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I am using PCA in R to analyze groundwater level changes. I used:

PC.data<-prcomp(data,center=T,scale. = T)   #prcomp
        scores<-PC.data$x
         head(scores)`
               PC1       PC2        PC3        PC4         PC5
    [1,] -5.921258 -2.704683 -0.5652839 0.04388705  0.84945464
    [2,] -5.991433 -2.890179 -0.5363959 0.16285301  0.68334358
    [3,] -5.954987 -2.978851 -0.7417375 0.33709042  0.36579053
    [4,] -5.650401 -3.256866 -1.1687620 0.39116229  0.18990946
    [5,] -5.278529 -3.316807 -1.7457909 0.49164240 -0.27280951
    [6,] -4.285867 -2.827633 -2.4929304 0.39444379 -0.08617519

When I plot PC1 with all of my wells in a time series, I get:

Plot of time series of PC1 scores with water level of wells Screenshot

I got an exact negative correlation between PC score and my original data. Is it reasonable to get PC component score in the inverse direction to the original data? What does this mean? Does this mean that PC1 has an inverse relationship with the wells?

Astha
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  • So if I flip the signs of PC 1 score because signs do not matter, do the interpretation also change. In the explanation given by other question answers, it just tells you that signs can be flipped if you flip the loadings too. But does it mean that the intterpretations change too? In this case can I say that PC1 has an inverse relationship with the original variables? or can I just flip it and say that the signs do not have any significance and cannot be used for interpretation? –  Feb 27 '18 at 13:12
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    I'm not sure why my first comment disappeared during the migration from SO to CV; just to reiterate: The signs of the principle components are undetermined (to be precise: the PCs are unique up to a sign). See for example here and references therein. In other words and in response to your comment, the signs should not be used for interpretation. – Maurits Evers Feb 27 '18 at 20:11
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    TBH, I don't understand why you want to show PC1 and your variable values in one plot. The relationship is trivial (i.e. trivial by design of the PCs), where the absolute value of PC1 increases with increasing variance in the variable values. – Maurits Evers Feb 27 '18 at 20:17
  • @MauritsEvers When I show PC and the variables in the same plot I can see which variable is closer to the PC and how do the time series of PC relate to other factors that contribute in the process. – Astha Feb 27 '18 at 20:37

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