= A centered dataset with n = 117 observations and p 9 variables was analysed to reduce its dimensionality. The following is a list of singular values of X in decreasing order, that is d₁, d2, . ,do: 336.0834, 188.9444, 180.4725, 168.4637, 156.0757, 153.8944, 147.5205, 126.4453, 118.5575. A) Compute and write the numerical value of the eigenvalue 27 of E. This eigenvalue is located in the position (7, 7) of the matrix A and is simultaneously the sample variance of the score PC7: B) Compute and write the percentage of total variability explained by the Principal component PC7. The number you write should be between 0 and 100 and you should include decimals in your answer. C) A threshold of total variability explained has been set at 70%. How many principal components must you select? Write your answer (integer value).
= A centered dataset with n = 117 observations and p 9 variables was analysed to reduce its dimensionality. The following is a list of singular values of X in decreasing order, that is d₁, d2, . ,do: 336.0834, 188.9444, 180.4725, 168.4637, 156.0757, 153.8944, 147.5205, 126.4453, 118.5575. A) Compute and write the numerical value of the eigenvalue 27 of E. This eigenvalue is located in the position (7, 7) of the matrix A and is simultaneously the sample variance of the score PC7: B) Compute and write the percentage of total variability explained by the Principal component PC7. The number you write should be between 0 and 100 and you should include decimals in your answer. C) A threshold of total variability explained has been set at 70%. How many principal components must you select? Write your answer (integer value).
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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A centered dataset with n = 117 observations and p 9 variables was analysed to reduce its dimensionality. The following is a list of singular values of X in
decreasing order, that is d₁, d2, . ,do: 336.0834, 188.9444, 180.4725, 168.4637, 156.0757, 153.8944, 147.5205, 126.4453, 118.5575.
A) Compute and write the numerical value of the eigenvalue 27 of E. This eigenvalue is located in the position (7, 7) of the matrix A and is simultaneously the
sample variance of the score PC7:
B) Compute and write the percentage of total variability explained by the Principal component PC7. The number you write should be between 0 and 100 and
you should include decimals in your answer.
C) A threshold of total variability explained has been set at 70%. How many principal components must you select? Write your answer (integer value).
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