Output from pca2.sas
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PCA: Crime rates per 100,000 population by state 1
Principal Component Analysis
50 Observations
7 Variables
Simple Statistics
MURDER RAPE ROBBERY ASSAULT
Mean 7.444000000 25.73400000 124.0920000 211.3000000
StD 3.866768941 10.75962995 88.3485672 100.2530492
BURGLARY LARCENY AUTO
Mean 1291.904000 2671.288000 377.5260000
StD 432.455711 725.908707 193.3944175
Correlation Matrix
MURDER RAPE ROBBERY ASSAULT BURGLARY LARCENY AUTO MURDER 1.0000 0.6012 0.4837 0.6486 0.3858 0.1019 0.0688 RAPE 0.6012 1.0000 0.5919 0.7403 0.7121 0.6140 0.3489 ROBBERY 0.4837 0.5919 1.0000 0.5571 0.6372 0.4467 0.5907 ASSAULT 0.6486 0.7403 0.5571 1.0000 0.6229 0.4044 0.2758 BURGLARY 0.3858 0.7121 0.6372 0.6229 1.0000 0.7921 0.5580 LARCENY 0.1019 0.6140 0.4467 0.4044 0.7921 1.0000 0.4442 AUTO 0.0688 0.3489 0.5907 0.2758 0.5580 0.4442 1.0000
Eigenvalues of the Correlation Matrix
Eigenvalue Difference Proportion Cumulative
PRIN1 4.11496 2.87624 0.587851 0.58785
PRIN2 1.23872 0.51291 0.176960 0.76481
PRIN3 0.72582 0.40938 0.103688 0.86850
PRIN4 0.31643 0.05846 0.045205 0.91370
PRIN5 0.25797 0.03593 0.036853 0.95056
PRIN6 0.22204 0.09798 0.031720 0.98228
PRIN7 0.12406 . 0.017722 1.00000
PCA: Crime rates per 100,000 population by state 2
Principal Component Analysis
Eigenvectors
PRIN1 PRIN2 PRIN3 PRIN4 PRIN5 PRIN6 PRIN7 MURDER 0.300279 -.629174 0.178245 -.232114 0.538123 0.259117 0.267593 RAPE 0.431759 -.169435 -.244198 0.062216 0.188471 -.773271 -.296485 ROBBERY 0.396875 0.042247 0.495861 -.557989 -.519977 -.114385 -.003903 ASSAULT 0.396652 -.343528 -.069510 0.629804 -.506651 0.172363 0.191745 BURGLARY 0.440157 0.203341 -.209895 -.057555 0.101033 0.535987 -.648117 LARCENY 0.357360 0.402319 -.539231 -.234890 0.030099 0.039406 0.601690 AUTO 0.295177 0.502421 0.568384 0.419238 0.369753 -.057298 0.147046
PCA: Crime rates per 100,000 population by state 3 States listed in order of overall crime rate as determined by the first principal component
STATE PRIN1 PRIN2 MURDER RAPE ROBBERY ASSAULT BURGLARY LARCENY AUTO
NORTH DAKO -3.96 0.39 0.9 9.0 13.3 43.8 446.1 1843.0 144.7 SOUTH DAKO -3.17 -0.25 2.0 13.5 17.9 155.7 570.5 1704.4 147.5 WEST VIRGI -3.15 -0.81 6.0 13.2 42.2 90.9 597.4 1341.7 163.3 IOWA -2.58 0.82 2.3 10.6 41.2 89.8 812.5 2685.1 219.9 WISCONSIN -2.50 0.78 2.8 12.9 52.2 63.7 846.9 2614.2 220.7 NEW HAMPSH -2.47 0.83 3.2 10.7 23.2 76.0 1041.7 2343.9 293.4 NEBRASKA -2.15 0.23 3.9 18.1 64.7 112.7 760.0 2316.1 249.1 