Total Variation in Data - Overall Importance of the Principal Components

P

Preetica

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 a moderator:

Miner

Forum Moderator
Staff member
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.

B Gage R&R Acceptable (10-30%), deduct Total Variation from Tolerance Gage R&R (GR&R) and MSA (Measurement Systems Analysis) 12
S Ppk & Cpk - Within Subgroup Variation is always smaller than Total Variation Capability, Accuracy and Stability - Processes, Machines, etc. 18
A %Total Variation & %Tolerance - Differences in Gage R&R Forms and Templates Gage R&R (GR&R) and MSA (Measurement Systems Analysis) 4
R Total Tolerance Method vs. Total Variation Method - Measurement System Analysis Gage R&R (GR&R) and MSA (Measurement Systems Analysis) 1
Total Variation Formula - Can someone provide a source for this formula Gage R&R (GR&R) and MSA (Measurement Systems Analysis) 11
P Calculating Gage R&R with Part Tolerance instead of Total Variation Gage R&R (GR&R) and MSA (Measurement Systems Analysis) 7
9 Process Variation and Total Variation - Relationship and Definitions Gage R&R (GR&R) and MSA (Measurement Systems Analysis) 9
W How Total Variation is calculated - Minitab Gage Question Using Minitab Software 2
F How to use Total Variation based on Process or Tolerance? Page 60 of the MSA manual Gage R&R (GR&R) and MSA (Measurement Systems Analysis) 2
G Tolerance vs Total Variation in Gage R&R report - MSA 3rd edition pg. 116 Gage R&R (GR&R) and MSA (Measurement Systems Analysis) 14
J Gage R&R - Tolerance vs. Total Variation - Process Variation vs. Gage Variation Gage R&R (GR&R) and MSA (Measurement Systems Analysis) 2
Total Productive Maintenance - Company Transport IATF 16949 - Automotive Quality Systems Standard 2
J Implementation of Total Quality Management/Starting a Quality Department Reliability Analysis - Predictions, Testing and Standards 9
K IATF16949 8.5.1.5 Total Productive Maintenance IATF 16949 - Automotive Quality Systems Standard 9
IATF 16949 Section 8.5.1.5 (Total Productive Maintenance) IATF 16949 - Automotive Quality Systems Standard 19
M Total number of Requirements for ISO 9001:2008 vs. ISO 9001:2015 ISO 9000, ISO 9001, and ISO 9004 Quality Management Systems Standards 9
One third of the total audit days on manufacturing (TS 16949) General Auditing Discussions 2
Total Productive Maintenance vs. Lean, Six sigma, Business Process Reengineering, etc Quality Tools, Improvement and Analysis 9
F What is the scope for "Total Numbers of Employees on site" per ISO/TS 16949 ? IATF 16949 - Automotive Quality Systems Standard 4
Total Lunar Eclipse Visible in North America - 15 April 2014 Coffee Break and Water Cooler Discussions 4
K Can I use ANSI/AQL for the Total Number of Containers for the entire Lot? Inspection, Prints (Drawings), Testing, Sampling and Related Topics 1
I Supplier Selection based on Total Cost question Supplier Quality Assurance and other Supplier Issues 4
B Total Resolution of an Measurement Instrument Gage R&R (GR&R) and MSA (Measurement Systems Analysis) 1
D Pls hlep me understand the "Total Anaerobic Plate Count" Food Safety - ISO 22000, HACCP (21 CFR 120) 1
How can Total Quality help a company or business compete in the world market? Preventive Action and Continuous Improvement 2
M How many documents total do you currently have? Document Control Systems, Procedures, Forms and Templates 6
5 Reasonable GRR result for a 0-1" micrometer with a total tolerance of .002" Gage R&R (GR&R) and MSA (Measurement Systems Analysis) 16
C A total newbie to AS 9101 needs general help AS9100, IAQG, NADCAP and Aerospace related Standards and Requirements 16
B Total Productive Maintenance Templates to Drive TPM Forward Lean in Manufacturing and Service Industries 1
N Total Productive Maintenance (TPM) Portuguese Definitions and Terms Quality Tools, Improvement and Analysis 4
V Differences between Business Process Reengineering (BPR) and Total Quality Management Quality Manager and Management Related Issues 3
Z KPI Formula Issue - "Change Requests Managed" = Changed/Total ISO 9000, ISO 9001, and ISO 9004 Quality Management Systems Standards 7
Circular Runout vs. Total Runout Inspection, Prints (Drawings), Testing, Sampling and Related Topics 3
Circular or Total Runout Gears and Splines? Inspection, Prints (Drawings), Testing, Sampling and Related Topics 6
Q Inspecting Total Runout Inspection, Prints (Drawings), Testing, Sampling and Related Topics 10
Uncertainty Measurement for Colour, Odour, Taste, Turbidity, Total Suspended Solids Calibration Frequency (Interval) 2
S Determining the Total Sample Size using AQL - AQL Lot Quantity question AQL - Acceptable Quality Level 8
D TQM (Total Quality Management) Diagram Software Quality Assurance and Compliance Software Tools and Solutions 4
R Total Quality Management (TQM) in the Aerospace Industry AS9100, IAQG, NADCAP and Aerospace related Standards and Requirements 3
A TQPC (Total Quality Process Control) for Injection Molding Quality Manager and Management Related Issues 4
C ASQ Quality Management Journal Vol. 17 Total Quality Management (TQM) Comments Wanted Book, Video, Blog and Web Site Reviews and Recommendations 8
N ISO 9001 and the HR Function - Developing a Total Quality Management System for HR ISO 9000, ISO 9001, and ISO 9004 Quality Management Systems Standards 16
K Where to obtain General Concepts of Total Organic Carbon (TOC) testing information? US Food and Drug Administration (FDA) 2
B Mojonnier method (determining fat and total solids) validation General Measurement Device and Calibration Topics 1
K Quality Assurance Clinical Research Auditor - Masters in Total Quality Management Career and Occupation Discussions 3
R TPM (Total Productive Maintenance) Reference Books Suggestions Book, Video, Blog and Web Site Reviews and Recommendations 3
M Top Three Reasons why TPM (Total Productive Maintenance) Initiatives Fail Manufacturing and Related Processes 39
N Journey towards total quality and Optimal results Misc. Quality Assurance and Business Systems Related Topics 4
Total Quality Management System Quality Manager and Management Related Issues 3
Total Variance Equation and process capability Imported Legacy Blogs 4