We will discuss principal component analysis and its uses.
Lay discussions about principal components are available in Chapter 17 of your text, The Statistical
Sleuth, in Chapter 14 of Biostatistics by van Belle, Fisher, Heagerty, and Lumley, as well as on the
WEB at: http://www.okstate.edu/artsci/botany/ordinate/PCA.htm
and
http://www.eng.man.ac.uk/mech/merg/Research/datafusion.org.uk/pca.html
A more technical discussion may be found in Chapter 8 of Applied Multivariate Statistical Analysis by Johnson and Wichern.
The first data set is our gene response to a drug treatment. The second list is summary data of various body measurements in adult females from the early 60's from Stoudt et al. (see http://www.cdc.gov/nchs/data/series/sr_11/sr11_035acc.pdf and Biostatistics by van Belle et al.
Responder_Type Individual Day_0 Day_1 Day_2 Day_7 Day_14 Day_28 log_0 log_1 log_2 log_7 log_14 log_28 Y 1 11414.9 17461.9 19303.3 11776.5 16481.6 18769.7 9.34267 9.7678 9.8680 9.3739 9.7100 9.8400 Y 2 11761.8 26143.5 24651.6 22734.7 16481.6 18769.7 9.37261 10.1714 10.1126 10.0316 9.7100 9.8400 Y 3 13664.3 26074.4 22826.3 18222.6 16155.2 18769.7 9.52254 10.1687 10.0357 9.8104 9.6900 9.8400 Y 4 11540.1 53371.2 61456.4 25517.4 26815.9 22790.4 9.35359 10.8850 11.0261 10.1471 10.1967 10.0341 Y 5 12081.6 21713.0 15061.9 18078.2 16990.9 18769.7 9.39944 9.9857 9.6199 9.8025 9.7404 9.8400 Y 6 9997.6 21122.8 18664.2 28093.0 17939.0 29943.9 9.21010 9.9581 9.8344 10.2433 9.7947 10.3071 Y 7 7507.8 21262.9 15972.3 16410.8 14589.2 17415.9 8.92369 9.9647 9.6786 9.7057 9.5880 9.7651 Y 8 8663.9 22601.0 18865.3 18441.0 18494.9 18851.7 9.06692 10.0257 9.8451 9.8223 9.8252 9.8444 Y 9 10706.0 22932.3 19430.3 22860.4 23034.1 19384.8 9.27856 10.0403 9.8746 10.0372 10.0447 9.8722 Y 10 11614.7 19930.5 21020.7 16272.9 15381.5 16397.6 9.36003 9.9000 9.9533 9.6973 9.6409 9.7049 Y 11 7802.8 25495.1 19997.9 18060.6 22315.5 23126.0 8.96224 10.1462 9.9034 9.8015 10.0130 10.0487 Y 12 11213.6 25262.6 18758.3 12626.1 11362.1 14796.9 9.32488 10.1371 9.8394 9.4435 9.3380 9.6022 Y 13 7521.9 18282.0 15244.6 10057.4 12532.0 14402.7 8.92557 9.8137 9.6320 9.2161 9.4360 9.5752 Y 14 10290.3 19072.7 20434.0 16148.9 16282.7 20384.0 9.23896 9.8560 9.9250 9.6896 9.6979 9.9225 Y 15 7518.6 21373.2 17259.6 14275.1 14281.1 14966.9 8.92513 9.9699 9.7561 9.5663 9.5667 9.6136 N 1 11693.3 20623.1 18839.2 23948.0 12456.5 13359.7 9.36677 9.9342 9.8437 10.0836 9.4300 9.5000 N 2 20489.0 