VERMONT -2.06 0.94 1.4 15.9 30.8 101.2 1348.2 2201.0 265.2 MAINE -1.83 0.58 2.4 13.5 38.7 170.0 1253.1 2350.7 246.9 KENTUCKY -1.73 -1.15 10.1 19.1 81.1 123.3 872.2 1662.1 245.4 PENNSYLVAN -1.72 -0.20 5.6 19.0 130.3 128.0 877.5 1624.1 333.2 MONTANA -1.67 0.27 5.4 16.7 39.2 156.8 804.9 2773.2 309.2 MINNESOTA -1.55 1.06 2.7 19.5 85.9 85.8 1134.7 2559.3 343.1 MISSISSIPP -1.51 -2.55 14.3 19.6 65.7 189.1 915.6 1239.9 144.4 IDAHO -1.43 -0.01 5.5 19.4 39.6 172.5 1050.8 2599.6 237.6 WYOMING -1.42 0.06 5.4 21.9 39.7 173.9 811.6 2772.2 282.0 ARKANSAS -1.05 -1.35 8.8 27.6 83.2 203.4 972.6 1862.1 183.4 UTAH -1.05 0.94 3.5 20.3 68.8 147.3 1171.6 3004.6 334.5 VIRGINIA -0.92 -0.69 9.0 23.3 92.1 165.7 986.2 2521.2 226.7 NORTH CARO -0.70 -1.67 10.6 17.0 61.3 318.3 1154.1 2037.8 192.1 KANSAS -0.63 -0.03 6.6 22.0 100.7 180.5 1270.4 2739.3 244.3 CONNECTICU -0.54 1.50 4.2 16.8 129.5 131.8 1346.0 2620.7 593.2 INDIANA -0.50 0.00 7.4 26.5 123.2 153.5 1086.2 2498.7 377.4 OKLAHOMA -0.32 -0.62 8.6 29.2 73.8 205.0 1288.2 2228.1 326.8 RHODE ISLA -0.20 2.15 3.6 10.5 86.5 201.0 1489.5 2844.1 791.4 TENNESSEE -0.14 -1.13 10.1 29.7 145.8 203.9 1259.7 1776.5 314.0 ALABAMA -0.05 -2.10 14.2 25.2 96.8 278.3 1135.5 1881.9 280.7 NEW JERSEY 0.22 0.96 5.6 21.0 180.4 185.1 1435.8 2774.5 511.5 OHIO 0.24 0.09 7.8 27.3 190.5 181.1 1216.0 2696.8 400.4 GEORGIA 0.49 -1.38 11.7 31.1 140.5 256.5 1351.1 2170.2 297.9 ILLINOIS 0.51 0.09 9.9 21.8 211.3 209.0 1085.0 2828.5 528.6 MISSOURI 0.56 -0.56 9.6 28.3 189.0 233.5 1318.3 2424.2 378.4 HAWAII 0.82 1.82 7.2 25.5 128.0 64.1 1911.5 3920.4 489.4 WASHINGTON 0.93 0.74 4.3 39.6 106.2 224.8 1605.6 3386.9 360.3 DELAWARE 0.96 1.30 6.0 24.9 157.0 194.2 1682.6 3678.4 467.0 MASSACHUSE 0.98 2.63 3.1 20.8 169.1 231.6 1532.2 2311.3 1140.1 LOUISIANA 1.12 -2.08 15.5 30.9 142.9 335.5 1165.5 2469.9 337.7 NEW MEXICO 1.21 -0.95 8.8 39.1 109.6 343.4 1418.7 3008.6 259.5 TEXAS 1.40 -0.68 13.3 33.8 152.4 208.2 1603.1 2988.7 397.6 OREGON 1.45 0.59 4.9 39.9 124.1 286.9 1636.4 3506.1 388.9 SOUTH CARO 1.60 -2.16 11.9 33.0 105.9 485.3 1613.6 2342.4 245.1 MARYLAND 2.18 -0.19 8.0 34.8 292.1 358.9 1400.0 3177.7 428.5 MICHIGAN 2.27 0.15 9.3 38.9 261.9 274.6 1522.7 3159.0 545.5 ALASKA 2.42 0.17 10.8 51.6 96.8 284.0 1331.7 3369.8 753.3 COLORADO 2.51 0.92 6.3 42.0 170.7 292.9 1935.2 3903.2 477.1 ARIZONA 3.01 0.84 9.5 34.2 138.2 312.3 2346.1 4467.4 439.5 FLORIDA 3.11 -0.60 10.2 39.6 187.9 449.1 1859.9 3840.5 351.4 NEW YORK 3.45 0.43 10.7 29.4 472.6 319.1 1728.0 2782.0 745.8 CALIFORNIA 4.28 0.14 11.5 49.4 287.0 358.0 2139.4 3499.8 663.5
