A threshold of total variability explained has been set at 85%. How many principal components must you select?
A threshold of total variability explained has been set at 85%. How many principal components must you select?
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A threshold of total variability explained has been set at 85%. How many principal components must you select?
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 Σ was
generated
993.944
194.202 26.336 15.803 41.983
194.202 228.703 -32.782 −1.11 36.289
26.336 -32.782 241.454 3.163 -7.056
19.991
15.803
-1.11
3.163
239.633
41.983 36.289 -7.056 19.991 250.303
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Step 1: Calculate the cumulative proportion of variability
VIEWStep 2: Compute the eigenvalues:
VIEWStep 3: Calculate the proportion of variability explained by each principal component:
VIEWStep 4: Compute the cumulative proportion of variability explained:
VIEWStep 5: Determine the number of principal components needed to achieve at least 85% of total variability exp
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