MTB > name c1 'test1', c2 'test2' MTB > read 'corr.dat' into c1 c2 28 ROWS READ ROW test1 test2 1 47 33 2 54 49 3 48 40 4 47 44 . . . MTB > describe c1 c2 N MEAN MEDIAN TRMEAN STDEV test1 28 48.571 48.500 48.692 4.246 test2 28 39.04 39.00 39.31 6.04 MIN MAX Q1 Q3 test1 38.000 56.000 47.000 52.000 test2 21.00 50.00 35.25 42.00 MTB > stem-and-leaf c1 c2 Stem-and-leaf of test1 N = 28 Leaf Unit = 1.0 1 3 8 2 4 0 4 4 23 5 4 5 9 4 7777 (8) 4 88888999 11 5 000 8 5 22333 3 5 44 1 5 6 Stem-and-leaf of test2 N = 28 Leaf Unit = 1.0 1 2 1 1 2 6 3 23444 (9) 3 567778999 13 4 00000224 5 4 6789 1 5 0 MTB > plot c2 c1 test2 - 50+ * * - * * - * - * - * * 40+ * 2 * * * 2 - * 2 * - * * - * * * * - * 30+ - - - - * 20+ - - ----+---------+---------+---------+---------+---------+test1 38.5 42.0 45.5 49.0 52.5 56.0 MTB > correlation c1 c2 Correlation of test1 and test2 = 0.672 MTB > regress c2 on 1 predictor in c1 resids in c3 fits in c4 The regression equation is test2 = - 7.4 + 0.956 test1 Predictor Coef Stdev t-ratio Constant -7.40 10.07 -0.73 test1 0.9560 0.2065 4.63 s = 4.557 R-sq = 45.2% R-sq(adj) = 43.1% Analysis of Variance SOURCE DF SS MS Regression 1 444.94 444.94 Error 26 540.02 20.77 Total 27 984.96 Unusual Observations Obs. test1 test2 Fit Stdev.Fit Residual St.Resid 13 38.0 32.000 28.930 2.347 3.070 0.79 X 23 43.0 21.000 33.710 1.437 -12.710 -2.94R R denotes an obs. with a large st. resid. X denotes an obs. whose X value gives it large influence. MTB > Note-- omit anomolous data point row 23 MTB > note ****************************************************** MTB > delete row 23 of c1 c2 MTB > plot c2 c1 50.0+ * - * test2 - * - * - * 45.0+ - * - - * * - 40.0+ * * * 2 - * * * - * - * * * - * 35.0+ * - * * * - * - * ----+---------+---------+---------+---------+---------+--test1 38.5 42.0 45.5 49.0 52.5 56.0 MTB > correlation c1 c2 Correlation of test1 and test2 = 0.666 MTB > regress c2 on 1 predictor c1 The regression equation is test2 = 0.95 + 0.794 test1 Predictor Coef Stdev t-ratio Constant 0.951 8.719 0.11 test1 0.7945 0.1781 4.46 s = 3.798 R-sq = 44.3% R-sq(adj) = 42.1% Analysis of Variance SOURCE DF SS MS Regression 1 286.98 286.98 Error 25 360.65 14.43 Total 26 647.63 Unusual Observations Obs. test1 test2 Fit Stdev.Fit Residual St.Resid 13 38.0 32.000 31.141 2.054 0.859 0.27 X X denotes an obs. whose X value gives it large influence. -------------------------------------------------- added 2/17/95 Subject: brief and regress To follow up from question in lecture and my comments about regression output, here are a few minitab tidbits. typing help brief does give a wealth of info; I excerpt just that for regress below (my guess that default was 2 in this version appears correct) MTB > help brief BRIEF [with output code = K] for commands that follow BRIEF controls the amount of output from the REGRESS, DISCRIMINANT, ARIMA and RLINE commands. The larger the value of K, the more output. In all cases, BRIEF 2 is the default. More? y For REGRESS the output is as follows: K = 0 No REGRESS output is displayed. However, all computations are performed, and output from subcommands (for example, PREDICT or PURE) is displayed. Caution, this is an experimental feature which may change in a future release. K = 1 The regression equation, table of coefficients, s, R- squared, R-squared adjusted, and the first part of the analysis of variance table are printed. K = 2 In addition to the output from BRIEF 1, the second part of the analysis of variance table, the "unusual" observa- tions in the table of fits and residuals are printed. Brief 2 is the default output (i.e., what you get if no BRIEF command has been given.) K = 3 In addition to the output from BRIEF 2, the full table of fits and residuals is printed. ----------------------------------------- taking this over to the corr.dat example, here's what you get for full output---fit residual etc for all data points, plus indication of unusual observations. MTB > regress c2 1 c1 The regression equation is C2 = - 7.4 + 0.956 C1 Predictor Coef Stdev t-ratio p Constant -7.40 10.07 -0.73 0.469 C1 0.9560 0.2065 4.63 0.000 s = 4.557 R-sq = 45.2% R-sq(adj) = 43.1% Analysis of Variance SOURCE DF SS MS F p Regression 1 444.94 444.94 21.42 0.000 Error 26 540.02 20.77 Total 27 984.96 Obs. C1 C2 Fit Stdev.Fit Residual St.Resid 1 47.0 33.000 37.533 0.920 -4.533 -1.02 2 54.0 49.000 44.225 1.414 4.775 1.10 3 48.0 40.000 38.489 0.869 1.511 0.34 4 47.0 44.000 37.533 0.920 6.467 1.45 5 50.0 48.000 40.401 0.910 7.599 1.70 6 45.0 36.000 35.621 1.134 0.379 0.09 Continue? y 7 50.0 35.000 40.401 0.910 -5.401 -1.21 8 56.0 50.000 46.137 1.760 3.863 0.92 9 54.0 46.000 44.225 1.414 1.775 0.41 10 48.0 37.000 38.489 0.869 -1.489 -0.33 11 53.0 40.000 43.269 1.256 -3.269 -0.75 12 47.0 39.000 37.533 0.920 1.467 0.33 13 38.0 32.000 28.930 2.347 3.070 0.79 X 14 47.0 42.000 37.533 0.920 4.467 1.00 15 48.0 39.000 38.489 0.869 0.511 0.11 16 49.0 37.000 39.445 0.866 -2.445 -0.55 17 53.0 42.000 43.269 1.256 -1.269 -0.29 18 53.0 40.000 43.269 1.256 -3.269 -0.75 19 49.0 40.000 39.445 0.866 0.555 0.12 20 52.0 47.000 42.313 1.115 4.687 1.06 21 40.0 37.000 30.842 1.969 6.158 1.50 22 48.0 34.000 38.489 0.869 -4.489 -1.00 23 43.0 21.000 33.710 1.437 -12.710 -2.94R 24 50.0 40.000 40.401 0.910 -0.401 -0.09 25 49.0 34.000 39.445 0.866 -5.445 -1.22 26 52.0 39.000 42.313 1.115 -3.313 -0.75 27 48.0 38.000 38.489 0.869 -0.489 -0.11 28 42.0 34.000 32.754 1.608 1.246 0.29 Continue? y R denotes an obs. with a large st. resid. X denotes an obs. whose X value gives it large influence. MTB > stop