PCA: Crime rates per 100,000 population by state 4 States listed in order of overall crime rate as determined by the first principal component
STATE PRIN1 PRIN2 MURDER RAPE ROBBERY ASSAULT BURGLARY LARCENY AUTO
NEVADA 5.27 -0.25 15.8 49.1 323.1 355 2453.1 4212.6 559.2
PCA: Crime rates per 100,000 population by state 5 States listed in order of Property vs. Violent crime as determined by the second principal component
STATE PRIN1 PRIN2 MURDER RAPE ROBBERY ASSAULT BURGLARY LARCENY AUTO
MISSISSIPP -1.51 -2.55 14.3 19.6 65.7 189.1 915.6 1239.9 144.4 SOUTH CARO 1.60 -2.16 11.9 33.0 105.9 485.3 1613.6 2342.4 245.1 ALABAMA -0.05 -2.10 14.2 25.2 96.8 278.3 1135.5 1881.9 280.7 LOUISIANA 1.12 -2.08 15.5 30.9 142.9 335.5 1165.5 2469.9 337.7 NORTH CARO -0.70 -1.67 10.6 17.0 61.3 318.3 1154.1 2037.8 192.1 GEORGIA 0.49 -1.38 11.7 31.1 140.5 256.5 1351.1 2170.2 297.9 ARKANSAS -1.05 -1.35 8.8 27.6 83.2 203.4 972.6 1862.1 183.4 KENTUCKY -1.73 -1.15 10.1 19.1 81.1 123.3 872.2 1662.1 245.4 TENNESSEE -0.14 -1.13 10.1 29.7 145.8 203.9 1259.7 1776.5 314.0 NEW MEXICO 1.21 -0.95 8.8 39.1 109.6 343.4 1418.7 3008.6 259.5 WEST VIRGI -3.15 -0.81 6.0 13.2 42.2 90.9 597.4 1341.7 163.3 VIRGINIA -0.92 -0.69 9.0 23.3 92.1 165.7 986.2 2521.2 226.7 TEXAS 1.40 -0.68 13.3 33.8 152.4 208.2 1603.1 2988.7 397.6 OKLAHOMA -0.32 -0.62 8.6 29.2 73.8 205.0 1288.2 2228.1 326.8 FLORIDA 3.11 -0.60 10.2 39.6 187.9 449.1 1859.9 3840.5 351.4 MISSOURI 0.56 -0.56 9.6 28.3 189.0 233.5 1318.3 2424.2 378.4 SOUTH DAKO -3.17 -0.25 2.0 13.5 17.9 155.7 570.5 1704.4 147.5 NEVADA 5.27 -0.25 15.8 49.1 323.1 355.0 2453.1 4212.6 559.2 PENNSYLVAN -1.72 -0.20 5.6 19.0 130.3 128.0 877.5 1624.1 333.2 MARYLAND 2.18 -0.19 8.0 34.8 292.1 358.9 1400.0 3177.7 428.5 KANSAS -0.63 -0.03 6.6 22.0 100.7 180.5 1270.4 2739.3 244.3 IDAHO -1.43 -0.01 5.5 19.4 39.6 172.5 1050.8 2599.6 237.6 INDIANA -0.50 0.00 7.4 26.5 123.2 153.5 1086.2 2498.7 377.4 WYOMING -1.42 0.06 5.4 21.9 39.7 173.9 811.6 2772.2 282.0 OHIO 0.24 0.09 7.8 27.3 190.5 181.1 1216.0 2696.8 400.4 ILLINOIS 0.51 0.09 9.9 21.8 211.3 209.0 1085.0 2828.5 528.6 CALIFORNIA 4.28 0.14 11.5 49.4 287.0 358.0 2139.4 3499.8 663.5 MICHIGAN 2.27 0.15 9.3 38.9 261.9 274.6 1522.7 3159.0 545.5 ALASKA 2.42 0.17 10.8 51.6 96.8 284.0 1331.7 3369.8 753.3 NEBRASKA -2.15 0.23 3.9 18.1 64.7 112.7 760.0 2316.1 249.1 MONTANA -1.67 0.27 5.4 16.7 39.2 156.8 804.9 2773.2 309.2 NORTH DAKO -3.96 0.39 0.9 9.0 13.3 43.8 446.1 1843.0 144.7 NEW YORK 3.45 0.43 10.7 