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A centered dataset with n = 115 observations and p = 12 variables was analysed to reduce its dimensionality. The following is a list of singular values of X in decreasing order, that is d1, d2, ..., d12: 42.273, 10.571, 10.32, 9.818, 9.638, 9.174, 8.364, 7.834, 7.522, 7.231, 6.824, 6.086. A) Compute and write the numerical value of the eigenvalue 16 of Σ. This eigenvalue is located in the position (6,6) of the matrix A and is simultaneously the sample variance of the score PC6: B) Compute and write the percentage of total variability explained by the Principal component PC6. 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. D) Write the value of the variance accounted for all those principal components you selected in the previous question. E) Besides being centered, was this data scaled as well? Select. This data was centered but not scaled. This data was centered and scaled.

A centered dataset with n = 115 observations and p = 12 variables was analysed to reduce its dimensionality. The following is a list of singular values of X in decreasing order, that is d1, d2, ..., d12: 42.273, 10.571, 10.32, 9.818, 9.638, 9.174, 8.364, 7.834, 7.522, 7.231, 6.824, 6.086. A) Compute and write the numerical value of the eigenvalue 16 of Σ. This eigenvalue is located in the position (6,6) of the matrix A and is simultaneously the sample variance of the score PC6: B) Compute and write the percentage of total variability explained by the Principal component PC6. 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. D) Write the value of the variance accounted for all those principal components you selected in the previous question. E) Besides being centered, was this data scaled as well? Select. This data was centered but not scaled. This data was centered and scaled.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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A centered dataset with n = 115 observations and p = 12 variables was analysed to reduce its dimensionality. The following is a list of singular values of X in decreasing order, that is d1, d2, ..., d12: 42.273, 10.571, 10.32, 9.818, 9.638, 9.174, 8.364, 7.834, 7.522, 7.231, 6.824, 6.086. A) Compute and write the numerical value of the eigenvalue 16 of Σ. This eigenvalue is located in the position (6,6) of the matrix A and is simultaneously the sample variance of the score PC6: B) Compute and write the percentage of total variability explained by the Principal component PC6. 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. D) Write the value of the variance accounted for all those principal components you selected in the previous question. E) Besides being centered, was this data scaled as well? Select. This data was centered but not scaled. This data was centered and scaled.
Transcribed Image Text:A centered dataset with n = 115 observations and p = 12 variables was analysed to reduce its dimensionality. The following is a list of singular values of X in decreasing order, that is d1, d2, ..., d12: 42.273, 10.571, 10.32, 9.818, 9.638, 9.174, 8.364, 7.834, 7.522, 7.231, 6.824, 6.086. A) Compute and write the numerical value of the eigenvalue 16 of Σ. This eigenvalue is located in the position (6,6) of the matrix A and is simultaneously the sample variance of the score PC6: B) Compute and write the percentage of total variability explained by the Principal component PC6. 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. D) Write the value of the variance accounted for all those principal components you selected in the previous question. E) Besides being centered, was this data scaled as well? Select. This data was centered but not scaled. This data was centered and scaled.
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