MTB > read data from 'marks.dat' c1 c2 c3 c4 17 ROWS READ MTB > name c1 'FINA' MTB > name c2 'HWB' MTB > name c3 'MTB' MTB > name c4 'FINB' MTB > describe c1-c4 N MEAN MEDIAN TRMEAN STDEV FINA 17 157.59 170.00 159.60 28.99 HWB 17 59.06 61.00 59.53 5.30 MTB 17 56.94 59.00 57.67 18.10 FINB 17 118.76 117.00 120.00 20.68 MIN MAX Q1 Q3 FINA 92.00 193.00 133.00 182.00 HWB 46.00 65.00 58.00 62.00 MTB 18.00 85.00 49.00 70.00 FINB 73.00 146.00 103.00 136.50 MTB > corr c1-c4 FINA HWB MTB HWB 0.485 MTB 0.770 0.385 FINB 0.854 0.397 0.731 MTB > brief 3 MTB > print c1 c3 c4 ROW FINA MTB FINB 1 92 18 73 2 131 50 115 3 193 85 146 4 132 43 103 5 130 62 115 6 176 66 117 7 153 53 103 8 170 59 142 9 179 52 132 10 135 48 121 11 177 56 141 12 187 75 136 13 185 74 137 14 134 66 92 15 140 21 94 16 192 78 136 17 173 62 116 MTB > regress c4 2 c1 c3 resids c5 fits c6; SUBC> residuals c7. The regression equation is FINB = 26.7 + 0.509 FINA + 0.208 MTB Predictor Coef Stdev t-ratio Constant 26.65 16.14 1.65 FINA 0.5092 0.1514 3.36 MTB 0.2083 0.2426 0.86 s = 11.21 R-sq = 74.3% R-sq(adj) = 70.6% Analysis of Variance SOURCE DF SS MS Regression 2 5083.2 2541.6 Error 14 1759.9 125.7 Total 16 6843.1 SOURCE DF SEQ SS FINA 1 4990.4 MTB 1 92.7 Obs. FINA FINB Fit Stdev.Fit Residual 1 92 73.00 77.25 7.13 -4.25 2 131 115.00 103.78 4.00 11.22 3 193 146.00 142.64 5.13 3.36 4 132 103.00 102.83 3.70 0.17 5 130 115.00 105.77 5.85 9.23 6 176 117.00 130.03 3.25 -13.03 7 153 103.00 115.61 2.79 -12.61 8 170 142.00 125.51 3.12 16.49 9 179 132.00 128.64 5.03 3.36 10 135 121.00 105.40 3.52 15.60 11 177 141.00 128.45 4.14 12.55 12 187 136.00 137.50 4.05 -1.50 13 185 137.00 136.28 3.91 0.72 14 134 92.00 108.64 6.09 -16.64 15 140 94.00 102.32 7.40 -8.32 16 192 136.00 140.68 4.44 -4.68 17 173 116.00 127.67 3.15 -11.67 MTB > name c5 'STDRES' MTB > name c6 'FITTED' MTB > namee c7 'RESIDS' MTB > describe c5-c7 N MEAN MEDIAN TRMEAN STDEV STDRES 17 -0.018 0.016 -0.005 1.025 FITTED 17 118.76 125.51 119.94 17.82 RESIDS 17 -0.00 0.17 0.01 10.49 MIN MAX Q1 Q3 STDRES -1.767 1.531 -1.036 1.018 FITTED 77.25 142.64 104.59 133.15 RESIDS -16.64 16.49 -9.99 10.23 MTB > plot c7 c6 - RESIDS - * * - - * * 10+ * - - - * * - 0+ * * - * - * * - - * -10+ - * * - * - * - ------+---------+---------+---------+---------+---------+FITTED 84 96 108 120 132 144 MTB > plot c4 c1 - 150+ - * FINB - * * - ** * - * 125+ - * - ** ** - - * * 100+ - * - * - - 75+ * - - ------+---------+---------+---------+---------+---------+FINA 100 120 140 160 180 200 MTB > plot c4 c3 - 150+ - * FINB - * * - ** * - * 125+ - * - * 2 * - - * * 100+ - * - * - - 75+ * - - ----+---------+---------+---------+---------+---------+--MTB 15 30 45 60 75 90 **************************************************** BEGIN ADJUSTED VARIABLE INTERPRETATION OF MULTIPLE REGRESSION COEEFICIENTS***************************** MTB > plot c1 c3 FINA - - * * - ** 180+ * * - * * - * - - * 150+ - - * * - * * * * - 120+ - - - - 90+ * ----+---------+---------+---------+---------+---------+--MTB 15 30 45 60 75 90 MTB > nobrief MTB > regress c1 1 c3 The regression equation is FINA = 87.4 + 1.23 MTB Predictor Coef