We will use the Places Rated Almanac data (Boyer and Savageau) which rates 329 communities according to nine criteria:

  1. Climate and Terrain
  2. Housing
  3. Health Care & Environment
  4. Crime
  5. Transportation
  6. Education
  7. The Arts
  8. Recreation
  9. Economics

We import our data set.

places <- read.table("D:/School/4th Year College/Second Semester/Multivariate Data Analysis/Activity/places.txt", quote="\"", comment.char="")
 View(places)

Here, we exclude column 10, i.e., ‘V10’ since it is the column for the 329 observations representing the 329 communities in our dataset.

library(dplyr)
## 
## Attaching package: 'dplyr'
## The following objects are masked from 'package:stats':
## 
##     filter, lag
## The following objects are masked from 'package:base':
## 
##     intersect, setdiff, setequal, union
placespc <- select(places, c('V1', 'V2', 'V3', 'V4', 'V5', 'V6', 'V7', 'V8', 'V9'))
placespc
##      V1    V2   V3   V4   V5   V6    V7   V8   V9
## 1   521  6200  237  923 4031 2757   996 1405 7633
## 2   575  8138 1656  886 4883 2438  5564 2632 4350
## 3   468  7339  618  970 2531 2560   237  859 5250
## 4   476  7908 1431  610 6883 3399  4655 1617 5864
## 5   659  8393 1853 1483 6558 3026  4496 2612 5727
## 6   520  5819  640  727 2444 2972   334 1018 5254
## 7   559  8288  621  514 2881 3144  2333 1117 5097
## 8   537  6487  965  706 4975 2945  1487 1280 5795
## 9   561  6191  432  399 4246 2778   256 1210 4230
## 10  609  6546  669 1073 4902 2852  1235 1109 6241
## 11  885 16047 2025  983 3954 2843  5632 3156 6220
## 12  195 12175  601 1223 5091 2414  2346 3000 7668
## 13  530  5704  580  878 2865 2469   430  838 3370
## 14  591  5725  820  975 2707 2772   169  613 4262
## 15  546 11014 2508 1067 3433 3346  7559 2288 4579
## 16  560  5530  598 1125 3051 2189   268 1165 4730
## 17  396  7877  833  525 3298 2844  1166 2315 5275
## 18  694  6722 1204  566 5086 2990  1391 1542 5196
## 19  601  6691  605  933 1866 2646  3546 1001 5193
## 20  696  8316 3195 1308 8409 3057  7559 1362 6315
## 21  615 11074  637 1878 3556 2929   621 2711 8107
## 22  534  6292 1798  872 2523 2915  1047  913 5431
## 23  474 10384 1203  821 3943 2208  3857 1800 5097
## 24  435  8831  782 1049 3670 3063  5355 1063 7439
## 25  560  8068  420 1561 3725 2564  1222 1568 6056
## 26  567  9148 3562 1730 7405 3471  9788 2925 5503
## 27  451  7277  780  651 5613 2934  1995 2148 5172
## 28  427  8083  342 1565 3329 2635  4237 1413 6308
## 29  527  6342  900 1031 4652 2483   354 1648 4008
## 30  423  6288  616 1313 2782 2745  1795 1813 6019
## 31  586  7866  861  310 2960 2535  1284 1480 3119
## 32  772  8329  240  825 3776 2778  1302 3200 4247
## 33  566  6761  570 1190 2989 2545    79 1477 3635
## 34  559 14607 2661  857 3511 3653  9304 1918 6016
## 35  452  8315  479  810 6285 3008   778 2046 5913
## 36  584  6458  441  810 2516 2592   679 2106 5801
## 37  550  8257 1007  415 4529 3052  1599 1722 5614
## 38  612  6811 1692 1123 5177 2851  3958 1234 4843
## 39  149  8365  804  413 4303 2686  1211 1630 6019
## 40  558  7056  731  657 1746 2873  2152 1990 4829
## 41  487  8654  815  673 5889 2854  1470 1605 5863
## 42  592  8221  453  880 6575 2391  2385 1672 4633
## 43  623 11609 5301 1215 6801 3479 21042 3066 6363
## 44  459 11914  962 1088 7108 2587  3663 4012 7127
## 45  440  8242  333 1093 3805 2712   154 1349 7437
## 46  423  8394  438  768 2391 2718  1506 1512 6020
## 47  808  9060  310  651 1670 2544   382 1973 5671
## 48  648 13429 2550  943 3197 3029  8368 1913 7197
## 49  516 10041  975  545 4495 2628   514  777 6527
## 50  575  8263  916 1336 3810 2729  2001 1217 6900
## 51  440  5376   91  974 3119 2413   162 3000 4968
## 52  383  8228  640 1016 2530 2973  2002 1413 8040
## 53  571  8064 2465  971 5384 3121  8567 2441 5047
## 54  637  6179  994  707 1910 2519   131  701 5680
## 55  383  9673 1809  494 7146 3323  1741 3357 6726
## 56  575  7332  443  650 4279 2754   989 1157 4847
## 57  401  9839  345  989 4410 2453   303 1435 6303
## 58  434  7774  837  714 5270 2619   904 1501 5009
## 59  525  8627  672 1022 7447 3147  2203 1700 5485
## 60  569  7402 1463 1495 4207 3164  2993 2561 5153
## 61  627  7789  708  721 5470 2894  2605  844 5257
## 62  644  7169  999 1273 6099 3031  4313 1236 5671
## 63  618  9531 1348  756 6041 3489  1422 1704 6055
## 64  576  6189  564  946 3401 2415  2483 1238 4487
## 65  514 10913 5766 1034 7742 3486 24846 2856 5205
## 66  603  8587  243  947 4067 3126  1647 1543 5307
## 67  584  8143 2138  978 5748 2918  9688 2451 5270
## 68  544  6007  446  736 2226 2654   111 2219 4880
## 69  579  9168 3167 1138 7333 2972 12679 3300 4879
## 70  526  8509  721 1086 3389 2754  1749 2375 7699
## 71  541  7702 1951 1065 3893 2377  2882 1331 5147
## 72  526  7519 1421 1524 5859 2908  2489 1484 5279
## 73  517  5817  833  820 2995 2665  1861 1214 4812
## 74  558  8093 1837 1092 4364 2928  6648 2020 5165
## 75  362  6929  458 1335 3626 2840  1992 2037 6690
## 76  591  6054  760  337 3709 3363   373 1036 4741
## 77  544  9318 2825 1529 6213 3269 10438 2310 7710
## 78  569 14420 2350  548 2715 3029  7415 1572 7060
## 79  545  5709  593  379 3161 2943    85  501 4491
## 80  440  8083 1113  834 3907 2901  1017 1920 4997
## 81  544  7635 2253 1151 4775 2772  6935 1122 4532
## 82  561  7203  723 1347 4117 2612   809 3967 6592
## 83  480  7395  732  897 3867 2683   298 1222 4274
## 84  521 10789 2533 1365 8145 3145  8477 2324 7164
## 85  444  8028 1256 1044 5521 2613  1857 1802 5346
## 86  536  8525 4142 1587 4808 3064 10389 2483 3904
## 87  336  5708  593  930 2232 2230   117  714 5453
## 88  419  7993  640  571 3668 2701   340 1587 3949
## 89  193  6040 1159  488 5205 2619  2377 3107 3922
## 90  537  6501  444 1096 6539 2630   904 1610 6113
## 91  257  7078  798  433 3197 2960  1807 1397 5348
## 92  592  7343  528 1323 3705 2479  3800 1101 5080
## 93  521  6573  596  524 4168 2537   353 1023 4214
## 94  467  7078  562  582 3324 3000  1048 1600 4813
## 95  461  6829  626  845 2312 2764   215 1200 8268
## 96  605  7715  529  635 5754 2641  2032 1340 4299
## 97  741  9370  539  874 5293 3118  2631 3400 3045
## 98  550  6743  783  864 3496 2797  1876 1622 5206
## 99  643  9017  900  861 4602 2439   749 2005 4884
## 100 148  8168  920  503 6325 2506  2111 1414 5594
## 101 561  6274  872 1150 4402 3051   844  709 5255
## 102 549  6686  594  545 3581 2334  1915 1695 4631
## 103 507  8252  655  655 2244 2799   270  790 5098
## 104 540  7204  724 1671 4912 2511  2163 1355 3724
## 105 546  5962  607  516 1454 2427  1021  994 4492
## 106 552  6508  818 1334 4963 3109   628  800 4842
## 107 490  9951  731  744 2637 2413  1609 4200 6631
## 108 572 10810 1252 1536 4186 2734  2027 2455 7136
## 109 342  9298  546  787 4583 2729   380 4005 7166
## 110 602  8842  527 1422 2143 3154   368 2058 7973
## 111 482  5784  466  663 3092 2927   145 1736 4849
## 112 536  7554  484  544 2886 2809    87 2092 6342
## 113 509  6733 1060  710 5416 2772  2846 1711 4195
## 114 528  7956 1038 1348 4472 2627  6466 2366 6862
## 115 559  9291  369 1483 4388 2407  3596 2984 5746
## 116 526  5382  622  749 2174 2299   153  300 4220
## 117 402  7388 1731 1658 3527 3094  3335 1237 5739
## 118 727  7767 1437 1213 3423 2809  1756 3000 6026
## 119 483  7641 1364  996 5855 2526  4115 1940 3826
## 120 476  7120   43  568 2241 2674   603 1883 5166
## 121 105  7898 1109  401 5587 2721  1921 1304 5646
## 122 513  7780 1274  952 3454 2705  3255 1909 4848
## 123 410  7143  667  792 3747 2737   401 2176 4697
## 124 490  8218  706  994 1641 2854  1254  739 5443
## 125 367  8401  916  583 3793 2622  2547 1925 5650
## 126 626  7064 1694  967 4453 3090  4188 1651 5204
## 127 655  6336 1260 1185 3950 3236  2569 1410 5012
## 128 568  7763  818  627 3431 2990   825 1491 4477
## 129 542  8227 1135  892 3338 2747  2316 1604 4618
## 130 556  7891 2087  629 6164 3224  3083 1532 5322
## 131 516 11652 2521 1279 7120 3628  3616 1790 6307
## 132 623  6760 1006  765 2703 2726   188  797 4728
## 133 717 17021 1298  891 5911 2502  7168 3703 5187
## 134 427  7094  583  400 1145 1995   725 2700 6662
## 135 424  9760 2467 1499 4626 3271 11073 1825 7464
## 136 636  6632  875  665 4001 2525  2195  840 4383
## 137 600  6283  685  924 2661 2257  1921 1075 6412
## 138 557  7012 2243 1000 5804 2690  6348 1906 5082
## 139 434  9429 2437  830 2770 2842  2255 1506 5165
## 140 518  6794  679 1021 4800 2654   323 1933 3822
## 141 412  7245 1792 1091 4917 3130  3209 1427 5186
## 142 457  6626 1181 1211 5611 3048  2162 2884 6139
## 143 564  6111  740  967 1780 2646   567 1177 6386
## 144 466  7447  700  858 3092 2532  1092 1615 4371
## 145 601  8810 1759 1434 4982 2574  7420 1001 4889
## 146 663  6119 1152  424 2532 2925  1925 2155 4903
## 147 547  6524  731  353 4343 2691   666  903 4181
## 148 479  9327 1058  837 4645 2868  3177 1636 4631
## 149 580  5159  500  628 2335 2871    80  801 5324
## 150 527  7919 1043 1120 5419 2896  2071 2163 4794
## 151 483  7230  609  976 3444 2855    75 1119 5579
## 152 549  8126 1711 1142 5006 3028  1167 1045 6166
## 153 549  7076 1939 1468 5869 2949  5553 2043 4865
## 154 496  8516 1067  911 4473 2918  3844 2224 5176
## 155 365  6463  398  733 2862 3167   920  931 6331
## 156 670  6692  960  622 4273 2761  3309 2514 5537
## 157 512  6616  596  413 1817 2904   285 1000 3429
## 158 352  8310  686  676 6096 3027  1466 1953 5648
## 159 494  7778  655  465 4956 2945  2235 1814 4333
## 160 429  8572  548 1030 5268 2305  1772 1734 9702
## 161 469  6921  314 1093 3549 2336  1456 1855 5872
## 162 514 13282 1237  822 3422 2607  3746 2435 5755
## 163 307  6680  323 1373 3412 2998   309 2513 5594
## 164 559  8631 1111  413 3908 3097  1015 1147 5120
## 165 480  7907 1371  894 5557 2891  4206 1609 4747
## 166 424  6152  465 1050 3322 2827   150  702 5264
## 167 552  6962  588 1457 2989 2736  2804 1609 5341
## 168 556  9906  412 1913 5900 2241  1586 3996 6035
## 169 513  7497  621 1018 2931 2700  3150 1752 4573
## 170 548 10414 1202  909 3575 2479  2111 1879 6527
## 171 479  5850  477 1156 2366 2375  1280 1757 6105
## 172 490  6876  759  764 2941 2694   736 1853 4444
## 173 635  8340 1860 1055 4080 2861  3596 1403 6245
## 174 522  6986  741  855 4084 2629  1352 1428 4313
## 175 398  8256  775  789 5618 2878  4523 1804 4908
## 176 497  7270 1861 1328 4186 2581  2180 1462 5273
## 177 500  6608  509  976 2680 2816   334  834 6898
## 178 579  8309 1105  609 3629 2582  2565 1602 3301
## 179 885 13868 5153 1960 4345 3195 23567 3948 5316
## 180 616  6812 2111  937 5420 3028  4916 1942 5402
## 181 526  9640 1083  819 3820 2479  3057 1129 6651
## 182 604  6990  900 1608 4158 2545  3402 1702 5923
## 183 642  6934  732  643 4909 2803  1079 1439 4926
## 184 447  6235  593  783 3144 2651  1435 1204 5659
## 185 378  9897 2168  779 6084 3047  5123 1944 5448
## 186 404  9860  737  633 4595 2728   475  837 7101
## 187 558  6881  303 1072 2876 2871   554 1133 4386
## 188 238  5345  372  836 2117 2644  1231 1059 5739
## 189 611  9008  256  728 3512 2797  1856 1416 3692
## 190 582  8721  517 1039 2560 2814   437 3800 7089
## 191 514  7015 2043 1488 6247 2804  4486 1994 5160
## 192 634 10267 2314 2459 5202 2879  4837 4300 5840
## 193 559 12135 2589  691 4198 3539  8058 1596 6324
## 194 593 11652  884  646 4636 3128   730 1682 6307
## 195 603  8672   97 1166 5310 2416   438 1502 9980
## 196 460 10176 3053  826 4945 3044  8766 2902 4982
## 197 293  9559 3934  906 5606 3013 11714 2158 5843
## 198 442  6704 1469 1511 3345 2779  1764 2164 4565
## 199 639  8630  347 1154 2000 2616   631  833 5107
## 200 615 11660 2482  819 2690 2787  7563 3544 6154
## 201 455  6190  331  957 3606 2453  1528 1541 5537
## 202 483  6754  832  815 3509 2388  1374 1112 4892
## 203 530  5800  949  783 4325 2965  2498 1428 3980
## 204 580  6391  699 1537 3353 2630   529 2666 3708
## 205 538 10757  853  452 3320 2728  2122 1523 6962
## 206 600  7800 1850  984 5030 2763  4342 1849 5938
## 207 656 11138 3919  566 2119 3234  8640 3705 7371
## 208 643  8087  519 1012 3219 2439   766 1450 4937
## 209 516 10509 1245  903 4900 3128  1360 1217 6470
## 210 583 11460 2068  893 5938 3495  7852 1604 5478
## 211 583 10218  556  633 4505 3244  1164 2281 6672
## 212 498  8515 2586 1604 4579 2995  7978 3500 6453
## 213 638 13358 7850 2498 8625 2984 56745 3579 5338
## 214 601 14220 4106 1461 3514 3362 14224 1818 5690
## 215 554  7686  507  775 5561 2538   966 1873 4463
## 216 632  8568 1932  997 3215 3014  7087 2964 5866
## 217 648 20151 2530  625 3536 3029  7273 2268 6432
## 218 910 13135 2362 1533 6430 2646  6162 2394 5457
## 219 333  6750  489 1327 3798 2864   266 3095 7060
## 220 603  6689  384 1698 1944 2721   259  900 7565
## 221 554  7186 1623 1297 4459 2908  4843 1742 8119
## 222 726  8263  338  752 4083 2625   708 1451 4912
## 223 440  7128 2559 1008 5806 3069  3787 1977 5853
## 224 509 10173 1574  804 3299 2754  6987 1866 5822
## 225 457  8196  765 1671 5887 2976  2681 2881 7413
## 226 524  6760  812  568 2273 2491   804  852 6062
## 227 890 14000 1106  791 2238 2155  2769 2135 5514
## 228 536  6373  201 1344 2778 2500   755 2089 6083
## 229 617  6657  665  488 4399 2503    91 1148 5187
## 230 584  6248  593  591 1750 1701   155 1956 4491
## 231 586  9462 1117  744 4738 3058   480 1513 5154
## 232 536  6479  563 1472 2918 2914  1954 2160 6029
## 233 491  8388 1184  921 2967 2452  2294 1688 4073
## 234 630  8310 5158 1059 5903 3781 17270 1979 5638
## 235 536  8921 1584 1268 4729 2942  4573 2472 6415
## 236 463  5674  617 1169 1671 2554   373  793 4247
## 237 586  8099 3413  687 5616 3544 11069 2145 5261
## 238 482  7807  694  638 3759 3264   228 1420 5483
## 239 483  8100  834  823 5185 2973  2351 3366 6186
## 240 768  9912 1590 1504 5947 3343  5160 2532 4535
## 241 469  9966  596  475 2321 3026   165 1390 8367
## 242 488  9981  355  633 4166 2898   785 1670 6746
## 243 586  9274 2467  998 5474 3558  6152 2263 5154
## 244 500  9321  198  485 4546 2618  1985 3300 3459
## 245 497  6637  468 1181 3501 2653  1307 1619 4646
## 246 496  8943  931 1055 3558 2732  1171 2016 4415
## 247 647  8230 3476  981 6544 3455  5730 1606 6405
## 248 614  7614 1154  522 3120 3028  1108 1549 5587
## 249 664  8584  274  892 5727 2471   845 2424 4459
## 250 535 12449  615 1116 6767 2529  2210 2386 5677
## 251 664  8461  300  779 4714 1728   529 1204 5326
## 252 585  8343 2448 1076 6680 2940  5697 1943 5870
## 253 615  9754 2201 1475 3141 2596  5327 1918 4923
## 254 652  7476 1036  784 3872 2723  1263 2036 5287
## 255 308  9193 2966  437 4399 2134   769 1503 6099
## 256 536  8609 1969  894 5165 3582  6956 2659 6304
## 257 466  7584  969 1156 2987 2680  1026  933 4592
## 258 576  9855 1027 1363 5097 2793  4483 2306 5309
## 259 515  7368 1022 1068 3186 2772  1708 2059 3709
## 260 195  7235  603  343 4565 2502  1871 1572 5488
## 261 475  5589  223  969 2689 2927   879 1265 5991
## 262 537  7605 2850 1306 7119 3530  8896 2243 5800
## 263 716  8378  749 1014 4732 3278   691 1873 3835
## 264 644 11622 1232  490 3459 2729  3276 2234 6309
## 265 843 13838  352 1107 4160 2439  1004 3179 5656
## 266 541  9466 1631  969 6228 2340  5528 3900 4942
## 267 488  6321  236 1032 2938 2707  1301 1136 7720
## 268 398  6898 1337 1197 5387 2938  4295 1509 6873
## 269 903 14465 2416 1099 5489 2794  8818 3347 5489
## 270 910 17158 3726 1619 8299 3371 14226 4600 6063
## 271 850 16048 2117 1065 5224 2709  6446 1964 7270
## 272 855 15547  532 1026 5662 2719  2684 3300 5821
## 273 843 14303 1035  964 5010 2611  3748 1703 5335
## 274 732 12931 1052  912 3313 2722  3457 2255 5703
## 275 391  9560  801  939 3742 2626   817 2535 7715
## 276 542  6896 1084 1614 5958 2456  2262 2237 5591
## 277 575  6697 1219  372 3683 3230  1832 1386 4907
## 278 808 10183 2715 1170 6634 2710  9577 4800 5901
## 279 570  6697  700  384 2017 3022    52 1100 4055
## 280 442  8121  593  450 3458 2557   268 1316 4765
## 281 524  5722  394 1035 1922 2652    68  937 6213
## 282 508  6534 1445 1197 4401 2858  2826 1389 6585
## 283 385  6528  846  759 4316 2673  1393 1359 4648
## 284 276  7983 1041  556 6271 2651   465 1324 5204
## 285 545  5938  830 1038 5634 2874  2672 1819 5056
## 286 574  6927  497  869 5534 2774  2988 1517 4722
## 287 524  7882 1877 1225 6172 3078  1983 1536 5384
## 288 453  8039  710 1212 6159 3525  3466 1514 5289
## 289 544  6343  577  892 3828 2709  1634 1737 5932
## 290 648 23640 2610  835 3110 3029  7865 1729 6158
## 291 575  8405  612  540 2740 3169  1271 1200 4677
## 292 542  6578  505  418 1532 2672   147 1460 3744
## 293 625  8474  342 1395 4427 2155  1579 1630 5672
## 294 548  7670 1040  689 6951 3144  5080 2851 4474
## 295 808  7770  539 1162 4730 2546  4297 4000 4887
## 296 404  8029  370 1161 5530 2790  2181 1936 6021
## 297 440  7442 1189 1493 5588 3044  5040 2943 7256
## 298 557  5527  453  630 3550 3012  1226 1401 4353
## 299 467  5717  343  822 2537 2899    63  669 4772
## 300 518  7767 1738  998 5323 2852  4389 1952 4534
## 301 501  7110 1148  999 5348 2795  1632 1141 5464
## 302 636 10616 1372 1181 4786 3311  5029 1646 5772
## 303 589  8548 1259 1400 4397 2685  4889 3131 6147
## 304 530  7498 1581 1080 3758 2628  4248 2024 7115
## 305 470  6464  674 1014 4723 2390  1432 1090 4900
## 306 500  7298  672  955 3460 3283   404  631 7327
## 307 548  6744  391  400 4592 2970   858 1750 5226
## 308 821 10503 1079  964 4153 2498  2962 1559 5819
## 309 768  9015  517  752 3817 2332  1557 1464 4571
## 310 336  7143  260 1092 2407 2696    87 1410 7599
## 311 615  7295  807 1135 4133 2747  2097 1474 5023
## 312 543  7778  210 1132 3094 2128   511 2800 5563
## 313 412  6106  538 1166 3018 2867  1141 1248 6259
## 314 631 13724 4361 1317 8236 3635 21701 1578 6072
## 315 569 10024 1218  789 2434 2995   318  946 5656
## 316 347  7881  925  700 3351 2889  3000 1900 4407
## 317 308  7642  818  442 3496 2749   761 1654 4300
## 318 509 10512  375 1783 5201 3224  2888 3772 7992
## 319 542  6576  791  308 2450 3002   422 1271 4740
## 320 494  7061  806 1164 3933 2981  2987 1508 6036
## 321 456  6404  549 1179 2793 2747   599 1126 6805
## 322 558  7284  860  464 3097 2906   196  726 3288
## 323 597  7927 1445 1115 4532 3112  4545 1923 6174
## 324 564  6858 1099 1423 2904 2876  1077 2668 5390
## 325 562  8715 1805  680 3643 3299  1784  910 5040
## 326 535  6440  317 1106 3731 2491   996 2140 4986
## 327 540  8371  713  440 2267 2903  1022  842 4946
## 328 570  7021 1097  938 3374 2920  2797 1327 3894
## 329 608  7875  212 1179 2768 2387   122  918 4694

