TSP Version 4.5 (01/23/01) DOS/Win 4MB Copyright (C) 2001 TSP International ALL RIGHTS RESERVED 01/24/01 10:22AM In case of questions or problems, see your local TSP consultant or send a description of the problem and the associated TSP output to: TSP International P.O. Box 61015 Palo Alto, CA 94306 USA PROGRAM COMMAND *************************************************************** 1 options double crt; 2 2 smpl 1,14; 3 read y x; 3 10.07 77.6 14.73 114.9 17.94 141.1 23.93 190.8 29.61 239.9 35.18 289.0 3 40.02 332.8 44.82 378.4 50.76 434.8 55.05 477.3 61.01 536.8 66.40 593.1 3 75.47 689.1 81.78 760.0 ; 4 ? or 4 ?read(file='misra1.xls'); 4 4 title 'Misra1a'; 5 frml eqa y = b1*(1-exp[-b2*x]); 6 6 title 'A: standard starting values'; 7 param b1,500 b2,.0001 ; 8 lsq eqa; ? default iteration options 9 9 param b1,500 b2,.0001 ; ? standard starting values 10 lsq(tol=1e-11,maxit=100,maxsqz=25) eqa; ? high accuracy iteration options 11 ? Note: this yields a "failure to improve objective function message", 11 ? so it shows the extra output provided in this case. I consider it to 11 ? be converged, on the basis of the very small norm of the gradient. 11 11 title 'A: very close starting values'; 12 param b1,250 b2,.0005 ; 13 lsq(tol=1e-11,maxit=100,maxsqz=25) eqa; 14 14 ?---------------- 14 14 title 'Misra1b'; 15 frml eqb y = b1 * (1-(1+b2*x/2)**(-2)); 16 16 title 'B: standard starting values'; 17 param b1,500 b2,.0001 ; 18 lsq eqb; ? default iteration options 19 19 title 'B: very close starting values'; 20 param b1,300 b2,.0002 ; 21 lsq eqb; 22 22 ?---------------- 22 22 title 'Misra1c'; 23 frml eqc y = b1 * (1-(1+2*b2*x)**(-.5)); 24 24 title 'C: standard starting values'; 25 param b1,500 b2,.0001 ; 26 lsq eqc; ? default iteration options 27 27 title 'C: very close starting values'; 28 param b1,600 b2,.0002 ; 29 lsq eqc; 30 30 ?---------------- 30 30 title 'Misra1d'; 31 frml eqd y = b1*b2*x*((1+b2*x)**(-1)); 32 32 title 'D: standard starting values'; 33 param b1,500 b2,.0001 ; 34 lsq eqd; ? default iteration options 35 35 title 'D: very close starting values'; 36 param b1,450 b2,.0003 ; 37 lsq eqd; EXECUTION ******************************************************************************* Current sample: 1 to 14 Misra1a ======= A: standard starting values =========================== NONLINEAR LEAST SQUARES ======================= EQUATIONS: EQA Working space used: 311 STARTING VALUES B1 B2 VALUE 500.00000 0.000100000 F= 66.389996551 FNEW= 66.336227686 ISQZ= 4 STEP= .796E-02 CRIT= 12.000 F= 66.336227686 FNEW= 66.297811603 ISQZ= 3 STEP= .016 CRIT= 12.000 F= 66.297811603 FNEW= 66.202980938 ISQZ= 3 STEP= .016 CRIT= 12.000 F= 66.202980938 FNEW= 66.117333367 ISQZ= 4 STEP= .031 CRIT= 12.000 F= 66.117333367 FNEW= 66.021204334 ISQZ= 2 STEP= .063 CRIT= 12.000 F= 66.021204334 FNEW= 65.581245517 ISQZ= 2 STEP= .165 CRIT= 12.000 F= 65.581245517 FNEW= 39.220884080 ISQZ= 0 STEP= 1. CRIT= 12.000 F= 39.220884080 FNEW= 39.208745447 ISQZ= 1 STEP= .750 CRIT= 11.991 F= 39.208745447 FNEW= 9.9034042691 