Question: After applying Principal Component Analysis (PCA) on five variables from the Breakfast Cereals dataset (calories, protein, fat, sodium, and fiber), the importance of components are

  1. After applying Principal Component Analysis (PCA) on five variables from the Breakfast Cereals dataset (calories, protein, fat, sodium, and fiber), the importance of components are summarized below:

PC1

PC2

PC3

PC4

PC5

Standard deviation

84.0474

18.55527

2.37106

0.91753

0.80417

Proportion of Variance

0.9526

0.04643

0.00076

0.00011

0.00009

Cumulative Proportion

0.9526

0.99904

0.9998

0.99991

1

The rotation matrix is:

PC1

PC2

PC3

PC4

PC5

calories

0.073

0.996

-0.032

0.027

0.021

protein

-0.001

0.002

-0.289

-0.821

0.493

fat

0.000

0.028

-0.091

-0.489

-0.867

sodium

0.997

-0.073

0.000

-0.002

-0.001

fiber

-0.002

-0.037

-0.952

0.295

-0.067

The mean of the five variables are listed below:

Mean

calories

106.883

protein

2.545

fat

1.013

sodium

159.675

fiber

2.152

Given the following three Breakfast Cereals products, compute their scores of the first and the second principal components.

Cereal Product

calories

protein

fat

sodium

fiber

PC1

PC2

Froot_Loops

110

2

1

125

1

Wheaties_Honey_Gold

110

2

1

200

1

100%_Natural_Bran

120

3

5

15

2

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