This is followed by simple statistics that report the means, standard deviations, median, min, max, mad, skew, kurtosis, and se for each variable.

library(psych)
describe(placespc)
##    vars   n    mean      sd median trimmed     mad  min   max range skew
## V1    1 329  538.73  120.81    542  537.77   87.47  105   910   805 0.04
## V2    2 329 8346.56 2385.26   7877 7966.74 1664.96 5159 23640 18481 2.23
## V3    3 329 1185.74 1003.00    833 1013.80  510.01   43  7850  7807 2.44
## V4    4 329  961.05  357.15    947  942.02  324.69  308  2498  2190 0.71
## V5    5 329 4210.08 1451.18   4080 4142.84 1498.91 1145  8625  7480 0.46
## V6    6 329 2814.89  320.79   2794 2805.92  293.55 1701  3781  2080 0.13
## V7    7 329 3150.88 4642.28   1871 2330.47 1936.28   52 56745 56693 5.92
## V8    8 329 1845.96  807.89   1670 1757.99  664.20  300  4800  4500 1.06
## V9    9 329 5525.36 1084.47   5384 5466.86  966.66 3045  9980  6935 0.64
##    kurtosis     se
## V1     2.10   6.66
## V2     7.62 131.50
## V3     8.64  55.30
## V4     1.14  19.69
## V5    -0.15  80.01
## V6     0.62  17.69
## V7    55.83 255.94
## V8     1.01  44.54
## V9     0.95  59.79
require(reshape2)
## Loading required package: reshape2
melt.placespc <- melt(placespc)
## No id variables; using all as measure variables
head(melt.placespc)
##   variable value
## 1       V1   521
## 2       V1   575
## 3       V1   468
## 4       V1   476
## 5       V1   659
## 6       V1   520
library(ggplot2)
## 
## Attaching package: 'ggplot2'
## The following objects are masked from 'package:psych':
## 
##     %+%, alpha
ggplot(data = melt.placespc, aes(x = value)) + 
stat_density() + 
facet_wrap(~variable, scales = "free")

Note that the data for many of the variables are strongly skewed to the right. Hence, the log transformation was used to normalize the data.

