I am trying to understand the technique behind using a PCA model to return predicted values of your original input variables, with retained_PC's < predictor_count. Ultimately, I'll be looking into residuals (original values - predicteds) for varying numbers of retained PC's. I've read that, to return from PCA space back to X space, you'll need to calculate: predicteds = scores*loadings' Whenever I look into the formula for the 'save predicteds' output, is this linear equation representative of the above concept? Thanks P.S. I know PCA is not meant for predictive modeling, I'm ultimately using it for fault detection with Hotelling's T2 and SPE output. My SPE (squared prediction error) would hinge on this predicteds output.
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