56887.2 39841.9 43468.9 11498.8 13226.8 9.92765 10.9488 10.5927 10.6798 9.3500 9.4900 N 3 7599.7 20925.4 6854.2 9596.4 13722.0 11977.9 8.93586 9.9487 8.8326 9.1691 9.5268 9.3908 N 4 7475.1 19415.8 15230.0 6848.3 11161.2 15119.8 8.91934 9.8738 9.6310 8.8318 9.3202 9.6238 N 5 10536.5 10951.1 10996.7 13369.7 10599.3 14111.2 9.26260 9.3012 9.3054 9.5007 9.2685 9.5547 N 6 10056.6 17893.1 16079.3 9024.5 9527.8 16989.9 9.21598 9.7922 9.6853 9.1077 9.1620 9.7404 N 7 13547.0 16276.9 19004.6 13346.8 14270.3 23868.3 9.51392 9.6975 9.8524 9.4990 9.5659 10.0803 N 8 9225.6 15606.1 14296.7 8159.4 9728.2 10655.3 9.12973 9.6554 9.5678 9.0069 9.1828 9.2738 N 9 6928.8 19736.4 16362.1 22876.9 17034.6 8942.5 8.84345 9.8902 9.7027 10.0379 9.7430 9.0986 N 10 8199.4 21073.4 17104.9 14532.5 19080.1 16211.2 9.01182 9.9558 9.7471 9.5841 9.8564 9.6935 N 11 4650.1 21729.2 17025.4 16531.0 13747.7 19303.6 8.44464 9.9864 9.7425 9.7130 9.5286 9.8680 N 12 15412.9 13787.9 16970.1 9014.1 10419.9 9833.3 9.64296 9.5315 9.7392 9.1065 9.2515 9.1935 N 13 9633.2 12790.3 15948.7 14265.2 16672.7 8620.1 9.17297 9.4564 9.6771 9.5656 9.7215 9.0619 N 14 9776.1 15146.7 25677.6 8918.9 9816.2 14995.3 9.18769 9.6255 10.1534 9.0959 9.1918 9.6155 N 15 10396.0 14976.9 9150.4 2070.1 8064.8 11081.9 9.24918 9.6143 9.1216 7.6353 8.9953 9.3131 N 16 12738.2 14799.0 11447.3 12654.1 13134.8 11278.5 9.45236 9.6023 9.3455 9.4457 9.4830 9.3307 N 17 10548.1 22913.1 20334.0 17160.7 16512.1 17327.8 9.26370 10.0395 9.9200 9.7504 9.7118 9.7601 N 18 7783.7 19817.7 18347.2 14450.5 19288.9 13262.9 8.95979 9.8943 9.8172 9.5785 9.8673 9.4927
Females:
Variable Sitting_height_erect Sitting_height_normal Knee_height Popliteal_height Elbow_rest_height Thigh_clearance_height Buttock_to_knee_length Buttock_to_popliteal_length Elbow_to_elbow_breadth Seat_breadth Biacromial_diameter Chest_girth Waist_girth Right_arm_girth Right_arm_skinfold Infrascapular_skinfold Height Weight Age Sitting_height_erect 1.000 0.907 0.440 0.364 0.585 0.209 0.347 0.231 -0.032 0.204 0.350 0.059 -0.076 0.052 0.057 -0.063 0.772 0.197 -0.339 Sitting_height_normal 0.907 1.000 0.420 0.352 0.533 0.199 0.327 0.230 -0.029 0.197 0.317 0.045 -0.091 0.034 0.064 -0.063 0.729 0.165 -0.300 Knee_height 0.440 0.420 1.000 0.747 0.023 0.196 0.689 0.585 0.106 0.254 0.406 0.180 -0.121 0.128 0.100 0.041 0.782 0.322 -0.128 Popliteal_height 0.364 0.352 0.747 1.000 -0.095 -0.141 0.429 0.387 -0.200 -0.101 0.255 -0.126 0.166 -0.219 -0.193 -0.248 0.723 -0.035 -0.196 Elbow_rest_height 0.585 0.533 0.023 -0.095 1.000 0.293 0.051 -0.045 0.143 0.275 0.094 0.179 0.111 0.222 0.191 0.150 0.258 0.253 -0.177 Thigh_clearance_height 0.209 0.199 0.196 -0.141 0.293 1.000 0.465 0.352 0.597 0.609 0.370 0.594 0.523 0.641 0.539 0.541 0.137 0.693 -0.026 Buttock_to_knee_length 0.347 0.327 0.689 0.429 0.051 0.465 1.000 0.786 0.413 0.552 0.426 0.441 0.410 0.450 0.343 0.296 0.609 0.620 -0.036 Buttock_to_popliteal_length 0.231 0.230 0.585 0.387 -0.045 0.352 0.786 1.000 0.326 0.390 0.341 0.371 0.333 0.355 0.269 0.243 0.514 0.490 -0.005 Elbow_to_elbow_breadth -0.032 -0.029 0.106 -0.200 0.143 0.597 0.413 0.326 1.000 0.696 0.331 0.878 0.870 0.835 0.619 0.751 -0.070 0.844 0.393 Seat_breadth 0.204 0.197 0.254 -0.101 0.275 0.609 0.552 0.390 0.696 1.000 0.327 0.680 0.666 0.746 0.614 0.596 0.137 0.805 0.187 Biacromial_diameter 0.350 0.317 0.406 0.255 0.094 0.370 0.426 0.341 0.331 0.327 1.000 0.433 0.301 0.331 0.209 0.243 0.407 0.443 -0.116 Chest_girth 0.059 0.045 0.180 -0.126 0.179 0.594 0.441 0.371 0.878 0.680 0.433 1.000 0.862 0.843 0.615 0.762 0.016 0.882 0.317 Waist_girth -0.076 -0.091 -0.121 0.166 0.111 0.523 0.410 0.333 0.870 0.666 0.301 0.862 1.000 0.803 0.589 0.747 -0.090 0.844 0.432 Right_arm_girth 0.052 0.034 0.128 -0.219 0.222 0.641 0.450 0.355 0.835 0.746 0.331 0.843 0.803 1.000 0.740 0.774 -0.026 0.888 0.272 Right_arm_skinfold 0.057 0.064 0.100 -0.193 0.191 0.539 0.343 0.269 0.619 0.614 0.209 0.615 0.589 0.740 1.000 0.755 -0.022 -0.641 0.203 Infrascapular_skinfold -0.063 -0.063 0.041 -0.248 0.150 0.541 0.296 0.243 0.751 0.596 0.243 0.762 0.747 0.774 0.755 1.000 -0.136 0.729 0.278 Height 0.772 0.729 0.782 0.723 0.258 0.137 0.609 0.514 -0.070 0.137 0.407 0.016 -0.090 -0.026 -0.022 -0.136 1.000 0.189 -0.289 Weight 0.197 0.165 0.322 -0.035 0.253 0.693 0.620 0.490 0.844 0.805 0.443 0.882 0.844 0.888 -0.641 0.729 0.189 1.000 0.204 Age -0.339 -0.300 -0.128 -0.196 -0.177 -0.026 -0.036 -0.005 0.393 0.187 -0.116 0.317 0.432 0.272 0.203 0.278 -0.289 0.204 1.000
Males
Variable Sitting_height_erect Sitting_height_normal Knee_height Popliteal_height Elbow_rest_height Thigh_clearance_height Buttock_to_knee_length Buttock_to_popliteal_length Elbow_to_elbow_breadth Seat_breadth Biacromial_diameter Chest_girth Waist_girth Right_arm_girth Right_arm_skinfold Infrascapular_skinfold Height Weight Age Sitting_height_erect 1.000 0.873 0.446 0.410 0.544 0.238 0.418 0.227 0.139 0.365 0.365 