log_places <- log10(placespc)
log_places
##           V1       V2       V3       V4       V5       V6       V7       V8
## 1   2.716838 3.792392 2.374748 2.965202 3.605413 3.440437 2.998259 3.147676
## 2   2.759668 3.910518 3.219060 2.947434 3.688687 3.387034 3.745387 3.420286
## 3   2.670246 3.865637 2.790988 2.986772 3.403292 3.408240 2.374748 2.933993
## 4   2.677607 3.898067 3.155640 2.785330 3.837778 3.531351 3.667920 3.208710
## 5   2.818885 3.923917 3.267875 3.171141 3.816771 3.480869 3.652826 3.416973
## 6   2.716003 3.764848 2.806180 2.861534 3.388101 3.473049 2.523746 3.007748
## 7   2.747412 3.918450 2.793092 2.710963 3.459543 3.497483 3.367915 3.048053
## 8   2.729974 3.812044 2.984527 2.848805 3.696793 3.469085 3.172311 3.107210
## 9   2.748963 3.791761 2.635484 2.600973 3.627980 3.443732 2.408240 3.082785
## 10  2.784617 3.815976 2.825426 3.030600 3.690373 3.455150 3.091667 3.044932
## 11  2.946943 4.205394 3.306425 2.992554 3.597037 3.453777 3.750663 3.499137
## 12  2.290035 4.085469 2.778874 3.087426 3.706803 3.382737 3.370328 3.477121
## 13  2.724276 3.756180 2.763428 2.943495 3.457125 3.392521 2.633468 2.923244
## 14  2.771587 3.757775 2.913814 2.989005 3.432488 3.442793 2.227887 2.787460
## 15  2.737193 4.041945 3.399328 3.028164 3.535674 3.524526 3.878464 3.359456
## 16  2.748188 3.742725 2.776701 3.051153 3.484442 3.340246 2.428135 3.066326
## 17  2.597695 3.896361 2.920645 2.720159 3.518251 3.453930 3.066699 3.364551
## 18  2.841359 3.827499 3.080626 2.752816 3.706376 3.475671 3.143327 3.188084
## 19  2.778874 3.825491 2.781755 2.969882 3.270912 3.422590 3.549739 3.000434
## 20  2.842609 3.919914 3.504471 3.116608 3.924744 3.485295 3.878464 3.134177
## 21  2.788875 4.044305 2.804139 3.273696 3.550962 3.466719 2.793092 3.433130
## 22  2.727541 3.798789 3.254790 2.940516 3.401917 3.464639 3.019947 2.960471
## 23  2.675778 4.016365 3.080266 2.914343 3.595827 3.343999 3.586250 3.255273
## 24  2.638489 3.946010 2.893207 3.020775 3.564666 3.486147 3.728759 3.026533
## 25  2.748188 3.906766 2.623249 3.193403 3.571126 3.408918 3.087071 3.195346
## 26  2.753583 3.961326 3.551694 3.238046 3.869525 3.540455 3.990694 3.466126
## 27  2.654177 3.861952 2.892095 2.813581 3.749195 3.467460 3.299943 3.332034
## 28  2.630428 3.907573 2.534026 3.194514 3.522314 3.420781 3.627058 3.150142
## 29  2.721811 3.802226 2.954243 3.013259 3.667640 3.394977 2.549003 3.216957
## 30  2.626340 3.798513 2.789581 3.118265 3.444357 3.438542 3.254064 3.258398
## 31  2.767898 3.895754 2.935003 2.491362 3.471292 3.403978 3.108565 3.170262
## 32  2.887617 3.920593 2.380211 2.916454 3.577032 3.443732 3.114611 3.505150
## 33  2.752816 3.830011 2.755875 3.075547 3.475526 3.405688 1.897627 3.169380
## 34  2.747412 4.164561 3.425045 2.932981 3.545431 3.562650 3.968670 3.282849
## 35  2.655138 3.919862 2.680336 2.908485 3.798305 3.478278 2.890980 3.310906
## 36  2.766413 3.810098 2.644439 2.908485 3.400711 3.413635 2.831870 3.323458
## 37  2.740363 3.916822 3.003029 2.618048 3.656002 3.484585 3.203848 3.236033
## 38  2.786751 3.833211 3.228400 3.050380 3.714078 3.454997 3.597476 3.091315
## 39  2.173186 3.922466 2.905256 2.615950 3.633771 3.429106 3.083144 3.212188
## 40  2.746634 3.848559 2.863917 2.817565 3.242044 3.458336 3.332842 3.298853
## 41  2.687529 3.937217 2.911158 2.828015 3.770042 3.455454 3.167317 3.205475
## 42  2.772322 3.914925 2.656098 2.944483 3.817896 3.378580 3.377488 3.223236
## 43  2.794488 4.064795 3.724358 3.084576 3.832573 3.541454 4.323087 3.486572
## 44  2.661813 4.076058 2.983175 3.036629 3.851747 3.412796 3.563837 3.603361
## 45  2.643453 3.916033 2.522444 3.038620 3.580355 3.433290 2.187521 3.130012
## 46  2.626340 3.923969 2.641474 2.885361 3.378580 3.434249 3.177825 3.179552
## 47  2.907411 3.957128 2.491362 2.813581 3.222716 3.405517 2.582063 3.295127
## 48  2.811575 4.128044 3.406540 2.974512 3.504743 3.481299 3.922622 3.281715
## 49  2.712650 4.001777 2.989005 2.736397 3.652730 3.419625 2.710963 2.890421
## 50  2.759668 3.917138 2.961895 3.125806 3.580925 3.436004 3.301247 3.085291
## 51  2.643453 3.730459 1.959041 2.988559 3.494015 3.382557 2.209515 3.477121
## 52  2.583199 3.915294 2.806180 3.006894 3.403121 3.473195 3.301464 3.150142
## 53  2.756636 3.906551 3.391817 2.987219 3.731105 3.494294 3.932829 3.387568
## 54  2.804139 3.790918 2.997386 2.849419 3.281033 3.401228 2.117271 2.845718
## 55  2.583199 3.985561 3.257439 2.693727 3.854063 3.521530 3.240799 3.525951
## 56  2.759668 3.865222 2.646404 2.812913 3.631342 3.439964 2.995196 3.063333
## 57  2.603144 3.992951 2.537819 2.995196 3.644439 3.389698 2.481443 3.156852
## 58  2.637490 3.890645 2.922725 2.853698 3.721811 3.418135 2.956168 3.176381
## 59  2.720159 3.935860 2.827369 3.009451 3.871981 3.497897 3.343014 3.230449
## 60  2.755112 3.869349 3.165244 3.174641 3.623973 3.500236 3.476107 3.408410
## 61  2.797268 3.891482 2.850033 2.857935 3.737987 3.461499 3.415808 2.926342
## 62  2.808886 3.855459 2.999565 3.104828 3.785259 3.481586 3.634779 3.092018
## 63  2.790988 3.979138 3.129690 2.878522 3.781109 3.542701 3.152900 3.231470
## 64  2.760422 3.791620 2.751279 2.975891 3.531607 3.382917 3.394977 3.092721
## 65  2.710963 4.037944 3.760875 3.014521 3.888853 3.542327 4.395256 3.455758
## 66  2.780317 3.933841 2.385606 2.976350 3.609274 3.494989 3.216694 3.188366
## 67  2.766413 3.910784 3.330008 2.990339 3.759517 3.465085 3.986234 3.389343
## 68  2.735599 3.778658 2.649335 2.866878 3.347525 3.423901 2.045323 3.346157
## 69  2.762679 3.962275 3.500648 3.056142 3.865282 3.473049 4.103085 3.518514
## 70  2.720986 3.929879 2.857935 3.035830 3.530072 3.439964 3.242790 3.375664
## 71  2.733197 3.886604 3.290257 3.027350 3.590284 3.376029 3.459694 3.124178
## 72  2.720986 3.876160 3.152594 3.182985 3.767823 3.463594 3.396025 3.171434
## 73  2.713491 3.764699 2.920645 2.913814 3.476397 3.425697 3.269746 3.084219
## 74  2.746634 3.908110 3.264109 3.038223 3.639885 3.466571 3.822691 3.305351
## 75  2.558709 3.840671 2.660865 3.125481 3.559428 3.453318 3.299289 3.308991
## 76  2.771587 3.782042 2.880814 2.527630 3.569257 3.526727 2.571709 3.015360
## 77  2.735599 3.969323 3.451018 3.184407 3.793301 3.514415 4.018617 3.363612
## 78  2.755112 4.158965 3.371068 2.738781 3.433770 3.481299 3.870111 3.196453
## 79  2.736397 3.756560 2.773055 2.578639 3.499824 3.468790 1.929419 2.699838
## 80  2.643453 3.907573 3.046495 2.921166 3.591843 3.462548 3.007321 3.283301
## 81  2.735599 3.882809 3.352761 3.061075 3.678973 3.442793 3.841046 3.049993
## 82  2.748963 3.857513 2.859138 3.129368 3.614581 3.416973 2.907949 3.598462
## 83  2.681241 3.868938 2.864511 2.952792 3.587374 3.428621 2.474216 3.087071
## 84  2.716838 4.032981 3.403635 3.135133 3.910891 3.497621 3.928242 3.366236
## 85  2.647383 3.904607 3.098990 3.018700 3.742018 3.417139 3.268812 3.255755
## 86  2.729165 3.930694 3.617210 3.200577 3.681964 3.486289 4.016574 3.394977
## 87  2.526339 3.756484 2.773055 2.968483 3.348694 3.348305 2.068186 2.853698
## 88  2.622214 3.902710 2.806180 2.756636 3.564429 3.431525 2.531479 3.200577
## 89  2.285557 3.781037 3.064083 2.688420 3.716421 3.418135 3.376029 3.492341
## 90  2.729974 3.812980 2.647383 3.039811 3.815511 3.419956 2.956168 3.206826
## 91  2.409933 3.849911 2.902003 2.636488 3.504743 3.471292 3.256958 3.145196
## 92  2.772322 3.865874 2.722634 3.121560 3.568788 3.394277 3.579784 3.041787
## 93  2.716838 3.817764 2.775246 2.719331 3.619928 3.404320 2.547775 3.009876
## 94  2.669317 3.849911 2.749736 2.764923 3.521661 3.477121 3.020361 3.204120
## 95  2.663701 3.834357 2.796574 2.926857 3.363988 3.441538 2.332438 3.079181
## 96  2.781755 3.887336 2.723456 2.802774 3.759970 3.421768 3.307924 3.127105
## 97  2.869818 3.971740 2.731589 2.941511 3.723702 3.493876 3.420121 3.531479
## 98  2.740363 3.828853 2.893762 2.936514 3.543571 3.446692 3.273233 3.210051
## 99  2.808211 3.955062 2.954243 2.935003 3.662947 3.387212 2.874482 3.302114
## 100 2.170262 3.912116 2.963788 2.701568 