STAT450/550 : Multivariate Statistical Analysis Midterm I (take-home due TBA) Note: Your report must be brief, concise, and easy to read. Include only discussed parts of the SAS output. Attach your SAS code as an appendix. The code and output must be well labeled. Consider the following US Crime data (source: Mult. Stat. Hardle and Hlavka). (a) Perform a preliminary analysis via covariance or correlation matrix (b) Perform a complete principal component analysis. Your analysis and discussion should include (but not limited) a choice of PCA on covariance or correlation matrix, number of PCs, adequacy of the number, interpretation of the selected PCs, scatter plots of eigenvectors and PCs and discussion on possible outliers and groups, and further discussions. (c) Perform a complete factor analysis. Your analysis and discussion should include (but not limited), a choice of the number of factors and a chi-square test for the adequacy, interpretation of the rotated and un-rotated factor loadings with plots, comparison of your findings with the preliminary analysis, interpretation of the communality and specific variance, scatter plots of factor scores and discussion on possible outliers and groups, and further discussions. /* US CRIME DATA This data consist of measurements of 50 states for 12 variables. It states for 1985 the reported number of crimes in the 50 states classified according to 7 categories (X4-X10) X1: State X2: land area (land) X3: population 1985 (popu) X4: murder (murd) X5: rape X6: robbery (robb) X7: assault (assa) X8: burglary (burg) X9: larceny (larc) X10: auto theft (auto) X11: US State region number (reg) X12: US State division number (div) */ DATA CRIME; INPUT state $ land popu murd rape robb assa burg larc auto reg div; DATALINES; ME 33265 1164 1.500 7 12.600 62 562 1055 146 1 1 NH 9279 998 2 6 12.100 36 566 929 172 1 1 VT 9614 535 1.300 10.300 7.600 55 731 969 124 1 1 MA 8284 5822 3.500 12 99.500 88 1134 1531 878 1 1 RI 1212 968 3.200 3.600 78.300 120 1019 2186 859 1 1 CT 5018 3174 3.500 9.100 70.400 87 1084 1751 484 1 1 NY 49108 17783 7.900 15.500 443.300 209 1414 2025 682 1 2 NJ 7787 7562 5.700 12.900 169.400 90 1041 1689 557 1 2 PA 45308 11853 5.300 11.300 106 90 594 1001 340 1 2 OH 41330 10744 6.600 16 145.900 116 854 1944 493 2 3 IN 36185 5499 4.800 17.900 107.500 95 860 1791 429 2 3 IL 56345 11535 9.600 20.400 251.100 187 765 2028 518 2 3 MI 58527 9088 9.400 27.100 346.600 193 1571 2897 464 2 3 WI 56153 4775 2 6.700 33.100 44 539 1860 218 2 3 MN 84402 4193 2 9.700 89.100 51 802 1902 346 2 4 IA 56275 2884 1.900 6.200 28.600 48 507 1743 175 2 4 MO 69697 5029 10.700 27.400 200.800 167 1187 2074 538 2 4 ND 70703 685 0.500 6.200 6.500 21 286 1295 91 2 4 SD 77116 708 3.800 11.100 17.100 60 471 1396 94 2 4 NE 77355 1606 3 9.300 57.300 115 505 1572 292 2 4 KS 82277 2450 4.800 14.500 75.100 108 882 2302 257 2 4 DE 2044 622 7.700 18.600 105.500 196 1056 2320 559 3 5 MD 10460 4392 9.200 23.900 338.600 253 1051 2417 548 3 5 VA 40767 5706 8.400 15.400 92 143 806 1980 297 3 5 WV 24231 1936 6.200 6.700 27.300 84 389 774 92 3 5 NC 52669 6255 11.800 12.900 53 293 766 1338 169 3 5 SC 31113 3347 14.600 18.100 60.100 193 1025 1509 256 3 5 GA 58910 5976 15.300 10.100 95.800 177 900 1869 309 3 5 FL 58664 11366 12.700 22.200 186.100 277 1562 2861 397 3 5 KY 40409 3726 11.100 13.700 72.800 123 704 1212 346 3 6 TN 42144 4762 8.800 15.500 82 169 807 1025 289 3 6 AL 51705 4021 11.700 18.500 50.300 215 763 1125 223 3 6 MS 47689 2613 11.500 8.900 19 140 351 694 78 3 6 AR 53187 2359 10.100 17.100 45.600 150 885 1211 109 3 7 LA 47751 4481 11.700 23.100 140.800 238 890 1628 385 3 7 OK 69956 3301 5.900 15.600 54.900 127 841 1661 280 3 7 TX 266807 16370 11.600 21 134.100 195 1151 2183 394 3 7 MT 147046 826 3.200 10.500 22.300 75 594 1956 222 4 8 ID 83564 1005 4.600 12.300 20.500 86 674 2214 144 4 8 WY 97809 509 5.700 12.300 22 73 646 2049 165 4 8 CO 104091 3231 6.200 36 129.100 185 1381 2992 588 4 8 NM 121593 1450 9.400 21.700 66.100 196 1142 2408 392 4 8 AZ 114000 3187 9.500 27 120.200 214 1493 3550 501 4 8 UT 84899 1645 3.400 10.900 53.100 70 915 2833 316 4 8 NV 110561 936 8.800 19.600 188.400 182 1661 3044 661 4 8 WA 68138 4409 3.500 18 93.500 106 1441 2853 362 4 9 OR 97073 2687 4.600 18 102.500 132 1273 2825 333 4 9 CA 158706 26365 6.900 35.100 206.900 226 1753 3422 689 4 9 AK 591004 521 12.200 26.100 71.800 168 790 2183 551 4 9 HI 6471 1054 3.600 11.800 63.300 43 1456 3106 581 4 9 ;