Principal components analysis, Applied Statistics

In the context of multivariate data analysis, one might be faced with a large number of v&iables that are correlated with each other, eventually acting as proxy of each other. This makes the coexistence of the variables in the framework redundant, thereby complicating the analyses. Under such circumstances, the investigator might be interested in reducing the dimensionality of the data set by identifying arid classifying the co~nmonality in the patterns of the related variables. Principal component analysis (PCA) is a mathematical procedure that transforms a number of (possibly) correlated variables into a (smaller) number of uncorrelated variables called principal components.

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In PCA the eigknvalues must ultimately account for all of the variance. There is no probability,'no hypothesis, no test because strictly speaking PCA is not a statistical procedure