3.801061 3.398981 3.324488 3.150449
## 101 2.748963 3.797545 2.940516 3.060698 3.643650 3.484442 2.926342 2.850646
## 102 2.739572 3.825166 2.773786 2.736397 3.554004 3.368101 3.282169 3.229170
## 103 2.705008 3.916559 2.816241 2.816241 3.351023 3.447003 2.431364 2.897627
## 104 2.732394 3.857574 2.859739 3.222976 3.691258 3.399847 3.335057 3.131939
## 105 2.737193 3.775392 2.783189 2.712650 3.162564 3.385070 3.009026 2.997386
## 106 2.741939 3.813448 2.912753 3.125156 3.695744 3.492621 2.797960 2.903090
## 107 2.690196 3.997867 2.863917 2.871573 3.421110 3.382557 3.206556 3.623249
## 108 2.757396 4.033826 3.097604 3.186391 3.621799 3.436799 3.306854 3.390051
## 109 2.534026 3.968390 2.737193 2.895975 3.661150 3.436004 2.579784 3.602603
## 110 2.779596 3.946551 2.721811 3.152900 3.331022 3.498862 2.565848 3.313445
## 111 2.683047 3.762228 2.668386 2.821514 3.490239 3.466423 2.161368 3.239550
## 112 2.729165 3.878177 2.684845 2.735599 3.460296 3.448552 1.939519 3.320562
## 113 2.706718 3.828209 3.025306 2.851258 3.733679 3.442793 3.454235 3.233250
## 114 2.722634 3.900695 3.016197 3.129690 3.650502 3.419460 3.810636 3.374015
## 115 2.747412 3.968062 2.567026 3.171141 3.642267 3.381476 3.555820 3.474799
## 116 2.720986 3.730944 2.793790 2.874482 3.337260 3.361539 2.184691 2.477121
## 117 2.604226 3.868527 3.238297 3.219585 3.547405 3.490520 3.523096 3.092370
## 118 2.861534 3.890253 3.157457 3.083861 3.534407 3.448552 3.244525 3.477121
## 119 2.683947 3.883150 3.134814 2.998259 3.767527 3.402433 3.614370 3.287802
## 120 2.677607 3.852480 1.633468 2.754348 3.350442 3.427161 2.780317 3.274850
## 121 2.021189 3.897517 3.044932 2.603144 3.747179 3.434729 3.283527 3.115278
## 122 2.710117 3.890980 3.105169 2.978637 3.538322 3.432167 3.512551 3.280806
## 123 2.612784 3.853881 2.824126 2.898725 3.573684 3.437275 2.603144 3.337659
## 124 2.690196 3.914766 2.848805 2.997386 3.215109 3.455454 3.098298 2.868644
## 125 2.564666 3.924331 2.961895 2.765669 3.578983 3.418633 3.406029 3.284431
## 126 2.796574 3.849051 3.228913 2.985426 3.648653 3.489958 3.622007 3.217747
## 127 2.816241 3.801815 3.100371 3.073718 3.596597 3.510009 3.409764 3.149219
## 128 2.754348 3.890030 2.912753 2.797268 3.535421 3.475671 2.916454 3.173478
## 129 2.733999 3.915241 3.054996 2.950365 3.523486 3.438859 3.364739 3.205204
## 130 2.745075 3.897132 3.319522 2.798651 3.789863 3.508395 3.488974 3.185259
## 131 2.712650 4.066400 3.401573 3.106871 3.852480 3.559667 3.558228 3.252853
## 132 2.794488 3.829947 3.002598 2.883661 3.431846 3.435526 2.274158 2.901458
## 133 2.855519 4.230985 3.113275 2.949878 3.771661 3.398287 3.855398 3.568554
## 134 2.630428 3.850891 2.765669 2.602060 3.058805 3.299943 2.860338 3.431364
## 135 2.627366 3.989450 3.392169 3.175802 3.665206 3.514681 4.044265 3.261263
## 136 2.803457 3.821645 2.942008 2.822822 3.602169 3.402261 3.341435 2.924279
## 137 2.778151 3.798167 2.835691 2.965672 3.425045 3.353532 3.283527 3.031408
## 138 2.745855 3.845842 3.350829 3.000000 3.763727 3.429752 3.802637 3.280123
## 139 2.637490 3.974466 3.386856 2.919078 3.442480 3.453624 3.353147 3.177825
## 140 2.714330 3.832126 2.831870 3.009026 3.681241 3.423901 2.509203 3.286232
## 141 2.614897 3.860038 3.253338 3.037825 3.691700 3.495544 3.506370 3.154424
## 142 2.659916 3.821251 3.072250 3.083144 3.749040 3.484015 3.334856 3.459995
## 143 2.751279 3.786112 2.869232 2.985426 3.250420 3.422590 2.753583 3.070776
## 144 2.668386 3.871981 2.845098 2.933487 3.490239 3.403464 3.038223 3.208173
## 145 2.778874 3.944976 3.245266 3.156549 3.697404 3.410609 3.870404 3.000434
## 146 2.821514 3.786680 3.061452 2.627366 3.403464 3.466126 3.284431 3.333447
## 147 2.737987 3.814514 2.863917 2.547775 3.637790 3.429914 2.823474 2.955688
## 148 2.680336 3.969742 3.024486 2.922725 3.666986 3.457579 3.502017 3.213783
## 149 2.763428 3.712566 2.698970 2.797960 3.368287 3.458033 1.903090 2.903633
## 150 2.721811 3.898670 3.018284 3.049218 3.733919 3.461799 3.316180 3.335057
## 151 2.683947 3.859138 2.784617 2.989450 3.537063 3.455606 1.875061 3.048830
## 152 2.739572 3.909877 3.233250 3.057666 3.699491 3.481156 3.067071 3.019116
## 153 2.739572 3.849788 3.287578 3.166726 3.768564 3.469675 3.744528 3.310268
## 154 2.695482 3.930236 3.028164 2.959518 3.650599 3.465085 3.584783 3.347135
## 155 2.562293 3.810434 2.599883 2.865104 3.456670 3.500648 2.963788 2.968950
## 156 2.826075 3.825556 2.982271 2.793790 3.630733 3.441066 3.519697 3.400365
## 157 2.709270 3.820595 2.775246 2.615950 3.259355 3.462997 2.454845 3.000000
## 158 2.546543 3.919601 2.836324 2.829947 3.785045 3.481012 3.166134 3.290702
## 159 2.693727 3.890868 2.816241 2.667453 3.695131 3.469085 3.349278 3.258637
## 160 2.632457 3.933082 2.738781 3.012837 3.721646 3.362671 3.248464 3.239049
## 161 2.671173 3.840169 2.496930 3.038620 3.550106 3.368473 3.163161 3.268344
## 162 2.710963 4.123263 3.092370 2.914872 3.534280 3.416141 3.573568 3.386499
## 163 2.487138 3.824776 2.509203 3.137671 3.533009 3.476832 2.489958 3.400192
## 164 2.747412 3.936061 3.045714 2.615950 3.591955 3.490941 3.006466 3.059563
## 165 2.681241 3.898012 3.137037 2.951338 3.744840 3.461048 3.623869 3.206556
## 166 2.627366 3.789016 2.667453 3.021189 3.521400 3.451326 2.176091 2.846337
## 167 2.741939 3.842734 2.769377 3.163460 3.475526 3.437116 3.447778 3.206556
## 168 2.745075 3.995898 2.614897 3.281715 3.770852 3.350442 3.200303 3.601625
## 169 2.710117 3.874888 2.793092 3.007748 3.467016 3.431364 3.498311 3.243534
## 170 2.738781 4.017618 3.079904 2.958564 3.553276 3.394277 3.324488 3.273927
## 171 2.680336 3.767156 2.678518 3.062958 3.374015 3.375664 3.107210 3.244772
## 172 2.690196 3.837336 2.880242 2.883093 3.468495 3.430398 2.866878 3.267875
## 173 2.802774 3.921166 3.269513 3.023252 3.610660 3.456518 3.555820 3.147058
## 174 2.717671 3.844229 2.869818 2.931966 3.611086 3.419791 3.130977 3.154728
## 175 2.599883 3.916770 2.889302 2.897077 3.749582 3.459091 3.655427 3.256237
## 176 2.696356 3.861534 3.269746 3.123198 3.621799 3.411788 3.338456 3.164947
## 177 2.698970 3.820070 2.706718 2.989450 3.428135 3.449633 2.523746 2.921166
## 178 2.762679 3.919549 3.043362 2.784617 3.559787 3.411956 3.409087 3.204663
## 179 2.946943 4.142014 3.712060 3.292256 3.637990 3.504471 4.372304 3.596377
## 180 2.789581 3.833275 3.324488 2.971740 3.733999 3.481156 3.691612 3.288249
## 181 2.720986 3.984077 3.034628 2.913284 3.582063 3.394277 3.485295 3.052694
## 182 2.781037 3.844477 2.954243 3.206286 3.618884 3.405688 3.531734 3.230960
## 183 2.807535 3.840984 2.864511 2.808211 3.690993 3.447623 3.033021 3.158061
## 184 2.650308 3.794836 2.773055 2.893762 3.497483 3.423410 3.156852 3.080626
## 185 2.577492 3.995504 3.336059 2.891537 3.784189 3.483872 3.709524 3.288696
## 186 2.606381 3.993877 2.867467 2.801404 3.662286 3.435844 2.676694 2.922725
## 187 2.746634 3.837652 2.481443 3.030195 3.458789 3.458033 2.743510 3.054230
## 188 2.376577 3.727948 2.570543 2.922206 3.325721 3.422261 3.090258 3.024896
## 189 2.786041 3.954628 2.408240 2.862131 3.545555 3.446692 3.268578 3.151063
## 190 2.764923 3.940566 2.713491 3.016616 3.408240 3.449324 2.640481 3.579784
## 191 2.710963 3.846028 3.310268 3.172603 3.795672 3.447778 3.651859 3.299725
## 192 2.802089 4.011444 3.364363 3.390759 3.716170 3.459242 3.684576 3.633468
## 193 2.747412 4.084040 3.413132 2.839478 3.623042 3.548881 3.906227 3.203033
## 194 2.773055 4.066400 2.946452 2.810233 3.666143 3.495267 2.863323 3.225826
## 195 2.780317 3.938119 1.986772 3.066699 3.725095 3.383097 2.641474 3.176670
## 196 2.662758 4.007577 3.484727 2.916980 3.694166 3.483445 3.942801 3.462697
## 197 2.466868 3.980412 3.594834 2.957128 3.748653 3.478999 4.068705 3.334051
## 198 2.645422 3.826334 3.167022 3.179264 3.524396 3.443889 3.246499 3.335257
## 199 2.805501 3.936011 2.540329 3.062206 3.301030 3.417638 2.800029 2.920645
## 200 2.788875 4.066699 3.394802 2.913284 3.429752 3.445137 3.878694 3.549494
## 201 2.658011 3.791691 2.519828 2.980912 