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Principal components analysis is a mathematical technique for creating new composite variables, called "principal components," from linear combinations of an existing set of variables. The transformations are made under two restrictions: a) the linear combinations create new variables that are uncorrelated with one another; and b) the first principal component is that linear combination of the existing variables having maximum variance, the second principal component is that linear combination of the existing variables uncorrelated with the first and having maximum variance, and so on for subsequent transformations. Each principal component can be thought of as defining a dimension held in common by the original variables. In the present example, we were testing whether anything held in common among knowledge, interest, and reading difficulty across all test sections provides greater predictability of performance on the interpretive questions than the original variables used either severely or jointly in a regression analysis. The first principal component represents the dimension along which the original variables have the most in common.
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