ISQZ= 0 STEP= 1. CRIT= 11.993 F= 9.9034042691 FNEW= -13.188889355 ISQZ= 0 STEP= 1. CRIT= 11.557 F= -13.188889355 FNEW= -13.189520042 ISQZ= 0 STEP= 1. CRIT= .10811E-02 F= -13.189520042 FNEW= -13.189520042 ISQZ= 0 STEP= 1. CRIT= .10283E-09 CONVERGENCE ACHIEVED AFTER 12 ITERATIONS 43 FUNCTION EVALUATIONS. Number of observations = 14 Log likelihood = 13.1895 Schwarz B.I.C. = -10.5505 Standard Parameter Estimate Error t-statistic P-value B1 238.942 2.70701 88.2680 [.000] B2 .550156E-03 .726687E-05 75.7075 [.000] Standard Errors computed from quadratic form of analytic first derivatives (Gauss) Equation: EQA Dependent variable: Y Mean of dep. var. = 43.3407 R-squared = .999985 Std. dev. of dep. var. = 22.8065 Adjusted R-squared = .999984 Sum of squared residuals = .124551 LM het. test = 2.21928 [.136] Variance of residuals = .010379 Durbin-Watson = .561045 [<.006] Std. error of regression = .101879 NONLINEAR LEAST SQUARES ======================= EQUATIONS: EQA Working space used: 311 STARTING VALUES B1 B2 VALUE 500.00000 0.000100000 F= 66.389996551 FNEW= 66.336227686 ISQZ= 4 STEP= .796E-02 CRIT= 12.000 F= 66.336227686 FNEW= 66.297811603 ISQZ= 3 STEP= .016 CRIT= 12.000 F= 66.297811603 FNEW= 66.202980938 ISQZ= 3 STEP= .016 CRIT= 12.000 F= 66.202980938 FNEW= 66.117333367 ISQZ= 4 STEP= .031 CRIT= 12.000 F= 66.117333367 FNEW= 66.021204334 ISQZ= 2 STEP= .063 CRIT= 12.000 F= 66.021204334 FNEW= 65.581245517 ISQZ= 2 STEP= .165 CRIT= 12.000 F= 65.581245517 FNEW= 39.220884080 ISQZ= 0 STEP= 1. CRIT= 12.000 F= 39.220884080 FNEW= 39.208745447 ISQZ= 1 STEP= .750 CRIT= 11.991 F= 39.208745447 FNEW= 9.9034042691 ISQZ= 0 STEP= 1. CRIT= 11.993 F= 9.9034042691 FNEW= -13.188889355 ISQZ= 0 STEP= 1. CRIT= 11.557 F= -13.188889355 FNEW= -13.189520042 ISQZ= 0 STEP= 1. CRIT= .10811E-02 F= -13.189520042 FNEW= -13.189520042 ISQZ= 0 STEP= 1. CRIT= .10283E-09 F= -13.189520042 FNEW= -13.189520042 ISQZ= 5 STEP= .977E-03 CRIT= .80474E-15 F= -13.189520042 FNEW= -13.189520042 ISQZ= 3 STEP= .016 CRIT= .80316E-15 F= -13.189520042 FNEW= -13.189520042 ISQZ= 11 STEP= .238E-06 CRIT= .77834E-15 F= -13.189520042 FNEW= -13.189520042 ISQZ= 26 STEP= .364E-11 CRIT= .77834E-15 B1 B2 ESTIMATE 238.94213 0.00055016 CHANGES 7.54329D-08 -2.02736D-13 FAILURE TO IMPROVE OBJECTIVE FUNCTION AFTER 16 ITERATIONS (MAXSQZ) 95 FUNCTION EVALUATIONS. Number of observations = 14 Log likelihood = 13.1895 Schwarz B.I.C. = -10.5505 Standard Parameter Estimate Error t-statistic P-value B1 238.942 2.70701 88.2680 [.000] B2 .550156E-03 .726687E-05 75.7075 [.000] Standard Errors computed from quadratic form of analytic first derivatives (Gauss) Equation: EQA Dependent variable: Y Mean of dep. var. = 43.3407 R-squared = .999985 Std. dev. of dep. var. = 22.8065 Adjusted R-squared = .999984 Sum of squared residuals = .124551 LM het. test = 2.21928 [.136] Variance of residuals = .010379 Durbin-Watson = .561045 [<.006] Std. error of regression = .101879 A: very close starting values ============================= NONLINEAR LEAST SQUARES ======================= EQUATIONS: EQA Working space used: 311 STARTING VALUES B1 B2 VALUE 250.00000 0.00050000 F= 28.002705698 FNEW= 2.5392486580 ISQZ= 0 STEP= 1. CRIT= 11.966 F= 2.5392486580 FNEW= -13.188712716 ISQZ= 0 STEP= 1. CRIT= 10.731 F= -13.188712716 FNEW= -13.189520042 ISQZ= 0 STEP= 1. CRIT= .13839E-02 F= -13.189520042 FNEW= -13.189520042 ISQZ= 0 STEP= 1. CRIT= .32087E-11 F= -13.189520042 FNEW= -13.189520042 ISQZ= 8 STEP= .153E-04 CRIT= .25871E-16 F= -13.189520042 FNEW= -13.189520042 ISQZ= 0 STEP= 1. CRIT= .25871E-16 F= -13.189520042 FNEW= -13.189520042 ISQZ= 1 STEP= .250 CRIT= .20467E-21 CONVERGENCE ACHIEVED AFTER 7 ITERATIONS 22 FUNCTION EVALUATIONS. Number of observations = 14 Log likelihood = 13.1895 Schwarz B.I.C. = -10.5505 Standard Parameter Estimate Error t-statistic P-value B1 238.942 2.70701 88.2680 [.000] B2 .550156E-03 .726687E-05 75.7075 [.000] Standard Errors computed from quadratic form of analytic first derivatives (Gauss) Equation: EQA Dependent variable: Y Mean of dep. var. = 43.3407 R-squared = .999985 Std. dev. of dep. var. = 22.8065 Adjusted R-squared = .999984 Sum of squared residuals = .124551 LM het. test = 2.21928 [.136] Variance of residuals = .010379 Durbin-Watson = .561045 [<.006] Std. error of regression = .101879 Misra1b ======= B: standard starting values =========================== NONLINEAR LEAST SQUARES ======================= EQUATIONS: EQB Working space used: 335 STARTING VALUES B1 B2 VALUE 500.00000 0.000100000 F= 66.527674763 FNEW= 66.370860145 ISQZ= 4 STEP= .025 CRIT= 12.000 F= 66.370860145 FNEW= 66.258311960 ISQZ= 2 STEP= .063 CRIT= 12.000 F= 66.258311960 FNEW= 65.751522701 ISQZ= 2 STEP= .160 CRIT= 12.000 F= 65.751522701 FNEW= 42.088197126 ISQZ= 0 STEP= 1. CRIT= 12.000 F= 42.088197126 FNEW= 40.619933963 ISQZ= 1 STEP= .693 CRIT= 11.996 F= 40.619933963 FNEW= 14.077114167 ISQZ= 0 STEP= 1. CRIT= 11.997 F= 14.077114167 FNEW= -16.693469308 ISQZ= 0 STEP= 1. CRIT= 11.852 F= -16.693469308 FNEW= -16.696895527 ISQZ= 0 STEP= 1. CRIT= .58719E-02 F= -16.696895527 FNEW= -16.696895527 ISQZ= 0 STEP= 1. CRIT= .71563E-09 CONVERGENCE ACHIEVED AFTER 9 ITERATIONS 27 FUNCTION EVALUATIONS. Number of observations = 14 Log likelihood = 16.6969 Schwarz B.I.C. = -14.0578 Standard Parameter Estimate Error t-statistic P-value B1 337.997 3.16440 106.813 [.000] B2 .390391E-03 .425473E-05 91.7545 [.000] Standard Errors computed from quadratic form of analytic first derivatives (Gauss) Equation: EQB Dependent variable: Y Mean of dep. var. = 43.3407 R-squared = .999990 Std. dev. of dep. var. = 22.8065 Adjusted R-squared = .999990 Sum of squared residuals = .075465 LM het. test = 3.08865 [.079] Variance of residuals = .628872E-02 Durbin-Watson = .731377 [<.014] Std. error of regression = .079301 B: very close starting values ============================= NONLINEAR LEAST SQUARES ======================= EQUATIONS: EQB Working space used: 335 STARTING VALUES B1 B2 VALUE 300.00000 0.00020000 F= 64.852736395 FNEW= 62.383234895 ISQZ= 1 STEP= .601 CRIT= 12.000 F= 