3.557026 3.389698 3.184123 3.187803
## 202 2.683947 3.829561 2.920123 2.911158 3.545183 3.378034 3.137987 3.046105
## 203 2.724276 3.763428 2.977266 2.893762 3.635986 3.472025 3.397592 3.154728
## 204 2.763428 3.805569 2.844477 3.186674 3.525434 3.419956 2.723456 3.425860
## 205 2.730782 4.031691 2.930949 2.655138 3.521138 3.435844 3.326745 3.182700
## 206 2.778151 3.892095 3.267172 2.992995 3.701568 3.441381 3.637690 3.266937
## 207 2.816904 4.046807 3.593175 2.752816 3.326131 3.509740 3.936514 3.568788
## 208 2.808211 3.907787 2.715167 3.005181 3.507721 3.387212 2.884229 3.161368
## 209 2.712650 4.021561 3.095169 2.955688 3.690196 3.495267 3.133539 3.085291
## 210 2.765669 4.059185 3.315551 2.950851 3.773640 3.543447 3.894980 3.205204
## 211 2.765669 4.009366 2.745075 2.801404 3.653695 3.511081 3.065953 3.358125
## 212 2.697229 3.930185 3.412629 3.205204 3.660771 3.476397 3.901894 3.544068
## 213 2.804821 4.125741 3.894870 3.397592 3.935759 3.474799 4.753928 3.553762
## 214 2.778874 4.152900 3.613419 3.164650 3.545802 3.526598 4.153022 3.259594
## 215 2.743510 3.885700 2.705008 2.889302 3.745153 3.404492 2.984977 3.272538
## 216 2.800717 3.932879 3.286007 2.998695 3.507181 3.479143 3.850462 3.471878
## 217 2.811575 4.304297 3.403121 2.795880 3.548512 3.481299 3.861714 3.355643
## 218 2.959041 4.118430 3.373280 3.185542 3.808211 3.422590 3.789722 3.379124
## 219 2.522444 3.829304 2.689309 3.122871 3.579555 3.456973 2.424882 3.490661
## 220 2.780317 3.825361 2.584331 3.229938 3.288696 3.434729 2.413300 2.954243
## 221 2.743510 3.856487 3.210319 3.112940 3.649237 3.463594 3.685114 3.241048
## 222 2.860937 3.917138 2.528917 2.876218 3.610979 3.419129 2.850033 3.161667
## 223 2.643453 3.852968 3.408070 3.003461 3.763877 3.486997 3.578295 3.296007
## 224 2.706718 4.007449 3.197005 2.905256 3.518382 3.439964 3.844291 3.270912
## 225 2.659916 3.913602 2.883661 3.222976 3.769894 3.473633 3.428297 3.459543
## 226 2.719331 3.829947 2.909556 2.754348 3.356599 3.396374 2.905256 2.930440
## 227 2.949390 4.146128 3.043755 2.898176 3.349860 3.333447 3.442323 3.329398
## 228 2.729165 3.804344 2.303196 3.128399 3.443732 3.397940 2.877947 3.319938
## 229 2.790285 3.823279 2.822822 2.688420 3.643354 3.398461 1.959041 3.059942
## 230 2.766413 3.795741 2.773055 2.771587 3.243038 3.230704 2.190332 3.291369
## 231 2.767898 3.975983 3.048053 2.871573 3.675595 3.485437 2.681241 3.179839
## 232 2.729165 3.811508 2.750508 3.167908 3.465085 3.464490 3.290925 3.334454
## 233 2.691081 3.923658 3.073352 2.964260 3.472318 3.389520 3.360593 3.227372
## 234 2.799341 3.919601 3.712481 3.024896 3.771073 3.577607 4.237292 3.296446
## 235 2.729165 3.950414 3.199755 3.103119 3.674769 3.468643 3.660201 3.393048
## 236 2.665581 3.753889 2.790285 3.067815 3.222976 3.407221 2.571709 2.899273
## 237 2.767898 3.908431 3.533136 2.836957 3.749427 3.549494 4.044108 3.331427
## 238 2.683047 3.892484 2.841359 2.804821 3.575072 3.513750 2.357935 3.152288
## 239 2.683947 3.908485 2.921166 2.915400 3.714749 3.473195 3.371253 3.527114
## 240 2.885361 3.996161 3.201397 3.177248 3.774298 3.524136 3.712650 3.403464
## 241 2.671173 3.998521 2.775246 2.676694 3.365675 3.480869 2.217484 3.143015
## 242 2.688420 3.999174 2.550228 2.801404 3.619719 3.462098 2.894870 3.222716
## 243 2.767898 3.967267 3.392169 2.999131 3.738305 3.551206 3.789016 3.354685
## 244 2.698970 3.969463 2.296665 2.685742 3.657629 3.417970 3.297761 3.518514
## 245 2.696356 3.821972 2.670246 3.072250 3.544192 3.423737 3.116276 3.209247
## 246 2.695482 3.951483 2.968950 3.023252 3.551206 3.436481 3.068557 3.304491
## 247 2.810904 3.915400 3.541080 2.991669 3.815843 3.538448 3.758155 3.205746
## 248 2.788168 3.881613 3.062206 2.717671 3.494155 3.481156 3.044540 3.190051
## 249 2.822168 3.933690 2.437751 2.950365 3.757927 3.392873 2.926857 3.384533
## 250 2.728354 4.095134 2.788875 3.047664 3.830396 3.402949 3.344392 3.377670
## 251 2.822168 3.927422 2.477121 2.891537 3.673390 3.237544 2.723456 3.080626
## 252 2.767156 3.921322 3.388811 3.031812 3.824776 3.468347 3.755646 3.288473
## 253 2.788875 3.989183 3.342620 3.168792 3.497068 3.414305 3.726483 3.282849
## 254 2.814248 3.873669 3.015360 2.894316 3.587935 3.435048 3.101403 3.308778
## 255 2.488551 3.963457 3.472171 2.640481 3.643354 3.329194 2.885926 3.176959
## 256 2.729165 3.934953 3.294246 2.951338 3.713070 3.554126 3.842360 3.424718
## 257 2.668386 3.879898 2.986324 3.062958 3.475235 3.428135 3.011147 2.969882
## 258 2.760422 3.993657 3.011570 3.134496 3.707315 3.446071 3.651569 3.362859
## 259 2.711807 3.867350 3.009451 3.028571 3.503246 3.442793 3.232488 3.313656
## 260 2.290035 3.859439 2.780317 2.535294 3.659441 3.398287 3.272074 3.196453
## 261 2.676694 3.747334 2.348305 2.986324 3.429591 3.466423 2.943989 3.102091
## 262 2.729974 3.881099 3.454845 3.115943 3.852419 3.547775 3.949195 3.350829
## 263 2.854913 3.923140 2.874482 3.006038 3.675045 3.515609 2.839478 3.272538
## 264 2.808886 4.065281 3.090611 2.690196 3.538951 3.436004 3.515344 3.349083
## 265 2.925828 4.141073 2.546543 3.044148 3.619093 3.387212 3.001734 3.502291
## 266 2.733197 3.976167 3.212454 2.986324 3.794349 3.369216 3.742568 3.591065
## 267 2.688420 3.800786 2.372912 3.013680 3.468052 3.432488 3.114277 3.055378
## 268 2.599883 3.838723 3.126131 3.078094 3.731347 3.468052 3.632963 3.178689
## 269 2.955688 4.160318 3.383097 3.040998 3.739493 3.446226 3.945370 3.524656
## 270 2.959041 4.234467 3.571243 3.209247 3.919026 3.527759 4.153083 3.662758
## 271 2.929419 4.205421 3.325721 3.027350 3.718003 3.432809 3.809290 3.293141
## 272 2.931966 4.191647 2.725912 3.011147 3.752970 3.434409 3.428783 3.518514
## 273 2.925828 4.155427 3.014940 2.984077 3.699838 3.416807 3.573800 3.231215
## 274 2.864511 4.111632 3.022016 2.959995 3.520221 3.434888 3.538699 3.353147
## 275 2.592177 3.980458 2.903633 2.972666 3.573104 3.419295 2.912222 3.403978
## 276 2.733999 3.838597 3.035029 3.207904 3.775100 3.390228 3.354493 3.349666
## 277 2.759668 3.825880 3.086004 2.570543 3.566202 3.509203 3.262925 3.141763
## 278 2.907411 4.007876 3.433770 3.068186 3.821775 3.432969 3.981229 3.681241
## 279 2.755875 3.825880 2.845098 2.584331 3.304706 3.480294 1.716003 3.041393
## 280 2.645422 3.909610 2.773055 2.653213 3.538825 3.407731 2.428135 3.119256
## 281 2.719331 3.757548 2.595496 3.014940 3.283753 3.423574 1.832509 2.971740
## 282 2.705864 3.815179 3.159868 3.078094 3.643551 3.456062 3.451172 3.142702
## 283 2.585461 3.814780 2.927370 2.880242 3.635081 3.426999 3.143951 3.133219
## 284 2.440909 3.902166 3.017451 2.745075 3.797337 3.423410 2.667453 3.121888
## 285 2.736397 3.773640 2.919078 3.016197 3.750817 3.458487 3.426836 3.259833
## 286 2.758912 3.840545 2.696356 2.939020 3.743039 3.443106 3.475381 3.180986
## 287 2.719331 3.896636 3.273464 3.088136 3.790426 3.488269 3.297323 3.186391
## 288 2.656098 3.905202 2.851258 3.083503 3.789510 3.547159 3.539829 3.180126
## 289 2.735599 3.802295 2.761176 2.950365 3.582972 3.432809 3.213252 3.239800
## 290 2.811575 4.373647 3.416641 2.921686 3.492760 3.481299 3.895699 3.237795
## 291 2.759668 3.924538 2.786751 2.732394 3.437751 3.500922 3.104146 3.079181
## 292 2.733999 3.818094 2.703291 2.621176 3.185259 3.426836 2.167317 3.164353
## 293 2.795880 3.928088 2.534026 3.144574 3.646110 3.333447 3.198382 3.212188
## 294 2.738781 3.884795 3.017033 2.838219 3.842047 3.497483 3.705864 3.454997
## 295 2.907411 3.890421 2.731589 3.065206 3.674861 3.405858 3.633165 3.602060
## 296 2.606381 3.904661 2.568202 3.064832 3.742725 3.445604 3.338656 3.286905
## 297 2.643453 3.871690 3.075182 3.174060 3.747256 3.483445 3.702431 3.468790
## 298 2.745855 3.742489 2.656098 2.799341 3.550228 3.478855 3.088490 3.146438
## 299 2.669317 3.757168 2.535294 2.914872 3.404320 3.462248 1.799341 2.825426
## 300 2.714330 3.890253 3.240050 2.999131 3.726156 3.455150 3.642366 3.290480
## 301 2.699838 3.851870 3.059942 2.999565 3.728191 3.446382 3.212720 3.057286
## 302 2.803457 4.025961 3.137354 3.072250 