options linesize=85 pagesize=85;

title "SAS principle component analysis example 2 from SAS PRINCOMP Crime Rates";

data Crime;

title 'Crime Rates per 100,000 Population by State';

input State $1-18 Murder Rape Robbery Assault

Burglary Larceny Auto_Theft;

datalines;

Alabama 14.2 25.2 96.8 278.3 1135.5 1881.9 280.7

Alaska 10.8 51.6 96.8 284.0 1331.7 3369.8 753.3

Arizona 9.5 34.2 138.2 312.3 2346.1 4467.4 439.5

Arkansas 8.8 27.6 83.2 203.4 972.6 1862.1 183.4

California 11.5 49.4 287.0 358.0 2139.4 3499.8 663.5

Colorado 6.3 42.0 170.7 292.9 1935.2 3903.2 477.1

Connecticut 4.2 16.8 129.5 131.8 1346.0 2620.7 593.2

Delaware 6.0 24.9 157.0 194.2 1682.6 3678.4 467.0

Florida 10.2 39.6 187.9 449.1 1859.9 3840.5 351.4

Georgia 11.7 31.1 140.5 256.5 1351.1 2170.2 297.9

Hawaii 7.2 25.5 128.0 64.1 1911.5 3920.4 489.4

Idaho 5.5 19.4 39.6 172.5 1050.8 2599.6 237.6

Illinois 9.9 21.8 211.3 209.0 1085.0 2828.5 528.6

Indiana 7.4 26.5 123.2 153.5 1086.2 2498.7 377.4

Iowa 2.3 10.6 41.2 89.8 812.5 2685.1 219.9

Kansas 6.6 22.0 100.7 180.5 1270.4 2739.3 244.3

Kentucky 10.1 19.1 81.1 123.3 872.2 1662.1 245.4

Louisiana 15.5 30.9 142.9 335.5 1165.5 2469.9 337.7

Maine 2.4 13.5 38.7 170.0 1253.1 2350.7 246.9

Maryland 8.0 34.8 292.1 358.9 1400.0 3177.7 428.5

Massachusetts 3.1 20.8 169.1 231.6 1532.2 2311.3 1140.1

Michigan 9.3 38.9 261.9 274.6 1522.7 3159.0 545.5

Minnesota 2.7 19.5 85.9 85.8 1134.7 2559.3 343.1

Mississippi 14.3 19.6 65.7 189.1 915.6 1239.9 144.4

Missouri 9.6 28.3 189.0 233.5 1318.3 2424.2 378.4

Montana 5.4 16.7 39.2 156.8 804.9 2773.2 309.2

Nebraska 3.9 18.1 64.7 112.7 760.0 2316.1 249.1

Nevada 15.8 49.1 323.1 355.0 2453.1 4212.6 559.2

New Hampshire 3.2 10.7 23.2 76.0 1041.7 2343.9 293.4

New Jersey 5.6 21.0 180.4 185.1 1435.8 2774.5 511.5

New Mexico 8.8 39.1 109.6 343.4 1418.7 3008.6 259.5

New York 10.7 29.4 472.6 319.1 1728.0 2782.0 745.8

North Carolina 10.6 17.0 61.3 318.3 1154.1 2037.8 192.1

North Dakota 0.9 9.0 13.3 43.8 446.1 1843.0 144.7

Ohio 7.8 27.3 190.5 181.1 1216.0 2696.8 400.4

Oklahoma 8.6 29.2 73.8 205.0 1288.2 2228.1 326.8

Oregon 4.9 39.9 124.1 286.9 1636.4 3506.1 388.9

Pennsylvania 5.6 19.0 130.3 128.0 877.5 1624.1 333.2

Rhode Island 3.6 10.5 86.5 201.0 1489.5 2844.1 791.4

South Carolina 11.9 33.0 105.9 485.3 1613.6 2342.4 245.1

South Dakota 2.0 13.5 17.9 155.7 570.5 1704.4 147.5

Tennessee 10.1 29.7 145.8 203.9 1259.7 1776.5 314.0

Texas 13.3 33.8 152.4 208.2 1603.1 2988.7 397.6

Utah 3.5 20.3 68.8 147.3 1171.6 3004.6 334.5

Vermont 1.4 15.9 30.8 101.2 1348.2 2201.0 265.2

Virginia 9.0 23.3 92.1 165.7 986.2 2521.2 226.7

Washington 4.3 39.6 106.2 224.8 1605.6 3386.9 360.3

West Virginia 6.0 13.2 42.2 90.9 597.4 1341.7 163.3

Wisconsin 2.8 12.9 52.2 63.7 846.9 2614.2 220.7

Wyoming 5.4 21.9 39.7 173.9 811.6 2772.2 282.0

;

ods html file="sas82.html";

ods graphics on;

proc princomp out=Crime_Components;

run;

ods graphics off;

ods html close;

ods html file="sas821.html";

proc sort;

by Prin1;

run;

proc print;

id State;

var Prin1 Prin2 Murder Rape Robbery

Assault Burglary Larceny Auto_Theft;

title2 'States Listed in Order of Overall Crime Rate';

title3 'As Determined by the First Principal Component';

run;

ods html close;

ods html file="sas822.html";

proc sort;

by Prin2;

run;

proc print;

id State;

var Prin1 Prin2 Murder Rape Robbery

Assault Burglary Larceny Auto_Theft;

title2 'States Listed in Order of Property Vs.

Violent Crime';

title3 'As Determined by the Second Principal Component';

run;

ods html close;

proc rank data=Crime_Components out=ranks;

var Prin1;

ranks R;

run;

proc print data=ranks;

var State Prin1 R;

run;

data plotdata;

set ranks;

NN=50;

Rstar=(R-.5)/NN;

HX=PROBIT(Rstar);

run;

proc sort data=plotdata;

by R;

run;

proc print data=plotdata;

var State prin1 R HX;

run;

/*proc plot data=plotdata;

plot Prin1*HX='*' HX*HX='+' /overlay vzero hzero;

run;*/

*filename gsasfile 'Q-Q-plot.ps';

*goptions reset=all device=pslmono;

goptions hsize=8in vsize-=5in;

proc gplot data=plotdata;

plot Prin1*HX=1 HX*HX=2/overlay hzero vzero;

symbol1 v=diamond;

symbol2 v=none I=rl0;

label HX='Standard Normal quantile'

Prin1='Principal Component 1';

run;

quit;

*%plotit(data=plotdata,labelvar=star, plotvars=Prin1 HX, color=black, colors=blue);

data chiq;

set Crime_Components;

dsq=uss(Prin1-Prin7);

proc capability data=chiq noprint graphics;

qqplot dsq/gamma(alpha=3.5 sigma=2 theta=0);

title2 h=1.5 'Q-Q Plot for Assessing Normality';

run;

proc capability data=chiq noprint graphics;

ppplot dsq/gamma(alpha=3.5 sigma=2 theta=0);

title2 h=1.5 'P-P Plot for Assessing Normality';

run;

proc capability data=chiq noprint graphics;

probplot dsq/gamma(alpha=3.5 sigma=2 theta=0);

title2 h=1.5 'PROB Plot for Assessing Normality';

run;

title2 'Plot of the First Two Principal Components';

%plotit(data=Crime_Components, labelvar=State,

plotvars=Prin2 Prin1, color=black, colors=blue);

run;

title2 'Plot of the First and Third Principal Components';

%plotit(data=Crime_Components, labelvar=State,

plotvars=Prin3 Prin1, color=red, colors=blue);

run;