﻿ ————— 8/11/2011 4:54:07 PM ———————————————————— Welcome to Minitab, press F1 for help. Executing from file: C:\Program Files\Minitab\Minitab 16\English\Macros\Startup.mac This Software was purchased for academic use only. Commercial use of the Software is prohibited. Retrieving worksheet from file: 'C:\Model_selection\nature08230-s2.xls' Worksheet was saved on Mon Jun 21 2010 Results for: nature08230-s2 Regression Analysis: TFR.2005 versus HDI.2005 The regression equation is TFR.2005 = 8.57 - 7.80 HDI.2005 140 cases used, 3 cases contain missing values Predictor Coef SE Coef T P Constant 8.5682 0.2577 33.25 0.000 HDI.2005 -7.8002 0.3500 -22.29 0.000 S = 0.764828 R-Sq = 78.3% R-Sq(adj) = 78.1% Analysis of Variance Source DF SS MS F P Regression 1 290.56 290.56 496.71 0.000 Residual Error 138 80.72 0.58 Total 139 371.28 Unusual Observations Obs HDI.2005 TFR.2005 Fit SE Fit Residual St Resid 42 0.624 5.8900 3.7030 0.0718 2.1870 2.87R 85 0.705 1.2700 3.0658 0.0647 -1.7958 -2.36R 110 0.803 3.8340 2.3062 0.0719 1.5278 2.01R 132 0.482 7.1000 4.8112 0.1036 2.2888 3.02R R denotes an observation with a large standardized residual. Nonlinear Regression: TFR.2005 = theta1 + theta2 * 'HDI.2005' Method Algorithm Gauss-Newton Max iterations 200 Tolerance 0.00001 3 cases with missing values were not used. Starting Values for Parameters Parameter Value theta1 2 theta2 0 Equation TFR.2005 = 8.56818 - 7.80019 * 'HDI.2005' Parameter Estimates Parameter Estimate SE Estimate theta1 8.56818 0.257714 theta2 -7.80019 0.349988 TFR.2005 = theta1 + theta2 * 'HDI.2005' Lack of Fit There are no replicates. Minitab cannot do the lack of fit test based on pure error. Summary Iterations 2 Final SSE 80.7248 DFE 138 MSE 0.584962 S 0.764828 Fitted Line: TFR.2005 versus HDI.2005 Nonlinear Regression: TFR.2005 = theta1 + theta2 * 'HDI.2005' + ... Method Algorithm Gauss-Newton Max iterations 200 Tolerance 0.00001 3 cases with missing values were not used. Starting Values for Parameters Parameter Value theta1 8.5 theta2 -7.8 theta3 0.1 theta4 2 Equation TFR.2005 = 9.3876 - 9.31704 * 'HDI.2005' + 2.30844 * 'HDI.2005' ** 12.86 Parameter Estimates Parameter Estimate SE Estimate theta1 9.3876 0.40152 theta2 -9.3170 0.73419 theta3 2.3084 0.73006 theta4 12.8600 7.85888 TFR.2005 = theta1 + theta2 * 'HDI.2005' + theta3 * 'HDI.2005' ** theta4 Lack of Fit There are no replicates. Minitab cannot do the lack of fit test based on pure error. Summary Iterations 18 Final SSE 70.0943 DFE 136 MSE 0.515400 S 0.717913 Fitted Line: TFR.2005 versus HDI.2005 Nonlinear Regression: TFR.2005 = theta1 + theta2 * 'HDI.2005' + ... Method Algorithm Gauss-Newton Max iterations 200 Tolerance 0.00001 3 cases with missing values were not used. Starting Values for Parameters Parameter Value theta1 8.5 theta2 -7.8 theta3 0.1 theta4 2 Estimates at Each Iteration Iteration SSE theta1 theta2 theta3 theta4 0 80.6140 8.50000 -7.80000 0.10000 2.0000 1 80.6064 8.49748 -7.77188 0.07524 2.3034 2 80.5945 8.49471 -7.74371 0.05156 2.9033 3 80.5824 8.49312 -7.71017 0.02680 5.2393 4 80.2139 8.60266 -7.88471 0.22763 39.5486 5 79.3263 8.62068 -7.91614 0.16012 12.9548 6 70.1907 9.38624 -9.31414 2.31111 12.1659 7 70.0949 9.39778 -9.33876 2.28709 12.5416 8 70.0944 9.39222 -9.32691 2.29903 12.7210 9 70.0944 9.38961 -9.32133 2.30441 12.8001 10 70.0943 9.38846 -9.31888 2.30672 12.8343 11 70.0943 9.38797 -9.31783 2.30770 12.8490 12 70.0943 9.38776 -9.31738 2.30812 12.8553 13 70.0943 9.38767 -9.31718 2.30830 12.8580 14 70.0943 9.38763 -9.31710 2.30838 12.8591 15 70.0943 9.38761 -9.31707 2.30841 12.8596 16 70.0943 9.38760 -9.31705 2.30843 12.8598 17 70.0943 9.38760 -9.31704 2.30843 12.8599 18 70.0943 9.38760 -9.31704 2.30844 12.8600 Equation TFR.2005 = 9.3876 - 9.31704 * 'HDI.2005' + 2.30844 * 'HDI.2005' ** 12.86 Parameter Estimates Parameter Estimate SE Estimate theta1 9.3876 0.40152 theta2 -9.3170 0.73419 theta3 2.3084 0.73006 theta4 12.8600 7.85888 TFR.2005 = theta1 + theta2 * 'HDI.2005' + theta3 * 'HDI.2005' ** theta4 Correlation Matrix for Parameter Estimates theta1 theta2 theta3 theta2 -0.973264 theta3 -0.160616 0.235956 theta4 -0.659614 0.769955 0.717814 Lack of Fit There are no replicates. Minitab cannot do the lack of fit test based on pure error. Summary Iterations 18 Final SSE 70.0943 DFE 136 MSE 0.515400 S 0.717913 Fitted Line: TFR.2005 versus HDI.2005