3.679973 3.519959 3.701482 3.216430
## 303 2.770115 3.931865 3.100026 3.146128 3.643156 3.428944 3.689220 3.495683
## 304 2.724276 3.874945 3.198932 3.033424 3.574957 3.419625 3.628185 3.306211
## 305 2.672098 3.810501 2.828660 3.006038 3.674218 3.378398 3.155943 3.037426
## 306 2.698970 3.863204 2.827369 2.980003 3.539076 3.516271 2.606381 2.800029
## 307 2.738781 3.828918 2.592177 2.602060 3.662002 3.472756 2.933487 3.243038
## 308 2.914343 4.021313 3.033021 2.984077 3.618362 3.397592 3.471585 3.192846
## 309 2.885361 3.954966 2.713491 2.876218 3.581722 3.367729 3.192289 3.165541
## 310 2.526339 3.853881 2.414973 3.038223 3.381476 3.430720 1.939519 3.149219
## 311 2.788875 3.863025 2.906874 3.054996 3.616265 3.438859 3.321598 3.168497
## 312 2.734800 3.890868 2.322219 3.053846 3.490520 3.327972 2.708421 3.447158
## 313 2.614897 3.785757 2.730782 3.066699 3.479719 3.457428 3.057286 3.096215
## 314 2.800029 4.137481 3.639586 3.119586 3.915716 3.560504 4.336480 3.198107
## 315 2.755112 4.001041 3.085647 2.897077 3.386321 3.476397 2.502427 2.975891
## 316 2.540329 3.896581 2.966142 2.845098 3.525174 3.460748 3.477121 3.278754
## 317 2.488551 3.883207 2.912753 2.645422 3.543571 3.439175 2.881385 3.218536
## 318 2.706718 4.021685 2.574031 3.251151 3.716087 3.508395 3.460597 3.576572
## 319 2.733999 3.817962 2.898176 2.488551 3.389166 3.477411 2.625312 3.104146
## 320 2.693727 3.848866 2.906335 3.065953 3.594724 3.474362 3.475235 3.178401
## 321 2.658965 3.806451 2.739572 3.071514 3.446071 3.438859 2.777427 3.051538
## 322 2.746634 3.862370 2.934498 2.666518 3.490941 3.463296 2.292256 2.860937
## 323 2.775974 3.899109 3.159868 3.047275 3.656290 3.493040 3.657534 3.283979
## 324 2.751279 3.836197 3.040998 3.153205 3.462997 3.458789 3.032216 3.426186
## 325 2.749736 3.940267 3.256477 2.832509 3.561459 3.518382 3.251395 2.959041
## 326 2.728354 3.808886 2.501059 3.043755 3.571825 3.396374 2.998259 3.330414
## 327 2.732394 3.922777 2.853090 2.643453 3.355452 3.462847 3.009451 2.925312
## 328 2.755875 3.846399 3.040207 2.972203 3.528145 3.465383 3.446692 3.122871
## 329 2.783904 3.896251 2.326336 3.071514 3.442166 3.377852 2.086360 2.962843
##           V9
## 1   3.882695
## 2   3.638489
## 3   3.720159
## 4   3.768194
## 5   3.757927
## 6   3.720490
## 7   3.707315
## 8   3.763053
## 9   3.626340
## 10  3.795254
## 11  3.793790
## 12  3.884682
## 13  3.527630
## 14  3.629613
## 15  3.660771
## 16  3.674861
## 17  3.722222
## 18  3.715669
## 19  3.715418
## 20  3.800373
## 21  3.908860
## 22  3.734880
## 23  3.707315
## 24  3.871515
## 25  3.782186
## 26  3.740600
## 27  3.713659
## 28  3.799892
## 29  3.602928
## 30  3.779524
## 31  3.494015
## 32  3.628082
## 33  3.560504
## 34  3.779308
## 35  3.771808
## 36  3.763503
## 37  3.749272
## 38  3.685114
## 39  3.779524
## 40  3.683857
## 41  3.768120
## 42  3.665862
## 43  3.803662
## 44  3.852907
## 45  3.871398
## 46  3.779596
## 47  3.753660
## 48  3.857152
## 49  3.814714
## 50  3.838849
## 51  3.696182
## 52  3.905256
## 53  3.703033
## 54  3.754348
## 55  3.827757
## 56  3.685473
## 57  3.799547
## 58  3.699751
## 59  3.739177
## 60  3.712060
## 61  3.720738
## 62  3.753660
## 63  3.782114
## 64  3.651956
## 65  3.716421
## 66  3.724849
## 67  3.721811
## 68  3.688420
## 69  3.688331
## 70  3.886434
## 71  3.711554
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## 73  3.682326
## 74  3.713070
## 75  3.825426
## 76  3.675870
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## 79  3.652343
## 80  3.698709
## 81  3.656290
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## 83  3.630835
## 84  3.855156
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## 86  3.591510
## 87  3.736635
## 88  3.596487
## 89  3.593508
## 90  3.786254
## 91  3.728191
## 92  3.705864
## 93  3.624695
## 94  3.682416
## 95  3.917400
## 96  3.633367
## 97  3.483587
## 98  3.716504
## 99  3.688776
## 100 3.747722
## 101 3.720573
## 102 3.665675
## 103 3.707400
## 104 3.571010
## 105 3.652440
## 106 3.685025
## 107 3.821579
## 108 3.853455
## 109 3.855277
## 110 3.901622
## 111 3.685652
## 112 3.802226
## 113 3.622732
## 114 3.836451
## 115 3.759366
## 116 3.625312
## 117 3.758836
## 118 3.780029
## 119 3.582745
## 120 3.713154
## 121 3.751741
## 122 3.685563
## 123 3.671821
## 124 3.735838
## 125 3.752048
## 126 3.716337
## 127 3.700011
## 128 3.650987
## 129 3.664454
## 130 3.726075
## 131 3.799823
## 132 3.674677
## 133 3.714916
## 134 3.823605
## 135 3.872972
## 136 3.641771
## 137 3.806994
## 138 3.706035
## 139 3.713070
## 140 3.582291
## 141 3.714833
## 142 3.788098
## 143 3.805229
## 144 3.640581
## 145 3.689220
## 146 3.690462
## 147 3.621280
## 148 3.665675
## 149 3.726238
## 150 3.680698
## 151 3.746556
## 152 3.790004
## 153 3.687083
## 154 3.713994
## 155 3.801472
## 156 3.743275
## 157 3.535167
## 158 3.751895
## 159 3.636789
## 160 3.986861
## 161 3.768786
## 162 3.760045
## 163 3.747722
## 164 3.709270
## 165 3.676419
## 166 3.721316
## 167 3.727623
## 168 3.780677
## 169 3.660201
## 170 3.814714
## 171 3.785686
## 172 3.647774
## 173 3.795532
## 174 3.634779
## 175 3.690905
## 176 3.722058
## 177 3.838723
## 178 3.518646
## 179 3.725585
## 180 3.732555
## 181 3.822887
## 182 3.772542
## 183 3.692494
## 184 3.752740
## 185 3.736237
## 186 3.851320
## 187 3.642069
## 188 3.758836
## 189 3.567262
## 190 3.850585
## 191 3.712650
## 192 3.766413
## 193 3.800992
## 194 3.799823
## 195 3.999131
## 196 3.697404
## 197 3.766636
## 198 3.659441
## 199 3.708166
## 200 3.789157
## 201 3.743275
## 202 3.689486
## 203 3.599883
## 204 3.569140
## 205 3.842734
## 206 3.773640
## 207 3.867526
## 208 3.693463
## 209 3.810904
## 210 3.738622
## 211 3.824256
## 212 3.809762
## 213 3.727379
## 214 3.755112
## 215 3.649627
## 216 3.768342
## 217 3.808346
## 218 3.736954
## 219 3.848805
## 220 3.878809
## 221 3.909503
## 222 3.691258
## 223 3.767379
## 224 3.765072
## 225 3.869994
## 226 3.782616
## 227 3.741467
## 228 3.784118
## 229 3.714916
## 230 3.652343
## 231 3.712144
## 232 3.780245
## 233 3.609914
## 234 3.751125
## 235 3.807197
## 236 3.628082
## 237 3.721068
## 238 3.739018
## 239 3.791410
## 240 3.656577
## 241 3.922570
## 242 3.829046
## 243 3.712144
## 244 3.538951
## 245 3.667079
## 246 3.644931
## 247 3.806519
## 248 3.747179
## 249 3.649237
## 250 3.754119
## 251 3.726401
## 252 3.768638
## 253 3.692230
## 254 3.723209
## 255 3.785259
## 256 3.799616
## 257 3.662002
## 258 3.725013
## 259 3.569257
## 260 3.739414
## 261 3.777499
## 262 3.763428
## 263 3.583765
## 264 3.799961
## 265 3.752509
## 266 3.693903
## 267 3.887617
## 268 3.837146
## 269 3.739493
## 270 3.782688
## 271 3.861534
## 272 3.764998
## 273 3.727134
## 274 3.756103
## 275 3.887336
## 276 3.747489
## 277 3.690816
## 278 3.770926
## 279 3.607991
## 280 3.678063
## 281 3.793301
## 282 3.818556
## 283 3.667266
## 284 3.716337
## 285 3.703807
## 286 3.674126
## 287 3.731105
## 288 3.723374
## 289 3.773201
## 290 3.789440
## 291 3.669967
## 292 3.573336
## 293 3.753736
## 294 3.650696
## 295 3.689042
## 296 3.779669
## 297 3.860697
## 298 3.638789
## 299 3.678700
## 300 3.656482
## 301 3.737511
## 302 3.761326
## 303 3.788663
## 304 3.852175
## 305 3.690196
## 306 3.864926
## 307 3.718169
## 308 3.764848
## 309 3.660011
## 310 3.880756
## 311 3.700963
## 312 3.745309
## 313 3.796505
## 314 3.783332
## 315 3.752509
## 316 3.644143
## 317 3.633468
## 318 3.902655
## 319 3.675778
## 320 3.780749
## 321 3.832828
## 322 3.516932
## 323 3.790567
## 324 3.731589
## 325 3.702431
## 326 3.697752
## 327 3.694254
## 328 3.590396
## 329 3.671543
require(reshape2)
melt.log_places <- melt(log_places)
## No id variables; using all as measure variables
head(melt.log_places)
##   variable    value
## 1       V1 2.716838
## 2       V1 2.759668
## 3       V1 2.670246
## 4       V1 2.677607
## 5       V1 2.818885
## 6       V1 2.716003
ggplot(data = melt.log_places, aes(x = value)) + 
stat_density() + 
facet_wrap(~variable, scales = "free")

