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Total Variation in Data - Overall Importance of the Principal Components

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  Post Number #1  
Old 9th April 2017, 06:17 AM

Total Posts: 1
Let Me Help You Total Variation in Data - Overall Importance of the Principal Components

As the system was not accepting spaces I gave comma instead of space.

Table 6.1 indicates the overall importance of the principal components. It
displays for each component ph the standard deviation, given by
√λh, the proportion of variance explained by each component, equal to λh/j λj, and the cumulative proportion explained by the first components up to ph included.The analysis shows that the first two components explain 84% of the total variation in the data while the first 5 explain 94%.

Table 6.1 Overall importance of principal components in the mtcars dataset
Standard deviation,,,,,,2.5706809,,,,1.6280258,,,0.7919578,,0.5192277
Proportion of variance,,0.6007637,,,,0.2409516,,,0.0570179,,0.0245088
Cumulative proportion,,0.6007637,,,,0.8417153,,,0.8987332,,0.9232420

Standard deviation,,,,,,0.4727061,,,0.4599957,,,,0.3677798,,,0.3505730
Proportion of variance,,0.0203137,,,0.0192360,,,,0.0122965,,,0.0111728
Cumulative proportion,,0.9435558,,,0.9627918,,,0.9750883,,,0.9862612

Standard deviation,,,,,,,0.2775727,,,,0.2281127,,,0.1484735
Proportion of variance,,,0.0070042,,,,0.0047304,,,0.0020040
Cumulative proportion,,,0.9932654,,,,,,0.9979959,,,,1.0000000

Can someone please the formula for total variation in data, how did we get the values 84% and 94%

Table 6.2 shows the values of the coefficients whj = uhj ; equivalently, it
indicates the eigenvectors of the covariance matrix V. The first component,
which alone explains 60% of the variance, is negatively correlated with the
attributes {cyl, disp,wt, carb}, whose meaning is explained in Appendix B,
while it is positively correlated with all the other attributes.

Table 6.2 Principal component coefficients for the mtcars dataset
disp,, −0.368,,,,,,,,,0.257,,,,,,−0.394,,,,,−0.336,,,,,,0.214,,,,,,,0.198
wt,,,,,,−0.346,,,,,,,,,0.143,,,,,,,0.342,,,,,,,0.246,,,,,−0.465,,,,,, 0.359

qsec,,,,,−0.528,,,,, −0.271,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,−0.181
vs,,,,,,,,−0.266,,,,,,,,0.359,,,,, −0.159

Can anyone please explain how the corelation is calculated like how did we get the value 60%

Thanks in advance

Last edited by Preetica; 9th April 2017 at 06:40 AM.

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  Post Number #2  
Old 20th April 2017, 09:54 AM
Miner's Avatar

Total Posts: 4,072
Look! Re: Total Variation in Data - Overall Importance of the Principal Components

This is pretty advanced statistics for this forum. I recommend asking this question on Talkstats is a statistics discussion forum, and I have seen PCA and Factor Analysis discussed periodically.
Thanks to Miner for your informative Post and/or Attachment!
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