Question

A centered dataset with n = 62 observations and p = 4 variables was analysed to reduce its dimensionality. As part of Principal Component Analysis, the following variance-covariance matrix was generated ? = (1088.07959 214.95849 -21.93971 64.75727 214.95849 235.85325 -9.18879 -20.28345 -21.93971 -9.18879 225.32522 30.37864 64.75727 -20.28345 30.37864 219.1761) A) Compute and write the numerical value of the eigenvalue ?2 of ?. This eigenvalue is located in the position (2, 2) of the matrix ? and is simultaneously the sample variance of the score PC2: B) Compute and write the percentage of total variability explained by the Principal component PC2. The number you write should be between 0 and 100 and you should include decimals in your answer. C) As seen in lectures, the eigenvalue ?2 is related to d2, one singular eigenvalue of the data matrix X. Compute and write the value of d2. D) A threshold of total variability explained has been set at 85%. How many principal components must you select? Write your answer.

          A centered dataset with n = 62 observations and p = 4 variables was analysed to reduce its dimensionality. As part of Principal Component Analysis, the following variance-covariance matrix was generated
? = 
(1088.07959 214.95849 -21.93971 64.75727
214.95849 235.85325 -9.18879 -20.28345
-21.93971 -9.18879 225.32522 30.37864
64.75727 -20.28345 30.37864 219.1761)

A) Compute and write the numerical value of the eigenvalue ?2 of ?. This eigenvalue is located in the position (2, 2) of the matrix ? and is simultaneously the sample variance of the score PC2:

B) Compute and write the percentage of total variability explained by the Principal component PC2. The number you write should be between 0 and 100 and you should include decimals in your answer.

C) As seen in lectures, the eigenvalue ?2 is related to d2, one singular eigenvalue of the data matrix X. Compute and write the value of d2.

D) A threshold of total variability explained has been set at 85%. How many principal components must you select? Write your answer.

A centered dataset with n = 62 observations and p = 4 variables was analysed to reduce its dimensionality. As part of Principal Component Analysis, the following variance-covariance matrix was generated
? =
(1088.07959 214.95849 -21.93971 64.75727
214.95849 235.85325 -9.18879 -20.28345
-21.93971 -9.18879 225.32522 30.37864
64.75727 -20.28345 30.37864 219.1761)

A) Compute and write the numerical value of the eigenvalue ?2 of ?. This eigenvalue is located in the position (2, 2) of the matrix ? and is simultaneously the sample variance of the score PC2:

B) Compute and write the percentage of total variability explained by the Principal component PC2. The number you write should be between 0 and 100 and you should include decimals in your answer.

C) As seen in lectures, the eigenvalue ?2 is related to d2, one singular eigenvalue of the data matrix X. Compute and write the value of d2.

D) A threshold of total variability explained has been set at 85%. How many principal components must you select? Write your answer.

Added by Sharon D.

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