Stdev t-ratio Constant 87.40 15.74 5.55 MTB 1.2326 0.2641 4.67 s = 19.12 R-sq = 59.2% R-sq(adj) = 56.5% Analysis of Variance SOURCE DF SS MS Regression 1 7959.7 7959.7 Error 15 5482.4 365.5 Total 16 13442.1 Obs. MTB FINA Fit Stdev.Fit Residual 1 18.0 92.00 109.59 11.28 -17.59 2 50.0 131.00 149.03 4.99 -18.03 3 85.0 193.00 192.17 8.74 0.83 4 43.0 132.00 140.40 5.92 -8.40 5 62.0 130.00 163.82 4.83 -33.82 6 66.0 176.00 168.75 5.22 7.25 7 53.0 153.00 152.73 4.75 0.27 8 59.0 170.00 160.13 4.67 9.87 9 52.0 179.00 151.50 4.82 27.50 10 48.0 135.00 146.57 5.20 -11.57 11 56.0 177.00 156.43 4.64 20.57 12 75.0 187.00 179.85 6.65 7.15 13 74.0 185.00 178.62 6.47 6.38 14 66.0 134.00 168.75 5.22 -34.75 15 21.0 140.00 113.29 10.57 26.71 16 78.0 192.00 183.55 7.24 8.45 17 62.0 173.00 163.82 4.83 9.18 MTB > let c8 = c1 - 1.2326*c3 MTB > describe c8 N MEAN MEDIAN TRMEAN STDEV C8 17 87.40 93.79 87.89 18.51 MIN MAX Q1 Q3 C8 52.65 114.90 72.82 96.93 MTB > name c8 'fdotm' MTB > plot c4 c8 - 150+ - * FINB - * * - *** - * 125+ - * - * * ** - - * * 100+ - * - * - - 75+ * - - +---------+---------+---------+---------+---------+------fdotm 48 60 72 84 96 108 MTB > regress c4 1 c8 The regression equation is FINB = 74.3 + 0.509 fdotm Predictor Coef Stdev t-ratio Constant 74.26 22.91 3.24 fdotm 0.5092 0.2568 1.98 s = 19.01 R-sq = 20.8% R-sq(adj) = 15.5% Analysis of Variance SOURCE DF SS MS Regression 1 1421.7 1421.7 Error 15 5421.3 361.4 Total 16 6843.1 Obs. fdotm FINB Fit Stdev.Fit Residual 1 70 73.00 109.81 6.45 -36.81 2 69 115.00 109.58 6.53 5.42 3 88 146.00 119.19 4.62 26.81 4 79 103.00 114.48 5.09 -11.48 5 54 115.00 101.54 9.83 13.46 6 95 117.00 122.45 4.97 -5.45 7 88 103.00 118.90 4.61 -15.90 8 97 142.00 123.79 5.26 18.21 9 115 132.00 132.77 8.43 -0.77 10 76 121.00 112.87 5.48 8.13 11 108 141.00 129.24 7.01 11.76 12 95 136.00 122.41 4.96 13.59 13 94 137.00 122.02 4.89 14.98 14 53 92.00 101.07 10.04 -9.07 15 114 94.00 132.37 8.26 -38.37 16 96 136.00 123.07 5.10 12.93 17 97 116.00 123.44 5.18 -7.44 R denotes an obs. with a large st. resid. MTB > regress c3 1 c1 The regression equation is MTB = - 18.8 + 0.480 FINA Predictor Coef Stdev t-ratio Constant -18.76 16.48 -1.14 FINA 0.4804 0.1029 4.67 s = 11.94 R-sq = 59.2% R-sq(adj) = 56.5% Analysis of Variance SOURCE DF SS MS Regression 1 3102.2 3102.2 Error 15 2136.7 142.4 Total 16 5238.9 Obs. FINA MTB Fit Stdev.Fit Residual 1 92 18.00 25.43 7.35 -7.43X 2 131 50.00 44.17 3.98 5.83 3 193 85.00 73.95 4.65 11.05 4 132 43.00 44.65 3.91 -1.65 5 130 62.00 43.69 4.06 18.31 6 176 66.00 65.79 3.46 0.21 7 153 53.00 54.74 2.93 -1.74 8 170 59.00 62.90 3.16 -3.90 9 179 52.00 67.23 3.64 -15.23 10 135 48.00 46.09 3.71 1.91 11 177 56.00 66.27 3.52 -10.27 12 187 75.00 71.07 4.19 3.93 13 185 74.00 70.11 4.04 3.89 14 134 66.00 45.61 3.78 20.39 15 140 21.00 48.49 3.41 -27.49 16 192 78.00 73.47 4.57 4.53 17 173 62.00 64.34 3.30 -2.34 R denotes an obs. with a large st. resid. X denotes an obs. whose X value gives it large influence. MTB > let c9 = c3 - .4804*c1 MTB > describe c9 N MEAN MEDIAN TRMEAN STDEV C9 17 -18.76 -18.55 -18.29 11.56 MIN MAX Q1 Q3 C9 -46.26 1.63 -24.43 -13.58 