62.383234895 FNEW= 34.782214920 ISQZ= 0 STEP= 1. CRIT= 12.000 F= 34.782214920 FNEW= -15.982081224 ISQZ= 0 STEP= 1. CRIT= 11.992 F= -15.982081224 FNEW= -16.696485350 ISQZ= 0 STEP= 1. CRIT= 1.1647 F= -16.696485350 FNEW= -16.696895527 ISQZ= 0 STEP= 1. CRIT= .70314E-03 CONVERGENCE ACHIEVED AFTER 5 ITERATIONS 11 FUNCTION EVALUATIONS. Number of observations = 14 Log likelihood = 16.6969 Schwarz B.I.C. = -14.0578 Standard Parameter Estimate Error t-statistic P-value B1 337.997 3.16439 106.813 [.000] B2 .390391E-03 .425473E-05 91.7545 [.000] Standard Errors computed from quadratic form of analytic first derivatives (Gauss) Equation: EQB Dependent variable: Y Mean of dep. var. = 43.3407 R-squared = .999990 Std. dev. of dep. var. = 22.8065 Adjusted R-squared = .999990 Sum of squared residuals = .075465 LM het. test = 3.08867 [.079] Variance of residuals = .628872E-02 Durbin-Watson = .731377 [<.014] Std. error of regression = .079301 Misra1c ======= C: standard starting values =========================== NONLINEAR LEAST SQUARES ======================= EQUATIONS: EQC Working space used: 335 STARTING VALUES B1 B2 VALUE 500.00000 0.000100000 F= 66.904880809 FNEW= 66.813438836 ISQZ= 1 STEP= .727 CRIT= 12.000 F= 66.813438836 FNEW= 64.564276188 ISQZ= 0 STEP= 1. CRIT= 12.000 F= 64.564276188 FNEW= 62.813813395 ISQZ= 2 STEP= .460 CRIT= 12.000 F= 62.813813395 FNEW= 30.890069360 ISQZ= 0 STEP= 1. CRIT= 12.000 F= 30.890069360 FNEW= -19.700810973 ISQZ= 0 STEP= 1. CRIT= 11.993 F= -19.700810973 FNEW= -20.973061317 ISQZ= 0 STEP= 1. CRIT= 1.9944 F= -20.973061317 FNEW= -20.973208600 ISQZ= 0 STEP= 1. CRIT= .25248E-03 CONVERGENCE ACHIEVED AFTER 7 ITERATIONS 17 FUNCTION EVALUATIONS. Number of observations = 14 Log likelihood = 20.9732 Schwarz B.I.C. = -18.3342 Standard Parameter Estimate Error t-statistic P-value B1 636.427 4.66383 136.460 [.000] B2 .208136E-03 .177284E-05 117.403 [.000] Standard Errors computed from quadratic form of analytic first derivatives (Gauss) Equation: EQC Dependent variable: Y Mean of dep. var. = 43.3407 R-squared = .999995 Std. dev. of dep. var. = 22.8065 Adjusted R-squared = .999994 Sum of squared residuals = .040967 LM het. test = 3.20136 [.074] Variance of residuals = .341390E-02 Durbin-Watson = 1.10078 [<.065] Std. error of regression = .058429 C: very close starting values ============================= NONLINEAR LEAST SQUARES ======================= EQUATIONS: EQC Working space used: 335 STARTING VALUES B1 B2 VALUE 600.00000 0.00020000 F= 40.382337849 FNEW= -11.614152472 ISQZ= 0 STEP= 1. CRIT= 11.998 F= -11.614152472 FNEW= -20.973078593 ISQZ= 0 STEP= 1. CRIT= 8.8483 F= -20.973078593 FNEW= -20.973208600 ISQZ= 0 STEP= 1. CRIT= .22286E-03 CONVERGENCE ACHIEVED AFTER 3 ITERATIONS 6 FUNCTION EVALUATIONS. Number of observations = 14 Log likelihood = 20.9732 Schwarz B.I.C. = -18.3342 Standard Parameter Estimate Error t-statistic P-value B1 636.427 4.66383 136.460 [.000] B2 .208136E-03 .177284E-05 117.403 [.000] Standard Errors computed from quadratic form of analytic first