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A centered dataset with n = 85 observations and p = 6 variables was analysed to reduce its dimensionality. As part of Principal Component Analysis, the following variance-covariance matrix Σ was generated 399.019 49.66 -1.793 1.7 8.333 16.583 49.66 38.529 -6.952 1.733 2.409 7.873 -1.793 -6.952 36.051 12.142 -4.986 2.841 1.7 1.733 12.142 37.132 4.093 -0.04 8.333 2.409 -4.986 -4.093 41.277 -3.757 16.583 7.873 2.841 -0.04 -3.757 45.062 A) Compute and write the numerical value of the eigenvalue 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. C) As seen in lectures, the eigenvalue X is related to d, one singular eigenvalue of the data matrix X. Compute and write the value of da. D) A threshold of total variability explained has been set at 80%. How many principal components must you select? Write your answer.

A centered dataset with n = 85 observations and p = 6 variables was analysed to reduce its dimensionality. As part of Principal Component Analysis, the following variance-covariance matrix Σ was generated 399.019 49.66 -1.793 1.7 8.333 16.583 49.66 38.529 -6.952 1.733 2.409 7.873 -1.793 -6.952 36.051 12.142 -4.986 2.841 1.7 1.733 12.142 37.132 4.093 -0.04 8.333 2.409 -4.986 -4.093 41.277 -3.757 16.583 7.873 2.841 -0.04 -3.757 45.062 A) Compute and write the numerical value of the eigenvalue 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. C) As seen in lectures, the eigenvalue X is related to d, one singular eigenvalue of the data matrix X. Compute and write the value of da. D) A threshold of total variability explained has been set at 80%. How many principal components must you select? Write your answer.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
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A centered dataset with n = 85 observations and p = 6 variables was analysed to reduce its dimensionality. As part of Principal Component Analysis, the following variance-covariance matrix Σ was generated 399.019 49.66 -1.793 1.7 8.333 16.583 49.66 38.529 -6.952 1.733 2.409 7.873 -1.793 -6.952 36.051 12.142 -4.986 2.841 1.7 1.733 12.142 37.132 4.093 -0.04 8.333 2.409 -4.986 -4.093 41.277 -3.757 16.583 7.873 2.841 -0.04 -3.757 45.062 A) Compute and write the numerical value of the eigenvalue 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. C) As seen in lectures, the eigenvalue X is related to d, one singular eigenvalue of the data matrix X. Compute and write the value of da. D) A threshold of total variability explained has been set at 80%. How many principal components must you select? Write your answer.
Transcribed Image Text:A centered dataset with n = 85 observations and p = 6 variables was analysed to reduce its dimensionality. As part of Principal Component Analysis, the following variance-covariance matrix Σ was generated 399.019 49.66 -1.793 1.7 8.333 16.583 49.66 38.529 -6.952 1.733 2.409 7.873 -1.793 -6.952 36.051 12.142 -4.986 2.841 1.7 1.733 12.142 37.132 4.093 -0.04 8.333 2.409 -4.986 -4.093 41.277 -3.757 16.583 7.873 2.841 -0.04 -3.757 45.062 A) Compute and write the numerical value of the eigenvalue 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. C) As seen in lectures, the eigenvalue X is related to d, one singular eigenvalue of the data matrix X. Compute and write the value of da. D) A threshold of total variability explained has been set at 80%. How many principal components must you select? Write your answer.
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