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I am running a PCA for quality in a water resource. I have 15 original variables. Running the PCA using Minitab, it turned out that the first PC is responsible for 99.7% of the variation. Looking at the eigenvectors, all the original values have almost the same correlation value with PC1 (about 0.25). What does that mean? Note: I tried to use the log of the data, and the results were very much the same.

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  • $\begingroup$ Did you set "Type of matrix" = Covariance? $\endgroup$ – Michael M Jan 11 '14 at 11:53
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    $\begingroup$ Water quality data tend to be very highly intercorrelated: the first PC of the raw data typically accounts for 90+% of all variation. For analyzing chemical composition, one usually bases the PCA on the log data and/or on the correlation matrix and often focuses on the PCs after the first. (Another approach is to standardize the concentrations as percentages of the total in each sample: this can work well provided few samples have missing values.) If you got the same extreme results with the logarithms, that could be due to how nondetects or low-level values have been processed. $\endgroup$ – whuber Jan 11 '14 at 14:44
  • $\begingroup$ Thanks Whuber. I got the same extreme results using the log scale with very slight difference. I will also try your suggestion and let you know. $\endgroup$ – user37178 Jan 12 '14 at 7:33
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It means that there is one very large component and that all the variables are roughly equal in its determination.

Since you haven't told us your variables, it's hard to say more, but something similar could happen if your 15 variables were all measurements of length of different parts of a human body. In this case, overall size of the person would be highly correlated to all the inidividual parts.

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  • $\begingroup$ That was my thinking, but I was worried since in all researches I have read they use a correlation value >0.5 to consider. and since all my correlation values were <0.5, I did not know how to use it. My variables are 15 stations that measure water quality along its path. $\endgroup$ – user37178 Jan 12 '14 at 7:30

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