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Following table provides information on standard deviations of Principal Component Analysis on a certain dataset. There are 15 variables in the data and PCA is run on scaled data. The following standard deviations of the variations that are being explained by the 4 Principal Components.

PC1 PC2 PC3 PC4
Stdev   2.3 2.1 1.5 0.960

What is the proportion of total variability explained by the 4 PC’s?

[here PC means Principal Component]

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  • $\begingroup$ "Following table" - may I ask you to display the table in formulas ? (using the Latex annotation available in this forum). Your question will benefit from this clarification. $\endgroup$ Aug 1, 2020 at 16:38

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Total variability is the sum of the standard deviations for all the Principal Components. To estimate the proportion for each Component you have to divide its standard deviation by the total amount: $Proportion_{i} = \frac{σ_{i}}{\sum_{i=1}^{14} σ_{i}}$

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If we know there are 15 items with sigma_i=1 then we can take the sum (2.3, 2.1, 1.5, 0.96) = 6.86 /15 = 0.457 ish.

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