* this is the tradional way to view the data, in variable space, with observations as points in the graph ; data vectoranova ; input one d1 d2 y ; cards ; 1 1 0 12 1 0 1 10 1 0 1 20 ; proc plot data = vectoranova ; plot y*d1 ; run ; proc print ; run ; proc reg data = vectoranova ; model y = d1 ; model y = d2 ; run ; * here we view the data in observation space, with the 1, d1, d2, and y vectors as points, along with some other points that are linear combinations of 1, d1, and d2 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 11 11 11 O 15 15 15 O 7 7 7 O -1 -1 -1 O -2 -2 -2 O 5 5 5 O 6 6 6 O -11 -11 -11 O -15 -15 -15 O 12 10 20 Y 12 15 15 LS 1 0 0 D1 2 0 0 D1 4 0 0 D1 7 0 0 D1 9 0 0 D1 11 0 0 D1 14 0 0 D1 -1 0 0 D1 -2 0 0 D1 -4 0 0 D1 -7 0 0 D1 -9 0 0 D1 -11 0 0 D1 -14 0 0 D1 0 1 1 D2 0 3 3 D2 0 5 5 D2 0 7 7 D2 0 10 10 D2 0 14 14 D2 0 17 17 D2 0 -1 -1 D2 0 -3 -3 D2 0 -5 -5 D2 0 -7 -7 D2 0 -10 -10 D2 0 -14 -14 D2 0 -17 -17 D2 -20 -40 -40 C -20 -36 -36 C -20 -32 -32 C -20 -28 -28 C -20 -24 -24 C -20 -20 -20 C -20 -16 -16 C -20 -12 -12 C -20 -8 -8 C -20 -4 -4 C -20 0 0 C -16 -36 -36 C -16 -32 -32 C -16 -28 -28 C -16 -24 -24 C -16 -20 -20 C -16 -16 -16 C -16 -12 -12 C -16 -8 -8 C -16 -4 -4 C -16 0 0 C -16 4 4 C -12 -32 -32 C -12 -28 -28 C -12 -24 -24 C -12 -20 -20 C -12 -16 -16 C -12 -12 -12 C -12 -8 -8 C -12 -4 -4 C -12 0 0 C -12 4 4 C -12 8 8 C -8 -28 -28 C -8 -24 -24 C -8 -20 -20 C -8 -16 -16 C -8 -12 -12 C -8 -8 -8 C -8 -4 -4 C -8 0 0 C -8 4 4 C -8 8 8 C -8 12 12 C -4 -24 -24 C -4 -20 -20 C -4 -16 -16 C -4 -12 -12 C -4 -8 -8 C -4 -4 -4 C -4 0 0 C -4 4 4 C -4 8 8 C -4 12 12 C -4 16 16 C 0 -20 -20 C 0 -16 -16 C 0 -12 -12 C 0 -8 -8 C 0 -4 -4 C 0 0 0 C 0 4 4 C 0 8 8 C 0 12 12 C 0 16 16 C 0 20 20 C 4 -16 -16 C 4 -12 -12 C 4 -8 -8 C 4 -4 -4 C 4 0 0 C 4 4 4 C 4 8 8 C 4 12 12 C 4 16 16 C 4 20 20 C 4 24 24 C 8 -12 -12 C 8 -8 -8 C 8 -4 -4 C 8 0 0 C 8 4 4 C 8 8 8 C 8 12 12 C 8 16 16 C 8 20 20 C 8 24 24 C 8 28 28 C 12 -8 -8 C 12 -4 -4 C 12 0 0 C 12 4 4 C 12 8 8 C 12 12 12 C 12 16 16 C 12 20 20 C 12 24 24 C 12 28 28 C 12 32 32 C 16 -4 -4 C 16 0 0 C 16 4 4 C 16 8 8 C 16 12 12 C 16 16 16 C 16 20 20 C 16 24 24 C 16 28 28 C 16 32 32 C 16 36 36 C 20 0 0 C 20 4 4 C 20 8 8 C 20 12 12 C 20 16 16 C 20 20 20 C 20 24 24 C 20 28 28 C 20 32 32 C 20 36 36 C 20 40 40 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 ; /* options nocenter ; data vectors ; do i = -20 to 20 by 4 ; do j = -20 to 20 by 4 ; o1 = 1*i + 0*j ; o2 = 1*i + 1*j ; o3 = 1*i + 1*j ; group = 'C' ; output ; end ; end ; proc print data = vectors noobs ; var o1 o2 o3 group ; run ; options center ; */