In a study a group of 50 adults were asked how comfortable they felt around 5 types of animals: dogs, cats, cows, horses and sheep. For each type of animal, each respondent gave a number between 0 and 100 to indicate their comfort level (0 being 'hate being around' to 100 being 'love being around'). The data are given in Table 10, along with the loadings of the first two principal components. Table 10

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In a study a group of 50 adults were asked how comfortable they felt around 5 types of animals:
dogs, cats, cows, horses and sheep. For each type of animal, each respondent gave a number
between 0 and 100 to indicate their comfort level (0 being 'hate being around' to 100 being 'love
being around').
The data are given in Table 10, along with the loadings of the first two principal components.
Variable
(b)
(c)
X₁
X₂
X3
X4
X5
Animal Mean
Dogs
74.5
Cats
76.2
Cows
45.2
Horses
51.2
Sheep 48.3
Table 10
Standard
Deviation Component 1
Loadings
8.1
7.5
7.1
8.6
6.9
0.724
-0.684
0.080
-0.040
-0.017
Component 2
0.387
0.425
0.464
0.449
0.503
(a)
The data were not standardized prior to being analyzed using principal components. Give 2
reasons why the decision not to standardize is reasonable for these data.
Interpret each of the 2 components. Justify your answer.
Suppose a decision was taken to standardize the data after all. Calculate the values of the
standardized variables for a person whose comfort level are as follows: Dogs, 84; Cats, 68;
Cows, 46; Horses, 55; Sheep, 58.
Transcribed Image Text:In a study a group of 50 adults were asked how comfortable they felt around 5 types of animals: dogs, cats, cows, horses and sheep. For each type of animal, each respondent gave a number between 0 and 100 to indicate their comfort level (0 being 'hate being around' to 100 being 'love being around'). The data are given in Table 10, along with the loadings of the first two principal components. Variable (b) (c) X₁ X₂ X3 X4 X5 Animal Mean Dogs 74.5 Cats 76.2 Cows 45.2 Horses 51.2 Sheep 48.3 Table 10 Standard Deviation Component 1 Loadings 8.1 7.5 7.1 8.6 6.9 0.724 -0.684 0.080 -0.040 -0.017 Component 2 0.387 0.425 0.464 0.449 0.503 (a) The data were not standardized prior to being analyzed using principal components. Give 2 reasons why the decision not to standardize is reasonable for these data. Interpret each of the 2 components. Justify your answer. Suppose a decision was taken to standardize the data after all. Calculate the values of the standardized variables for a person whose comfort level are as follows: Dogs, 84; Cats, 68; Cows, 46; Horses, 55; Sheep, 58.
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