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As stated in How does centering the data get rid of the intercept in regression and PCA?,

PCA is a regressional model without intercept. Thus, principal components inevitably come through the origin.

Why is that so? The principal components are the eigenvectors, right?

(Sorry I know this is probably a naive question but I don't understand much about math.)

kjetil b halvorsen
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mtest
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    "Regressional model" in that phrase of mine should not be taken literally as if "PCA is a regression analysis". [PCA "model"](http://stats.stackexchange.com/a/94104/3277) is a linear combination wherein principal components predict or restore the manifest variables, while the components are, backwardly, the linear combinations of the variables. Equations are like a linear regression model, albeit not the regression procedure. – ttnphns Sep 16 '16 at 12:06
  • The piece you are citing has no deep meaning. It just trivially states - by the analogy with linear regression w/o intercept, and since the models are formally same - that because there is no constant term in the equation while the variables has been centered, the prediction line (the principal component, in this instance) pierces the origin which coincides with the data mean. If you don't center the data, it still pierces the origin which isn't the mean then. – ttnphns Sep 16 '16 at 12:11
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    `I don't understand much about math` [You will be explained the essence of PCA over the dinner](http://stats.stackexchange.com/a/140579/3277), call for your household. – ttnphns Sep 16 '16 at 12:34

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