derivatives (Gauss) Equation: EQC Dependent variable: Y Mean of dep. var. = 43.3407 R-squared = .999995 Std. dev. of dep. var. = 22.8065 Adjusted R-squared = .999994 Sum of squared residuals = .040967 LM het. test = 3.20138 [.074] Variance of residuals = .341390E-02 Durbin-Watson = 1.10078 [<.065] Std. error of regression = .058429 Misra1d ======= D: standard starting values =========================== NONLINEAR LEAST SQUARES ======================= EQUATIONS: EQD Working space used: 347 STARTING VALUES B1 B2 VALUE 500.00000 0.000100000 F= 66.659081842 FNEW= 66.273932581 ISQZ= 2 STEP= .063 CRIT= 12.000 F= 66.273932581 FNEW= 65.583213937 ISQZ= 1 STEP= .250 CRIT= 12.000 F= 65.583213937 FNEW= 44.324003948 ISQZ= 0 STEP= 1. CRIT= 12.000 F= 44.324003948 FNEW= 20.106463664 ISQZ= 0 STEP= 1. CRIT= 11.998 F= 20.106463664 FNEW= -16.273627235 ISQZ= 0 STEP= 1. CRIT= 11.953 F= -16.273627235 FNEW= -18.732870193 ISQZ= 0 STEP= 1. CRIT= 3.5549 F= -18.732870193 FNEW= -18.732870291 ISQZ= 0 STEP= 1. CRIT= .16842E-06 CONVERGENCE ACHIEVED AFTER 7 ITERATIONS 17 FUNCTION EVALUATIONS. Number of observations = 14 Log likelihood = 18.7329 Schwarz B.I.C. = -16.0938 Standard Parameter Estimate Error t-statistic P-value B1 437.370 3.64892 119.863 [.000] B2 .302273E-03 .293344E-05 103.044 [.000] Standard Errors computed from quadratic form of analytic first derivatives (Gauss) Equation: EQD Dependent variable: Y Mean of dep. var. = 43.3407 R-squared = .999993 Std. dev. of dep. var. = 22.8065 Adjusted R-squared = .999992 Sum of squared residuals = .056419 LM het. test = 3.31624 [.069] Variance of residuals = .470161E-02 Durbin-Watson = .878842 [<.027] Std. error of regression = .068568 D: very close starting values ============================= NONLINEAR LEAST SQUARES ======================= EQUATIONS: EQD Working space used: 347 STARTING VALUES B1 B2 VALUE 450.00000 0.00030000 F= 20.968531281 FNEW= -18.587899930 ISQZ= 0 STEP= 1. CRIT= 11.959 F= -18.587899930 FNEW= -18.732870290 ISQZ= 0 STEP= 1. CRIT= .24596 F= -18.732870290 FNEW= -18.732870291 ISQZ= 0 STEP= 1. CRIT= .21525E-08 CONVERGENCE ACHIEVED AFTER 3 ITERATIONS 6 FUNCTION EVALUATIONS. Number of observations = 14 Log likelihood = 18.7329 Schwarz B.I.C. = -16.0938 Standard Parameter Estimate Error t-statistic P-value B1 437.370 3.64892 119.863 [.000] B2 .302273E-03 .293344E-05 103.044 [.000] Standard Errors computed from quadratic form of analytic first derivatives (Gauss) Equation: EQD Dependent variable: Y Mean of dep. var. = 43.3407 R-squared = .999993 Std. dev. of dep. var. = 22.8065 Adjusted R-squared = .999992 Sum of squared residuals = .056419 LM het. test = 3.31624 [.069] Variance of residuals = .470161E-02 Durbin-Watson = .878842 [<.027] Std. error of regression = .068568 ******************************************************************************* END OF OUTPUT. MEMORY USAGE: ITEM: DATA ARRAY TOTAL MEMORY UNITS: (4-BYTE WORDS) (MEGABYTES) MEMORY ALLOCATED : 500000 4.0 MEMORY ACTUALLY REQUIRED : 1765 2.1 CURRENT VARIABLE STORAGE : 1410