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I understand the working of NIPALS algorithm but while doing the regression using PLS how exactly the relation between known and unknown is established using Principle Component Analysis. The idea is clear up to the points both dependent and independent are expressed in form of their principle components. After I am not able to understand.

PS: I have read text and some papers about it but they are very difficult to understand. This Question may sound a trivial one, but please bear with me. Correct me if I am wrong.

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This lecture helped me get my head around PCA: https://www.youtube.com/watch?v=a9jdQGybYmE

The analogy that I am sharing with you comes directly from this lecture:

Imagine that you have a weight that is on a spring. It can bounce up and down and thus is a one degree of freedom system. Imagine that you have three sensors which record the (x,y) position of the weight as it bounces up and down. Now you have six vectors of data (a set of x,y from each camera). PCA tries to infer the actual (x,y) coordinates of the weight as it bounces based only on the data that you get from the cameras.

This analogy is very rough and I highly recommend that you watch the linked video. There is really no short answer to your question!

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