* this is the tradional way to view the data, in variable space, with observations as points in the graph ; data vectorobs ; input one x y ; cards ; 1 1 15 1 2 11 1 4 21 ; proc plot data = vectorobs ; plot y*x ; run ; proc print ; run ; proc reg data = vectorobs ; model y = x ; run ; * here we view the data in observation space, with the 1, x, and y vectors as points, along with some other points that are linear combinations of 1 and x to form the plane of the simple linear regression model ; data vectorvars ; input obs1 obs2 obs3 group $ @@ ; cards ; 1 1 1 O 2 2 2 O 3 3 3 O .5 .5 .5 O 4 4 4 O 7 7 7 O -1 -1 -1 O -2 -2 -2 O 5 5 5 O 6 6 6 O 1 2 4 X 5 10 20 X 1.5 3 6 X -1 -2 -4 X -.5 -1 -2 X 2 4 8 X 3 6 12 X .5 1 2 X 4 8 16 X 2 4 8 X 3 6 12 X .5 1 2 X 4 8 16 X 15 11 21 Y 0 0 0 C 12.43 14.86 19.72 LS 2 3 5 C 1 1.5 2.5 C 4 6 10 C 3 4 6 C 3 5 9 C .5 .75 1.25 C 0 -1 -3 C 0 1 3 C 6.2692 6.4330 6.7606 C 4.1903 5.5531 8.2786 C 6.8041 8.6291 12.2791 C 10.5598 14.6451 22.8158 C 7.9881 11.4267 18.3041 C 1.9391 2.4488 3.4684 C 11.7591 17.5498 29.1311 C 9.9124 14.6514 24.1293 C 11.2966 18.1140 31.7486 C 12.4382 18.6435 31.0539 C 6.9384 13.7480 27.3672 C 7.3754 9.3819 13.3948 C 7.2504 13.9287 27.2854 C 0.7874 0.9127 1.1634 C 5.5404 10.7532 21.1787 C 3.2510 3.3618 3.5833 C 7.0391 13.6197 26.7807 C 8.2119 13.5018 24.0815 C 4.6811 6.4237 9.9087 C 7.1833 13.5381 26.2477 C 6.7923 11.2099 20.0453 C 10.4030 16.5577 28.8673 C 5.7630 9.2017 16.0791 C 9.2233 15.8668 29.1539 C 2.7183 4.3109 7.4960 C 8.6274 14.8792 27.3829 C 4.5184 6.5873 10.7251 C 8.1615 11.1563 17.1458 C 7.0037 8.2303 10.6835 C 3.2611 4.5645 7.1714 C 5.2721 7.6898 12.5251 C 7.9144 10.1550 14.6363 C 6.6672 10.4695 18.0743 C 6.8277 9.5046 14.8584 C 6.0128 10.5502 19.6250 C 2.3488 3.5433 5.9323 C 1.3625 2.2773 4.1069 C 6.7410 11.1441 19.9501 C 3.2528 5.0218 8.5598 C 11.3295 18.2075 31.9634 C 7.3813 8.9665 12.1368 C 5.6741 10.5100 20.1818 C 7.5726 10.9845 17.8083 C 8.8693 10.7446 14.4952 C 6.1496 7.1323 9.0978 C 7.7533 10.2998 15.3929 C 8.4348 11.8583 18.7052 C 6.6508 13.0890 25.9654 C 2.7096 4.5569 8.2514 C 5.4548 6.8388 9.6069 C 7.3181 10.2783 16.1988 C 8.8043 13.3780 22.5254 C 6.75664 6.5737 6.2077 C 1.02031 -0.2135 -2.6811 C -0.65115 -2.7032 -6.8074 C 0.82385 -0.5888 -3.4140 C 1.03612 -2.5736 -9.7931 C -0.12114 -2.4559 -7.1254 C 1.38884 -2.6958 -10.8652 C -2.21697 -6.8578 -16.1396 C 4.48298 2.1402 -2.5452 C 0.92611 -4.2055 -14.4686 C -0.93468 -6.8927 -18.8087 C 0.52481 -3.0283 -10.1344 C -3.76671 -9.7893 -21.8344 C 3.52579 0.3291 -6.0644 C -1.43122 -3.9172 -8.8893 C 3.40557 0.3139 -5.8695 C -0.52976 -3.9863 -10.8994 C 0.95329 -3.7354 -13.1129 C -4.76866 -9.7038 -19.5739 C 4.57198 4.4286 4.1418 C 1.94013 -1.5534 -8.5404 C 6.12274 5.5649 