A) Compute and write the numerical value of the eigenvalue 14 of Σ. This eigenvalue is located in the position (4, 4) of the matrix A and is simultaneously the sample variance of the score PC4: B) Compute and write the percentage of total variability explained by the Principal component PC4. The number you write should be between 0 and 100 and you should include decimals in your answer.
A) Compute and write the numerical value of the eigenvalue 14 of Σ. This eigenvalue is located in the position (4, 4) of the matrix A and is simultaneously the sample variance of the score PC4: B) Compute and write the percentage of total variability explained by the Principal component PC4. The number you write should be between 0 and 100 and you should include decimals in your answer.
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Transcribed Image Text:A centered dataset with n = 80 observations and p = 5 variables was analysed to reduce its
dimensionality. As part of Principal Component Analysis, the following variance-covariance matrix was
generated
993.944 194.202 26.336 15.803
41.983
194.202 228.703 -32.782
26.336 -32.782 241.454
15.803 −1.11 3.163
41.983 36.289 -7.056 19.991 250.303
−1.11 36.289
3.163 -7.056
239.633 19.991
A) Compute and write the numerical value of the eigenvalue 14 of Σ. This eigenvalue is located in the
position (4, 4) of the matrix ▲ and is simultaneously the sample variance of the score PC4:
B) Compute and write the percentage of total variability explained by the Principal component PC4. The
number you write should be between 0 and 100 and you should include decimals in your answer.
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