Continued+on+Next+Page

Importance of components: Comp.1 Comp.2 Comp.3 Comp.4 Standard deviation 1.5748783 0.9948694 0.5971291 0.41644938 Proportion of Variance 0.6200604 0.2474413 0.0891408 0.04335752 Cumulative Proportion 0.6200604 0.8675017 0.9566425 1.00000000

loadings( pc.cr ) ## note that blank entries are small but not zero

Loadings: Comp.1 Comp.2 Comp.3 Comp.4 Murder -0.536 0.418 -0.341 0.649 Assault -0.583 0.188 -0.268 -0.743 UrbanPop -0.278 -0.873 -0.378 0.134 Rape -0.543 -0.167 0.818 Comp.1 Comp.2 Comp.3 Comp.4 SS loadings 1.00 1.00 1.00 1.00 Proportion Var 0.25 0.25 0.25 0.25 Cumulative Var 0.25 0.50 0.75 1.00

plot( pc.cr ) # shows a screeplot.

biplot( pc.cr )

**## This is the R biplot, I find it a bit confusing. I had difficulty interpreting the loadings.**

princomp (~ ., data = USArrests, cor = TRUE )
 * 1) Formula interface
 * Note this command outputs component scores.**

Call: princomp(formula = ~., data = USArrests, cor = TRUE)

Standard deviations: Comp.1 Comp.2 Comp.3 Comp.4 1.5748783 0.9948694 0.5971291 0.4164494 4 variables and 50 observations.


 * 1) NA-handling

USArrests[1, 2] <- NA  pc.cr <- princomp(~ Murder + Assault + UrbanPop,    data = USArrests, na.action=na.exclude, cor = TRUE ) pc.cr$scores

Comp.1 Comp.2 Comp.3 Alabama NA NA NA Alaska -0.80197919 -1.42047055 -0.642322193 Arizona -1.38652787 0.78609767 -0.845544816 Arkansas -0.04279066 -1.13077106 -0.179125425 California -1.58764207 1.45847270 -0.421715531 Colorado -0.56226927 0.75677639 -0.122722599 Connecticut 0.95738374 1.11944316 -0.051315808 Delaware -0.42169552 0.47726094 -0.801961912 Florida -2.86046014 0.21123562 -0.042644564 Georgia -1.74365763 -1.12618762 1.116850812 Hawaii 1.06835061 1.42799051 0.887049305 Idaho 1.42665263 -0.34633005 -0.511478111 Illinois -1.42330487 0.85764489 -0.058026400 Indiana 0.56048601 0.04414174 0.403782728 Iowa 1.96718910 -0.05845077 0.012207438 Kansas 0.71015966 0.19572170 0.207737252 Kentucky 0.45836082 -0.98728711 0.686018346 Louisiana -1.86866310 -0.62309659 0.540194317 Maine 1.87230442 -0.47048688 -0.305422092 Maryland -1.68087144 -0.30632760 -0.538735534 Massachusetts 0.30538917 1.52537563 -0.122409079 Michigan -1.56277060 0.13734831 0.056746149 Minnesota 1.58159551 0.47926709 0.056105941 Mississippi -1.63547395 -2.12596825 0.313357619 Missouri -0.35987183 0.17697476 0.184779464 Montana 1.01184498 -0.65048911 0.111001744 Nebraska 1.15969539 0.07077521 0.004866721 Nevada -1.68845513 0.59169868 0.178502782 New Hampshire 1.99362277 -0.11762698 -0.023707680 New Jersey -0.32025388 1.55791837 0.312422046 New Mexico -1.62859289 -0.10252360 -0.359039556 New York -1.63160995 0.99810647 0.044018129 North Carolina -1.82888530 -1.90864100 -0.840286980 North Dakota 2.52754088 -0.79718469 -0.263238298 Ohio 0.29294448 0.68543417 0.473447326 Oklahoma 0.27674762 0.24797518 0.014740863 Oregon 0.49219479 0.29932571 -0.335234496 Pennsylvania 0.62315668 0.57567606 0.401590996 Rhode Island 0.21191502 1.70557498 -0.473990230 South Carolina -1.61732656 -1.75853156 -0.083129342 South Dakota 1.69998263 -0.99126092 -0.130453732 Tennessee -0.88124402 -0.86155489 0.638392599 Texas -1.31890758 0.53885660 0.686838134 Utah 0.83100839 1.31371651 -0.119257691 Vermont 2.51768427 -1.68920353 -0.204385942 Virginia 0.03735647 -0.22385715 0.215561608 Washington 0.63289498 0.77209435 -0.288391286 West Virginia 1.56377506 -1.51895574 0.145314536 Wisconsin 1.75638622 0.50498526 0.204369100 Wyoming 0.31663111 -0.30068300 -0.131356659

=References:= Crawley, M. J. (2007). //The R Book//. John Wiley & Sons, Ltd.: Chichester, West Sussex, England.

McGarigal, K, Cushman, S. and Stafford, S. (2000). //Multivariate Statistics for Wildlife and Ecology Research//. Springer: New York, USA.

For Further References: Mardia, K. V., J. T. Kent and J. M. Bibby (1979). //Multivariate Analysis//, London: Academic Press. Venables, W. N. and B. D. Ripley (2002). //Modern Applied Statistics with S//, Springer-Verlag.