pc.places <- princomp(log_places)
names(pc.places)
## [1] "sdev"     "loadings" "center"   "scale"    "n.obs"    "scores"   "call"
summary(pc.places)
## Importance of components:
##                           Comp.1     Comp.2    Comp.3     Comp.4     Comp.5
## Standard deviation     0.6134452 0.22560372 0.1668374 0.15131845 0.12930691
## Proportion of Variance 0.7226740 0.09774248 0.0534537 0.04397184 0.03210956
## Cumulative Proportion  0.7226740 0.82041652 0.8738702 0.91784205 0.94995161
##                            Comp.6     Comp.7      Comp.8      Comp.9
## Standard deviation     0.10916208 0.09182048 0.062627954 0.042330504
## Proportion of Variance 0.02288413 0.01619086 0.007532295 0.003441103
## Cumulative Proportion  0.97283574 0.98902660 0.996558897 1.000000000

These are the principal components that determine the directions of the new feature space

eigenvectors<-pc.places$loadings
eigenvectors 
## 
## Loadings:
##    Comp.1 Comp.2 Comp.3 Comp.4 Comp.5 Comp.6 Comp.7 Comp.8 Comp.9
## V1                0.141  0.153  0.398  0.831         0.315       
## V2                0.129 -0.178  0.175  0.209 -0.696 -0.614       
## V3  0.408 -0.859  0.276                                          
## V4  0.100  0.220  0.593  0.724        -0.164        -0.182       
## V5  0.150         0.221 -0.126 -0.870  0.372                     
## V6                                                   0.204 -0.973
## V7  0.874  0.304 -0.363                                          
## V8  0.159  0.334  0.584 -0.628  0.213 -0.142  0.235              
## V9                0.121               -0.265 -0.664  0.662  0.168
## 
##                Comp.1 Comp.2 Comp.3 Comp.4 Comp.5 Comp.6 Comp.7 Comp.8 Comp.9
## SS loadings     1.000  1.000  1.000  1.000  1.000  1.000  1.000  1.000  1.000
## Proportion Var  0.111  0.111  0.111  0.111  0.111  0.111  0.111  0.111  0.111
## Cumulative Var  0.111  0.222  0.333  0.444  0.556  0.667  0.778  0.889  1.000

