Suppose a dataset has 3 variables, X₁, X₂ and X3. Each variable is standardized and a principal component analysis is then carried out using the standardized data. (a) Write down the total variance that would result. Justify your answer. (b) Suppose that Kaiser's criterion indicates 2 components should be retained. Write down variances for each of the 3 components that would be compatible with this observation. (c) Sketch a scree plot that indicates only one of the 3 components should be retained. (Note the corresponding variances for the components need not match those you give in part (b).)

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Suppose a dataset has 3 variables, X₁, X₂ and X3. Each variable is standardized and a principal
component analysis is then carried out using the standardized data.
(a) Write down the total variance that would result. Justify your answer.
(b)
Suppose that Kaiser's criterion indicates 2 components should be retained. Write down
variances for each of the 3 components that would be compatible with this observation.
(c)
Sketch a scree plot that indicates only one of the 3 components should be retained. (Note the
corresponding variances for the components need not match those you give in part (b).)
Transcribed Image Text:Suppose a dataset has 3 variables, X₁, X₂ and X3. Each variable is standardized and a principal component analysis is then carried out using the standardized data. (a) Write down the total variance that would result. Justify your answer. (b) Suppose that Kaiser's criterion indicates 2 components should be retained. Write down variances for each of the 3 components that would be compatible with this observation. (c) Sketch a scree plot that indicates only one of the 3 components should be retained. (Note the corresponding variances for the components need not match those you give in part (b).)
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