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I am terribly confused by all the technical answers out there on this question. Suppose I have conducted a survey with the variables age, income, gender, education level, and home purchase price. The question that I'd like answered is "How much variance in home purchase price is explained by age? By income? By gender? By education level?"

What methodology should I use to get this kind of output?

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    $\begingroup$ Sounds like regression. Not factor analysis, and not pca. $\endgroup$ – Jeremy Miles Jan 27 at 3:24
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Neither factor analysis nor PCA is appropriate for answering this type of question. The method that would answer this question best is regression. You can regress home purchase price on your predictors and compute semi-partial $R^2$s, which represent the unique contribution of each predictor over and above the other predictors to explaining the variance in the outcome.

PCA and factor analysis are dimension reduction methods. PCA is used to extract components that contain approximately the same amount of information as the predictors, and factor analysis is used to extract an underlying construct that is the cause of the observed variables. Neither method would serve to answer your question.

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