MTB > regress c4 1 c9 The regression equation is FINB = 123 + 0.208 C9 Predictor Coef Stdev t-ratio Constant 122.67 10.03 12.23 C9 0.2083 0.4589 0.45 s = 21.21 R-sq = 1.4% R-sq(adj) = 0.0% Analysis of Variance SOURCE DF SS MS Regression 1 92.7 92.7 Error 15 6750.3 450.0 Total 16 6843.1 Obs. C9 FINB Fit Stdev.Fit Residual 1 -26.2 73.00 117.22 6.17 -44.22 2 -12.9 115.00 119.98 5.80 -4.98 3 -7.7 146.00 121.07 7.22 24.93 4 -20.4 103.00 118.42 5.20 -15.42 5 -0.5 115.00 122.58 9.85 -7.58 6 -18.6 117.00 118.81 5.15 -1.81 7 -20.5 103.00 118.40 5.21 -15.40 8 -22.7 142.00 117.95 5.45 24.05 9 -34.0 132.00 115.59 8.68 16.41 10 -16.9 121.00 119.16 5.22 1.84 11 -29.0 141.00 116.63 6.98 24.37 12 -14.8 136.00 119.58 5.45 16.42 13 -14.9 137.00 119.58 5.45 17.42 14 1.6 92.00 123.01 10.68 -31.01 15 -46.3 94.00 113.04 13.63 -19.04X 16 -14.2 136.00 119.71 5.55 16.29 17 -21.1 116.00 118.28 5.26 -2.28 R denotes an obs. with a large st. resid. X denotes an obs. whose X value gives it large influence. MTB > plot c4 c9 - 150+ - * FINB - * * - 2* - * 125+ - * - * * * * - - ** 100+ - * - * - - 75+ * - - --+---------+---------+---------+---------+---------+----C9 -50 -40 -30 -20 -10 0 FORMATION OF ADJUSTED VARIABLE FOR PARTIAL CORRELATION ************************************************* MTB > MTB > regress c4 1 c1 The regression equation is FINB = 22.7 + 0.609 FINA Predictor Coef Stdev t-ratio Constant 22.75 15.34 1.48 FINA 0.60931 0.09586 6.36 s = 11.11 R-sq = 72.9% R-sq(adj) = 71.1% Analysis of Variance SOURCE DF SS MS Regression 1 4990.4 4990.4 Error 15 1852.6 123.5 Total 16 6843.1 Obs. FINA FINB Fit Stdev.Fit Residual 1 92 73.00 78.80 6.84 -5.80X 2 131 115.00 102.56 3.71 12.44 3 193 146.00 140.34 4.33 5.66 4 132 103.00 103.17 3.64 -0.17 5 130 115.00 101.96 3.78 13.04 6 176 117.00 129.98 3.22 -12.98 7 153 103.00 115.97 2.73 -12.97 8 170 142.00 126.33 2.95 15.67 9 179 132.00 131.81 3.39 0.19 10 135 121.00 105.00 3.46 16.00 11 177 141.00 130.59 3.28 10.41 12 187 136.00 136.69 3.90 -0.69 13 185 137.00 135.47 3.76 1.53 14 134 92.00 104.39 3.52 -12.39 15 140 94.00 108.05 3.18 -14.05 16 192 136.00 139.73 4.26 -3.73 17 173 116.00 128.16 3.07 -12.16 X denotes an obs. whose X value gives it large influence. MTB > let c10 = c4 - .60931 * c1 MTB > plot c10 c9 - 40+ - * * C10 - * * - * - 30+ - * - - * - * * * 20+ * - - * - - 10+ 2 * * - * - --+---------+---------+---------+---------+---------+----C9 -50 -40 -30 -20 -10 0 MTB > name c10 'bdota' MTB > name c9 'mdotf' MTB > plot c10 c9 - 40+ - * * bdota - * * - * - 30+ - * - - * - * * * 20+ * - - * - - 10+ 2 * * - * - --+---------+---------+---------+---------+---------+----mdotf -50 -40 -30 -20 -10 0 MTB > MTB > corr c10 c9 Correlation of bdota and mdotf = 0.224 MTB > corr c1-c10 FINA HWB MTB FINB STDRES FITTED RESIDS fdotm HWB 0.485 MTB 0.770 0.385 FINB 0.854 0.397 0.731 STDRES 0.026 -0.038 0.033 0.531 FITTED 0.991 0.483 0.849 0.862 0.029 RESIDS -0.000 -0.038 -0.000 0.507 0.998 -0.000 fdotm 0.639 0.294 0.000 0.456 0.002 0.529 0.000 mdotf -0.000 0.020 0.639 0.116 0.019 0.135 -0.000 -0.770 bdota -0.000 -0.033 0.143 0.520 0.977 0.030 0.975 -0.172 mdotf bdota 0.224