I ran a principal component analysis and got these values what do these values m
ID: 3327019 • Letter: I
Question
I ran a principal component analysis and got these values what do these values mean for the effect of multicolinearity?
Rotation (n x k) = (15 x 15):
PC1 PC2 PC3 PC4 PC5 PC6 PC7
B 0.30011092 0.22394235 -0.209396685 0.04893193 -0.05595656 0.18350536 -0.02707739
C -0.10879951 -0.13416187 -0.039441546 0.78879434 -0.55995956 -0.15316858 0.04000431
D 0.29817912 0.15704233 0.005456567 0.26929423 0.13179468 0.36038244 -0.10743587
E -0.28194241 -0.25372825 -0.109200208 0.13203789 0.20969701 0.13466632 -0.63472472
F 0.08730349 0.09496546 0.732325794 0.12165568 0.12304152 -0.03989509 0.33954555
G 0.30140783 -0.17948766 0.119149117 0.18741006 0.23520296 -0.19820683 -0.11513614
H 0.28395860 -0.30316400 -0.112323119 -0.15102526 -0.19227887 -0.08623753 0.19657650
I 0.31975915 -0.12669200 0.105215070 0.04255542 0.07370050 0.05164030 -0.24542805
J 0.30148140 -0.18149399 0.114121909 0.18639702 0.23570609 -0.19975246 -0.11561923
K 0.25658682 -0.37977158 -0.104305798 -0.21101354 -0.22394209 -0.03503878 0.04422493
L 0.27285275 -0.35591818 -0.069187777 -0.17138738 -0.18191215 -0.02596938 0.01559479
M 0.20120923 0.31449281 -0.467482894 0.13957610 0.06580484 0.14230685 0.30424159
N -0.20736835 -0.42747682 0.134306029 0.03477943 -0.02355568 0.74229377 0.26393277
O -0.17264466 -0.32624629 -0.321156347 0.23130015 0.58845453 -0.20215925 0.41634385
P 0.32230016 0.04115210 0.006959562 0.16756640 0.13836753 0.29991770 -0.06849286
PC8 PC9 PC10 PC11 PC12 PC13 PC14
B -0.13829387 -0.15473650 0.25598169 -0.382883810 0.150580245 -0.701328774 -0.077668773
C 0.02482244 -0.01964523 -0.06557860 -0.014795462 -0.023330215 -0.041358112 0.002969716
D 0.36943499 -0.38049640 0.23474811 0.223051579 0.388288059 0.342981487 -0.011901542
E 0.31266121 0.36914082 0.26250136 -0.229102422 -0.058562535 -0.052889531 0.011849749
F 0.36652199 0.29832724 0.12708313 -0.179555639 0.008258124 -0.168491267 0.005800204
G -0.39352711 0.12662364 0.15252256 0.131580751 0.054947363 0.028082829 0.140432799
H 0.04795818 -0.10641712 0.33838100 -0.586156502 -0.197071525 0.442865767 0.047985452
I 0.02346622 0.01310993 -0.75765936 -0.394761256 0.252517634 0.066872511 0.029007260
J -0.38701218 0.11464154 0.19255785 0.138707636 0.061575855 0.044180240 -0.154726376
K 0.25221871 0.12243750 0.02383027 0.300559575 0.170997823 -0.256368320 0.631561326
L 0.27078663 0.10956246 -0.05049737 0.259965270 -0.030281338 -0.141435677 -0.728260422
M 0.02743296 0.67955461 -0.06182454 0.010209626 0.064585960 0.186498818 -0.001107561
N -0.34134278 0.07651546 -0.00457003 -0.007551878 0.103194825 0.001021866 -0.026325578
O 0.20903546 -0.24207250 -0.10791725 -0.071111535 0.026370916 -0.164013091 -0.005699731
P 0.07928060 -0.10822809 -0.15003611 0.139984334 -0.816963652 -0.082765173 0.129914157
PC15
B 0.0154693446
C -0.0032082310
D 0.0206393471
E 0.0020696259
F -0.0041796586
G 0.6962418831
H 0.0028250419
I -0.0283449393
J -0.6860407075
K -0.1336146604
L 0.1547833987
M -0.0038706016
N 0.0028493510
O 0.0007823943
P -0.0353857610
Explanation / Answer
you have 15 variable in your analysis the results you have obtained are the Principle componants using the statistical technique called Principal Componant analysis. Principal component analysis (PCA) is a statistical procedure that uses an orthogonal transformation to convert a set of observations of possibly correlated variables into a set of values of linearly uncorrelated variables called principal components. This transformation is defined in such a way that the first principal component has the largest possible variance (that is, accounts for as much of the variability in the data as possible), and each succeeding component in turn has the highest variance possible under the constraint that it is orthogonal to the preceding components. The resulting vectors are an uncorrelated orthogonal basis set.
In simple words, principal component analysis is a method of extracting important variables (in form of components) from a large set of variables available in a data set. It extracts low dimensional set of features from a high dimensional data set with a motive to capture as much information as possible.
The first principal component covers maximum of the information and second component will fallow the first principal components in discribing the information in the data and third will fallow the second and so on. only few four or five priciple components may be covering almost 100% of the information in the data. Now we can use these first five principle components instead of 15 orginal variable.
The Principle component does both eliminates multicolinearity and reduce the no of variables so sometime it is also called variable reduction technique.
i have generated a random data and carry out the principle component analysis for the same using minitab as below
Welcome to Minitab, press F1 for help.
Principal Component Analysis: Sale1, Sale2, Sale3, Sale4, Sale5
Eigenanalysis of the Covariance Matrix
proportion is the amount of the information described by principle components. here in my example first principle component describe 61% of the data and collectively first two describes almost 90% of information.
Eigenvalue 11905 5357 1195 630 210 Proportion 0.617 0.278 0.062 0.033 0.011 Cumulative 0.617 0.895 0.956 0.989 1