (and of centered X) is given by:
2.32 1.61 -0.43
1.61 2.50 -1.28
|-0.43 -1.28 7.88
The eigen vectors and the corresponding eigen values of the covariance
matrix are given by:
|-0.70 0.70 -0.14
0.71 0.66 -0.25
0.08 0.27 0.96
and
0.75
3.68
8.27
respectively.
Apply PCA to the centered version of the data set showed above, using
only the top principal component to embed data into a 1-D latent space.
Answer the following questions about the location of the data points
(A,B.C.D) in the latent space (rounded the second decimal):
a) I: 0.28, J: -2.09
b) I: -0.23, J: -2.75
c) E: 0.45, F: -0.80
d) G: 0.80, H: -0.17

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