4.4494 C 0.78182 -1.6005 -6.3652 C 1.17466 -4.1262 -14.7278 C -2.16198 -8.2530 -20.4351 C -0.76868 -1.9214 -4.2269 C -2.30410 -5.4790 -11.8287 C 0.26330 -2.3156 -7.4733 C 3.91517 3.2424 1.8970 C -1.77830 -4.0741 -8.6657 C 0.58284 -5.4453 -17.5015 C -4.05648 -9.6938 -20.9685 C -2.09981 -9.0482 -22.9450 C -3.99732 -9.5783 -20.7402 C -1.76282 -7.0250 -17.5493 C -2.60495 -9.2173 -22.4421 C 4.32058 3.1077 0.6820 C -4.17563 -10.9843 -24.6016 C 1.79233 -2.4123 -10.8215 C -1.86776 -6.7720 -16.5805 C -3.89591 -9.3882 -20.3728 C 4.10632 3.0657 0.9845 C -4.49423 -11.1797 -24.5506 C -3.85591 -8.9147 -19.0321 C 0.75163 -5.3509 -17.5558 C 4.44698 2.8789 -0.2574 C -5.33033 -11.1752 -22.8649 C 4.64168 4.1111 3.0499 C 1.17781 4.9125 12.3819 C -0.25834 5.5486 17.1624 C -1.41950 3.8597 14.4182 C 1.65739 7.5460 19.3234 C -1.30404 0.2520 3.3640 C 5.46426 11.5383 23.6863 C -2.87702 -1.0599 2.5745 C -3.50523 -3.4632 -3.3791 C -2.78419 -1.7519 0.3128 C -0.37378 3.3334 10.7477 C 0.15696 6.5661 19.3843 C 3.89508 9.0753 19.4356 C 3.97829 9.5320 20.6393 C -6.16545 -5.7023 -4.7761 C -2.64930 -0.4946 3.8149 C 2.67387 8.3082 19.5770 C -3.45693 -2.5997 -0.8852 C -5.70009 -4.8815 -3.2442 C -2.58761 1.3495 9.2238 C 6.42469 13.1265 26.5302 C -4.09274 -3.9796 -3.7533 C -0.30689 4.0143 12.6566 C 0.33465 0.8132 1.7704 C -3.02408 -1.0177 2.9951 C -3.21788 0.1392 6.8535 C 0.01371 3.3593 10.0506 C -0.29007 0.5146 2.1240 C 1.81192 7.4410 18.6993 C -4.55895 -3.6840 -1.9340 C -2.96570 -0.4354 4.6252 C 2.20803 6.7573 15.8559 C -3.10435 -2.8931 -2.4705 C -1.86822 0.6175 5.5891 C -2.82534 -2.5542 -2.0121 C -5.82915 -5.6438 -5.2732 C -0.12565 6.0374 18.3634 C -4.91165 -3.2409 0.1005 C 4.49401 10.3043 21.9249 C 2.06580 7.6442 18.8009 C 2.38764 5.0991 10.5219 C -3.55024 -1.6202 2.2399 C 3.39133 9.3506 21.2692 C -3.47137 -1.2376 3.2298 C 0.52489 2.7187 7.1064 C -0.36950 0.2026 1.3469 C -2.71047 -2.2299 -1.2687 C -4.33951 -2.6797 0.6400 C -0.94298 3.7672 13.1875 C ; proc print ; run ; * By coloring the points based on group value, one can visualize the vector space approach to simple regression. One color is used for the 1 (1,1,1) vector and its multiples, another color is used for the x vector (1,2,4) and its multiples, a third color is used for linear combinations of 1 and x to form a plane, another color is used for the response vector y (15,11,21), and a last color is used for the point in the 1,x plane that is the least squares fit. ; proc insight data = vectorvars tools ; rotate obs1 * obs2 * obs3 ; run ; /* data vectors ; do i = 1 to 100 ; u1 = 7*ranuni(0) ; u2 = 7*ranuni(0) ; o1 = -1*u1 + 1*u2 ; o2 = -1*u1 + 2*u2 ; o3 = -1*u1 + 4*u2 ; group = 'C' ; output ; end ; proc print data = vectors noobs ; var o1 o2 o3 group ; run ; */