Re: about PCA and variability??

On Jun 27, 3:47 am, xhos...@xxxxxxxxx wrote:
onyourmark <william...@xxxxxxxxx> wrote:

Hi and thanks to all you have responded to my query. My question is, I
suppose, say in regard to the above post, why are we interested in
whether one of the original variables or one of the new derived
variables might capture 98% of the variance of all of the original
variables or not. I mean, I guess this is a very basic question, but
why are we interested in the variation of the variables in the first
place.

Maybe you aren't interested in that.  In which case, you probably shouldn't
do aPCAanalysis.  It's a tool for a job.  If you have no need for that
job, you have no need for that tool.

Xho

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Hi and thanks to all again. I am interested in PCA. May I ask, (sorry
for being obtuse), when you say "that is where all the action occurs"
you are saying that all the variability is in those two dimensions and
that only 0.01 percent of all the variability lies in the z axis, but
aren't you concerned with predicting a fourth variable (a response
variable, say Y)? Otherwise I don't understand what you mean by that
is where the action occurs. I mean, I understand that most of the
variation occurs in those two dimensions but why is the variation
important?
I can see that, for example, if data is constant with respect to a
certain variable, say X1, so that for every case/individual X1 has the
same value, say X1=5, across all observations, then X1 will be useless
in predicting Y (or as it is sometimes said "variation in Y") because
X1 is 5 no matter what value Y is (if you tell me that for this
individual/observation/case X1 is 5, that is not going to help me to
predict Y at all). And by extension if X1 is not constant but has
almost no variation then it will be almost useless in predicting the
variation in Y.
So is this why we are interested in the variation of the variables?
Because they are input variables? Or is there some other reason?
Thanks again.
.

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