Problem: The following data are the rates per 100,000 of various crimes by state for the United States in 2003. The data come from the FBI: http://www.fbi.gov/ucr/ucr.htm
How many factors are needed to explain these data? Before conducting any analysis, think of reasonable names for factors that might be involved. As a hint, the FBI breaks down these crimes into two groups. You can find out how by looking at the data on the FBI link given above.
After conducting a factor analysis with appropriate rotations considered, do your factor loadings make sense in terms of you prior beliefs about the names of the factors? Can you come up with other names for the factors as determined by these data?
How would you verify that your factors are real?
State Murder_and_manslaughter rape robbery aggravated_assualt burglary larceny_theft motor_vehicle_theft ALABAMA 6.6 36.8 134.2 251.9 960.8 2756.0 332.3 ALASKA 6.0 92.5 68.4 426.5 594.2 2770.7 377.3 ARIZONA 7.9 33.3 136.5 335.5 1050.3 3560.9 1021.3 ARKANSAS 6.4 33.1 81.7 334.8 913.6 2487.3 220.5 CALIFORNIA 6.8 28.2 179.7 364.6 682.8 2061.4 680.1 COLORADO 3.9 41.6 82.1 217.6 711.3 2730.8 498.8 CONNECTICUT 3.0 18.7 119.0 167.5 448.1 1842.1 316.5 DELAWARE 2.9 43.2 169.9 442.0 729.8 2302.3 352.3 DISTRICT_OF_COLUMBIA 44.2 48.6 699.5 815.8 829.1 3213.4 1757.8 FLORIDA 5.4 39.5 185.2 500.1 1002.7 2970.1 479.2 GEORGIA 7.6 25.7 161.8 258.8 909.2 2846.0 499.4 HAWAII 1.7 29.2 92.9 146.5 907.2 3562.9 767.4 IDAHO 1.8 37.2 17.9 185.8 570.2 2147.5 190.9 ILLINOIS 7.1 32.9 188.2 328.6 618.7 2335.6 330.1 INDIANA 5.5 27.8 103.3 216.2 671.1 2351.4 335.2 IOWA 1.6 25.9 38.1 206.8 596.0 2174.9 190.2 KANSAS 4.5 38.3 82.5 270.2 803.6 2904.8 285.6 KENTUCKY 4.6 25.6 77.6 153.9 671.6 1782.4 227.5 LOUISIANA 13.0 41.1 157.2 435.0 998.1 2909.3 442.2 MAINE 1.2 27.1 22.1 58.4 503.9 1841.3 111.5 MARYLAND 9.5 24.7 241.5 428.3 701.4 2439.2 660.8 MASSACHUSETTS 2.2 27.9 124.1 315.1 539.7 1613.3 396.5 MICHIGAN 6.1 54.1 111.7 339.3 677.2 2067.1 533.1 MINNESOTA 2.5 41.2 77.2 141.8 547.4 2297.4 272.0 MISSISSIPPI 9.3 37.4 104.8 174.1 1035.6 2374.2 310.6 MISSOURI 5.0 24.4 108.7 334.5 717.1 2794.9 502.4 MONTANA 3.3 26.8 32.5 302.6 405.6 2484.7 207.7 NEBRASKA 3.2 28.5 66.8 190.5 579.1 2780.2 352.1 NEVADA 8.8 39.0 230.3 336.1 980.6 2378.0 929.8 NEW_HAMPSHIRE 1.4 33.2 37.1 77.1 353.5 1551.5 148.9 NEW_JERSEY 4.7 15.3 154.7 191.0 503.0 1641.3 400.2 NEW_MEXICO 6.0 50.0 104.0 505.2 1025.2 2711.3 387.1 NEW_YORK 4.9 19.7 186.3 254.3 393.4 1619.3 235.6 NORTH_CAROLINA 6.1 25.4 145.5 278.0 1197.6 2760.5 319.9 NORTH_DAKOTA 1.9 23.8 8.0 44.0 306.2 1619.8 170.1 OHIO 4.6 40.1 147.7 140.8 830.1 2451.9 358.5 OKLAHOMA 5.9 42.7 91.8 365.3 992.3 2944.7 369.0 OREGON 1.9 34.2 80.1 179.3 804.2 3444.6 533.5 PENNSYLVANIA 5.3 28.8 145.4 218.6 436.0 1724.8 270.4 PUERTO_RICO 20.1 5.3 199.5 81.6 537.8 949.5 314.8 RHODE_ISLAND 2.3 46.9 77.1 159.3 513.3 2074.0 407.7 SOUTH_CAROLINA 7.2 44.4 136.7 605.1 1050.9 3046.1 380.1 SOUTH_DAKOTA 1.3 46.3 13.6 112.1 375.9 1511.4 114.4 TENNESSEE 6.8 35.7 160.4 484.9 1082.0 2845.3 452.1 TEXAS 6.4 36.2 167.4 342.5 993.7 3157.7 444.0 UTAH 2.5 37.9 53.4 154.8 713.1 3182.2 330.2 VERMONT 2.3 19.5 9.7 78.7 477.8 1618.0 104.3 VIRGINIA 5.6 24.0 90.3 155.9 391.5 2070.0 242.5 WASHINGTON 3.0 46.7 93.3 204.0 950.3 3142.1 662.5 WEST VIRGINIA 3.5 16.4 40.3 197.3 562.2 1602.6 194.7 WISCONSIN 3.3 21.9 80.1 115.7 485.4 2172.1 225.1 WYOMING 2.8 27.1 16.8 215.5 520.9 2641.2 159.2