MTB > read 'cnrl.dat' c1-c3 20 ROWS READ ROW C1 C2 C3 1 2.23 0.28 1 2 4.99 0.97 1 3 3.37 1.25 1 4 8.54 2.46 1 . . . MTB > describe c1-c2; SUBC> by c3. C3 N MEAN MEDIAN TRMEAN STDEV SEMEAN C1 0 10 3.874 3.550 3.849 1.696 0.536 1 10 5.543 5.195 5.582 2.589 0.819 C2 0 10 1.419 1.515 1.426 0.699 0.221 1 10 1.524 1.440 1.556 0.690 0.218 C3 MIN MAX Q1 Q3 C1 0 1.390 6.560 2.687 5.437 1 2.230 8.540 3.135 8.410 C2 0 0.420 2.360 0.653 2.095 1 0.280 2.510 1.120 2.100 MTB > brief 3 MTB > let c4 = c2*c3 MTB > regress c1 3 c3 c2 c4; SUBC> mse K1; SUBC> coefficients c10; SUBC> xpxinv m1. The regression equation is C1 = 2.01 - 1.51 C3 + 1.31 C2 + 2.00 C4 Predictor Coef Stdev t-ratio p Constant 2.010 1.050 1.91 0.074 C3 -1.513 1.540 -0.98 0.341 C2 1.3134 0.6704 1.96 0.068 C4 1.9975 0.9544 2.09 0.053 s = 1.407 R-sq = 68.4% R-sq(adj) = 62.5% Analysis of Variance SOURCE DF SS MS F p Regression 3 68.512 22.837 11.54 0.000 Error 16 31.655 1.978 Total 19 100.167 SOURCE DF SEQ SS C3 1 13.928 C2 1 45.918 C4 1 8.666 Obs. C3 C1 Fit Stdev.Fit Residual St.Resid 1 1.00 2.230 1.424 0.955 0.806 0.78 2 1.00 4.990 3.709 0.583 1.281 1.00 3 1.00 3.370 4.636 0.482 -1.266 -0.96 4 1.00 8.540 8.642 0.776 -0.102 -0.09 5 1.00 8.400 8.808 0.804 -0.408 -0.35 6 1.00 3.700 4.371 0.506 -0.671 -0.51 7 1.00 7.930 6.391 0.478 1.539 1.16 8 1.00 2.430 4.503 0.493 -2.073 -1.57 9 1.00 5.400 5.894 0.451 -0.494 -0.37 10 1.00 8.440 7.053 0.542 1.387 1.07 11 0.00 3.250 5.110 0.772 -1.860 -1.58 12 0.00 5.300 4.782 0.642 0.518 0.41 13 0.00 1.390 2.601 0.787 -1.211 -1.04 14 0.00 4.690 4.322 0.500 0.368 0.28 15 0.00 6.560 4.755 0.633 1.805 1.44 16 0.00 3.000 3.980 0.448 -0.980 -0.74 17 0.00 5.850 3.652 0.459 2.198 1.65 18 0.00 1.900 2.956 0.646 -1.056 -0.85 19 0.00 3.850 2.562 0.804 1.288 1.12 20 0.00 2.950 4.020 0.451 -1.070 -0.80 MTB > print m1 MATRIX M1 0.55737 -0.55737 -0.32232 0.32232 -0.55737 1.19921 0.32232 -0.67786 -0.32232 0.32232 0.22714 -0.22714 0.32232 -0.67786 -0.22714 0.46044 MTB > print k1 K1 1.97847 (* form var-covar matrix for the betahat *) MTB > multiply k1 m1 m2 MTB > print m2 MATRIX M2 1.10274 -1.10274 -0.63769 0.63769 -1.10274 2.37260 0.63769 -1.34112 -0.63769 0.63769 0.44940 -0.44940 0.63769 -1.34112 -0.44940 0.91096 MTB > print c10 C10 2.01028 -1.51317 1.31340 1.99755 (* ANCOVA REGRESSION *) MTB > regress c1 2 c3 c2 The regression equation is C1 = 0.612 + 1.43 C3 + 2.30 C2 Predictor Coef Stdev t-ratio p Constant 0.6120 0.8870 0.69 0.500 C3 1.4276 0.6909 2.07 0.054 C2 2.2988 0.5225 4.40 0.000 s = 1.540 R-sq = 59.7% R-sq(adj) = 55.0% Analysis of Variance SOURCE DF SS MS F p Regression 2 59.846 29.923 12.62 0.000 Error 17 40.322 2.372 Total 19 100.167 SOURCE DF SEQ SS C3 1 13.928 C2 1 45.918 Obs. C3 C1 Fit Stdev.Fit Residual St.Resid 1 1.00 2.230 2.683 0.812 -0.453 -0.35 2 1.00 4.990 4.269 0.567 0.721 0.50 3 1.00 3.370 4.913 0.508 -1.543 -1.06 4 1.00 8.540 7.695 0.690 0.845 0.61 5 1.00 8.400 7.810 0.709 0.590 0.43 6 1.00 3.700 4.729 0.521 -1.029 -0.71 7 1.00 7.930 6.132 0.505 1.798 1.24 8 1.00 2.430 4.821 0.514 -2.391 -1.65 9 1.00 5.400 5.787 0.490 -0.387 -0.26 10 1.00 8.440 6.591 0.542 1.849 1.28 11 0.00 3.250 6.037 0.692 -2.787 -2.03R 12 0.00 5.300 5.462 0.606 -0.162 -0.11 13 0.00 1.390 1.646 0.702 -0.256 -0.19 14 0.00 4.690 4.658 0.519 0.032 0.02 15 0.00 6.560 5.417 0.600 1.143 0.81 16 0.00 3.000 4.060 0.489 -1.060 -0.73 17 0.00 5.850 3.485 0.495 2.365 1.62 18 0.00 1.900 2.267 0.609 -0.367 -0.26 19 0.00 3.850 1.577 0.714 2.273 1.67 20 0.00 2.950 4.129 0.490 -1.179 -0.81 R denotes an obs. with a large st. resid.