29.4 472.6 319.1 1728.0 2782.0 745.8 MAINE -1.83 0.58 2.4 13.5 38.7 170.0 1253.1 2350.7 246.9 OREGON 1.45 0.59 4.9 39.9 124.1 286.9 1636.4 3506.1 388.9 WASHINGTON 0.93 0.74 4.3 39.6 106.2 224.8 1605.6 3386.9 360.3 WISCONSIN -2.50 0.78 2.8 12.9 52.2 63.7 846.9 2614.2 220.7 IOWA -2.58 0.82 2.3 10.6 41.2 89.8 812.5 2685.1 219.9 NEW HAMPSH -2.47 0.83 3.2 10.7 23.2 76.0 1041.7 2343.9 293.4 ARIZONA 3.01 0.84 9.5 34.2 138.2 312.3 2346.1 4467.4 439.5 COLORADO 2.51 0.92 6.3 42.0 170.7 292.9 1935.2 3903.2 477.1 UTAH -1.05 0.94 3.5 20.3 68.8 147.3 1171.6 3004.6 334.5 VERMONT -2.06 0.94 1.4 15.9 30.8 101.2 1348.2 2201.0 265.2 NEW JERSEY 0.22 0.96 5.6 21.0 180.4 185.1 1435.8 2774.5 511.5 MINNESOTA -1.55 1.06 2.7 19.5 85.9 85.8 1134.7 2559.3 343.1 DELAWARE 0.96 1.30 6.0 24.9 157.0 194.2 1682.6 3678.4 467.0 CONNECTICU -0.54 1.50 4.2 16.8 129.5 131.8 1346.0 2620.7 593.2 HAWAII 0.82 1.82 7.2 25.5 128.0 64.1 1911.5 3920.4 489.4 RHODE ISLA -0.20 2.15 3.6 10.5 86.5 201.0 1489.5 2844.1 791.4
PCA: Crime rates per 100,000 population by state 6 States listed in order of Property vs. Violent crime as determined by the second principal component
STATE PRIN1 PRIN2 MURDER RAPE ROBBERY ASSAULT BURGLARY LARCENY AUTO
MASSACHUSE 0.98 2.63 3.1 20.8 169.1 231.6 1532.2 2311.3 1140.1
PCA: Crime rates per 100,000 population by state 7 Plot of the first two principal components
Plot of PRIN2*PRIN1$ST. Symbol points to label.
PRIN2 |
3.00 +
|
|
| > MA
|
|
| > RI
2.00 +
| > HI
|
| > CT
|
| > DE
| VT MN
1.00 + ^ ^ > UT > NJ
| IA <> NH CO < > AZ
| > WI > WA
| > ME > OR
|> ND > NY
| NE < > MT
| KS OH < > IL MI <> AK > CA
0.00 + WY 2 ID ^> IN
| > PA > MD
| > SD > NV
|
| > OK > MO > FL
| > VA > TX
| > WV
-1.00 + > NM
| > KY > TN
| > AR
| > GA
|
| > NC
|
-2.00 +
| > AL LA < > SC
|
|
| > MS
|
|
-3.00 +
-+-------------+-------------+-------------+-------------+-------------+
-4.00 -2.00 0.00 2.00 4.00 6.00
PRIN1
PCA: Crime rates per 100,000 population by state 8 Plot of the first and third principal components
Plot of PRIN3*PRIN1$ST. Symbol points to label.
PRIN3 |
|
3 +
|
| > NY
| > MA
|
|
|
2 +
|
|
|
|
|
| > IL
1 + > PA > RI
| CT
| KY <> MS ^ > TN NJ
| > WV AL < ^ > MO > MI
| > OH > LA > MD
| > IN > GA > CA
|
0 + NH NE MN > AR > AK
|> ND > SD ^ ^ ^ VA <v > OK > TX
| MT NC > NV
| > WI ^ WY > KS
| IA < vv 2 > UT DE < > SC
| VT ME ID > HI
|
-1 +
| > NM > CO
| WA < > OR > FL
|
|
| > AZ
|
-2 +
|
-+-------------+-------------+-------------+-------------+-------------+
-4.00 -2.00 0.00 2.00 4.00 6.00
PRIN1