The Elsmar Cove Business Systems and Standards Discussion Forums Total Variation in Data - Overall Importance of the Principal Components
 Forum User Name Keep Me Logged In Password
 Register Photo Albums Blogs FAQ Registered Visitors Social Groups Calendar Search Today's Posts Mark Forums Read

 Elsmar Cove Forum Visitor Notice(s)

# Total Variation in Data - Overall Importance of the Principal Components

 Elsmar XML RSS Feed Monitor the Elsmar Forum Sponsor Links Courtesy Quick Links Links Elsmar Cove visitors will find useful in the quest for knowledge and support: International Standards Bodies - World Wide Standards Bodies International Standards Organization - ISO Standards and Information Quality Digest

Post Number #1
9th April 2017, 06:17 AM
 Preetica Total Posts: 1
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
,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,Comp.1,,,,,,,,,Comp.2,,,,,,Comp.3,,,,,Comp.4
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

,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,Comp.5,,,,,,,,,Comp.6,,,,,,Comp.7,,,,,,Comp.8
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

,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,Comp.9,,,,,,,,,Comp.10,,,,Comp.11
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
,,,,,,,,,,Comp.1,,,,,,,Comp.2,,,,Comp.3,,,,Comp.4,,,Comp.5,,,,Comp.6
mpg,,,,,0.363,,,,,,−0.226,,,,,,−0.103,,,,,−0.109,,,,,0.368,,,,,,,0.754
cyl,,,,,−0.374,,,,,,−0.175,,,,,,,,0.169,,,,,,,0.231,,,−0.846
disp,, −0.368,,,,,,,,,0.257,,,,,,−0.394,,,,,−0.336,,,,,,0.214,,,,,,,0.198
hp,,,,,,−0.33,,,,,,,,−0.249,,,,,,,,0.14,,,,,,,−0.54,,,,,,,0.222,,,,,−0.576
drat,,,,,,0.294,,,,,,,−0.275,,,,,,,0.161,,,,,,,,0.855,,,,,0.244,,,,,,−0.101
wt,,,,,,−0.346,,,,,,,,,0.143,,,,,,,0.342,,,,,,,0.246,,,,,−0.465,,,,,, 0.359
qsec,,,,,,0.2,,,,,,,,,,,,0.463,,,,,,,0.403,,,,,,,0.165,,,,−0.33,,,,,,,,0.232
vs,,,,,,,,,0.307,,,,,,,,,0.232,,,,,,,0.429,,,,,,,−0.215,,−0.6,,,,,,,,,0.194
am,,,,,,,0.235,,,,,,,,−0.429,,,,,,−0.206,,,,,,−0.571,,−0.587,,,,,−0.178
gear,,,,,,0.207,,,,,,,,−0.462,,,,,,,,0.29,,,,,,,−0.265,,−0.244,,,,,,,0.605
carb,,,,−0.214,,,,,,,,−0.414,,,,,,,0.529,,,,,,−0.127,,,,0.361,,,,,,,,0.184

,,,,,,,,,,,Comp.7,,,,,Comp.8,,,,,Comp.9,,,,,Comp.10,,,Comp.11
mpg,,,,,0.236,,,,,,,,,0.139,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,0.125
cyl,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,0.141
disp,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,−0.661
hp,,,,,,,0.248,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,0.256
drat
wt,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,0.567
qsec,,,,,−0.528,,,,, −0.271,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,−0.181
vs,,,,,,,,−0.266,,,,,,,,0.359,,,,, −0.159
am
gear,,,,,−0.336,,,,,,−0.214
carb,,,,,−0.175,,,,,,,,,,0.396,,,,,,,,0.171,,,,,,,,,,,,,,,,,,,,−0.32

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

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

Post Number #2
20th April 2017, 09:54 AM
 Miner Total Posts: 4,072
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.com. 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!

 The Elsmar Cove Business Systems and Standards Discussion Forums Total Variation in Data - Overall Importance of the Principal Components

 Bookmarks

 Visitors Currently Viewing this Thread: 1 (0 Registered Visitors (Members) and 1 Unregistered Guest Visitors)

 Forum Posting Settings You may not post new threads You may not post replies You may not post attachments You may not edit your posts BB code is On Emoticons are On [IMG] code is On HTML code is Off Forum Rules

 Similar Discussion Threads Discussion Thread Title Thread Starter Forum Replies Last Post or Poll Vote Stevenli Capability, Accuracy and Stability - Processes, Machines, etc. 18 12th February 2014 12:31 AM Brad Gover Quality Tools, Improvement and Analysis 4 12th November 2011 09:52 AM ram4302 Gage R&R (GR&R) and MSA (Measurement Systems Analysis) 1 11th July 2010 01:16 PM 9876543219 Gage R&R (GR&R) and MSA (Measurement Systems Analysis) 9 5th March 2009 05:07 AM Jrodrigu Gage R&R (GR&R) and MSA (Measurement Systems Analysis) 2 29th August 2002 08:09 AM

The time now is 02:31 PM. All times are GMT -4.