0.238 0.106 0.221 0.133 0.096 0.770 0.403 -0.272 Sitting_height_normal 0.873 1.000 0.443 0.382 0.454 0.284 0.429 0.274 0.212 0.422 0.335 0.298 0.184 0.265 0.191 0.152 0.717 0.433 -0.183 Knee_height 0.446 0.443 1.000 0.798 -0.029 0.228 0.743 0.626 0.139 0.311 0.352 0.229 0.138 0.194 0.081 0.038 0.802 0.404 -0.172 Popliteal_height 0.410 0.382 0.798 1.000 -0.062 -0.029 0.619 0.524 -0.114 0.050 0.275 0.000 -0.097 -0.059 -0.097 -0.166 0.767 0.153 -0.215 Elbow_rest_height 0.544 0.454 -0.029 -0.062 1.000 0.217 0.005 -0.145 0.231 0.286 0.127 0.258 0.191 0.269 0.216 0.247 0.212 0.324 -0.192 Thigh_clearance_height 0.238 0.284 0.228 -0.029 0.217 1.000 0.348 0.237 0.063 0.579 0.303 0.605 0.537 0.663 0.480 0.503 0.210 0.684 -0.190 Buttock_to_knee_length 0.418 0.429 0.743 0.619 0.005 0.348 1.000 0.736 0.299 0.449 0.365 0.386 0.323 0.342 0.240 0.212 0.751 0.551 -0.151 Buttock_to_popliteal_length 0.227 0.274 0.626 0.524 -0.145 0.237 0.736 1.000 0.193 0.265 0.252 0.252 0.216 0.224 0.128 0.106 0.600 0.379 -0.108 Elbow_to_elbow_breadth 0.139 0.212 0.139 -0.114 0.231 0.063 0.299 0.193 1.000 0.707 0.311 0.833 0.820 0.755 0.524 0.674 0.069 0.804 0.156 Seat_breadth 0.365 0.422 0.311 0.050 0.286 0.579 0.449 0.265 0.707 1.000 0.343 0.732 0.717 0.675 0.546 0.610 0.309 0.813 0.043 Biacromial_diameter 0.365 0.335 0.352 0.275 0.127 0.303 0.365 0.252 0.311 0.343 1.000 0.418 0.249 0.379 0.183 0.242 0.381 0.474 -0.261 Chest_girth 0.238 0.298 0.229 0.000 0.258 0.605 0.386 0.252 0.833 0.732 0.418 1.000 0.837 0.784 0.558 0.710 0.189 0.885 0.062 Waist_girth 0.106 0.184 0.138 -0.097 0.191 0.537 0.323 0.216 0.820 0.717 0.249 0.837 1.000 0.712 0.552 0.727 0.054 0.821 0.299 Right_arm_girth 0.221 0.265 0.194 -0.059 0.269 0.663 0.342 0.224 0.755 0.675 0.379 0.784 0.712 1.000 0.570 0.667 0.139 0.849 -0.115 Right_arm_skinfold 0.133 0.191 0.081 -0.097 0.216 0.480 0.240 0.128 0.524 0.546 0.183 0.558 0.552 0.570 1.000 0.697 0.060 0.562 -0.039 Infrascapular_skinfold 0.096 0.152 0.038 -0.166 0.247 0.503 0.212 0.106 0.674 0.610 0.242 0.710 0.727 0.667 0.697 1.000 -0.003 0.709 0.045 Height 0.770 0.717 0.802 0.767 0.212 0.210 0.751 0.600 0.069 0.309 0.381 0.189 0.054 0.139 0.060 -0.003 1.000 0.394 -0.270 Weight 0.403 0.433 0.404 0.153 0.324 0.684 0.551 0.379 0.804 0.813 0.474 0.885 0.821 0.849 0.562 0.709 0.394 1.000 -0.058 Age -0.272 -0.183 -0.172 -0.215 -0.192 -0.190 -0.151 -0.108 0.156 0.043 -0.261 0.062 0.299 -0.115 -0.039 0.045 -0.270 -0.058 1.000 <\pre>