Eigenvalues determine the magnitude. Magnitudes give the contributions of each variable to that component. So, we examine the eigenvalues to determine how many principal components should be considered:

eigenvalues <- pc.places$sdev*pc.places$sdev 
eigenvalues
##      Comp.1      Comp.2      Comp.3      Comp.4      Comp.5      Comp.6 
## 0.376315063 0.050897040 0.027834722 0.022897273 0.016720276 0.011916361 
##      Comp.7      Comp.8      Comp.9 
## 0.008431000 0.003922261 0.001791872

A sharp drop from one eigenvalue to the next may serve as another indicator of how many eigenvalues to consider. From the result above on the summary of pc.places, the first three principal components explain 87% of the variation. This is an acceptably large percentage.

below is the correlation matrix between our given data and principal components. This will determine if there is relevancy between the components and the actual data or how related our components to the actual data.

round( cor(places, pc.places$scores) , 3) 
##     Comp.1 Comp.2 Comp.3 Comp.4 Comp.5 Comp.6 Comp.7 Comp.8 Comp.9
## V1   0.236  0.027  0.204  0.130  0.439  0.782 -0.003  0.102  0.058
## V2   0.508  0.001  0.188 -0.232  0.254  0.225 -0.600 -0.372 -0.034
## V3   0.763 -0.425  0.178  0.003  0.046 -0.013 -0.018 -0.011 -0.063
## V4   0.373  0.268  0.592  0.595 -0.007 -0.123  0.042 -0.070 -0.027
## V5   0.594  0.054  0.244 -0.119 -0.677  0.245 -0.044  0.038  0.019
## V6   0.407 -0.281  0.031 -0.020 -0.119  0.059 -0.112  0.256 -0.806
## V7   0.724 -0.108  0.111  0.047  0.049  0.020 -0.025 -0.061 -0.068
## V8   0.469  0.359  0.558 -0.469  0.173 -0.062  0.098  0.015  0.008
## V9   0.112  0.165  0.243  0.086  0.049 -0.339 -0.723  0.478  0.077
## V10  0.028  0.040  0.048 -0.007  0.069  0.070 -0.041 -0.026 -0.026

An Alternative Method to determine the number of principal components is to look at a Scree Plot. With the eigenvalues ordered from largest to the smallest, a scree plot is the plot of versus i. The number of components is determined at the point beyond which the remaining eigenvalues are all relatively small and of comparable size.

screeplot(pc.places,type='l',main='Screeplot for places rated almanac data') 
abline(1,0,col='red',lty=2)

As you see, we could have stopped at the second principal component, but we continued till the third component. Relatively speaking, the contribution of the third component is small compared to the second component.

plot(pc.places$scores[,1:2], type='n',xlab="PC1", ylab="PC2" )
points(pc.places$scores[,1:2], cex=0.5)   # this puts a small point at the center

#text(pc.places$scores[,1:2],label=places[,10], cex=0.5) #add tname to plot 
pc.places_2 <- prcomp(~  V1 +V2 +   V3 +   V4   +  V5 +
                   V6   +     V7  + V8+V9,
                 data=log_places     )
eigenvalues <- pc.places_2$sdev * pc.places_2$sdev
eigenvalues
## [1] 0.377462365 0.051052214 0.027919584 0.022967082 0.016771253 0.011952691
## [7] 0.008456704 0.003934219 0.001797335
eigenvectors <- pc.places_2$rotation
eigenvectors_r<-round(eigenvectors,3)
eigenvectors_r
##      PC1    PC2    PC3    PC4    PC5    PC6    PC7    PC8    PC9
## V1 0.035  0.009 -0.141  0.153 -0.398  0.831 -0.056 -0.315 -0.064
## V2 0.093  0.009 -0.129 -0.178 -0.175  0.209  0.696  0.614  0.087
## V3 0.408 -0.859 -0.276 -0.035 -0.050 -0.090 -0.062 -0.021 -0.066
## V4 0.100  0.220 -0.593  0.724  0.013 -0.164 -0.056  0.182  0.054
## V5 0.150  0.059 -0.221 -0.126  0.870  0.372  0.072 -0.057 -0.072
## V6 0.032 -0.061 -0.008 -0.005  0.048  0.024  0.057 -0.204  0.973
## V7 0.874  0.304  0.363  0.081 -0.055 -0.028 -0.023 -0.017 -0.005
## V8 0.159  0.334 -0.584 -0.628 -0.213 -0.142 -0.235 -0.084  0.017
## V9 0.019  0.056 -0.121  0.052 -0.030 -0.265  0.664 -0.662 -0.168
summary(pc.places_2)
## Importance of components:
##                           PC1     PC2     PC3     PC4     PC5     PC6     PC7
## Standard deviation     0.6144 0.22595 0.16709 0.15155 0.12950 0.10933 0.09196
## Proportion of Variance 0.7227 0.09774 0.05345 0.04397 0.03211 0.02288 0.01619
## Cumulative Proportion  0.7227 0.82042 0.87387 0.91784 0.94995 0.97284 0.98903
##                            PC8     PC9
## Standard deviation     0.06272 0.04239
## Proportion of Variance 0.00753 0.00344
## Cumulative Proportion  0.99656 1.00000