The principal components of a set of m variables are m artificially constructed variables with the following properties. The first component ‘explains’ as much as possible of the total variance of the original variables. The second has the same property under the additional condition that it is uncorrelated with the first, and so on. It often happens that a few principal components account for a large part of the total variance of the original variables. In such a case one may omit the remaining components. The effect is a substantial reduction of the dimension of the problem. The method is used to explore the relations present in a set of data or to combat the problems created by multicollinearity.
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