A threshold of total variability explained has been set at 85%. How many principal components must you select? A centered dataset with n = 80 observations and p = 5 variables was analysed to reduce itsdimensionality. As part of Principal Component Analysis, the following variance-covariance matrix Σ wasgenerated993.944194.202 26.336 15.803 41.983194.202 228.703 -32.782 −1.11 36.28926.336 -32.782 241.454 3.163 -7.05619.99115.803-1.113.163239.63341.983 36.289 -7.056 19.991 250.303

Given the variance-covariance matrix, we would typically first perform eigenvalue decomposition to…

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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?

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Step 1: Calculate the cumulative proportion of variability

Step 2: Compute the eigenvalues:

Step 3: Calculate the proportion of variability explained by each principal component:

Step 4: Compute the cumulative proportion of variability explained:

Step 5: Determine the number of principal components needed to achieve at least 85% of total variability exp

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