--------------------------------------- BETA - GAUSS1 --------------------------------------- NLS Y B1*EXP( -B2*X )+B3*EXP( -(X-B4)**2/B5**2 )+B6*EXP(-(X-B7)**2/B8**2 ) / INPUTB B1=97.0 B2=0.009 B3=100.0 B4=65.0 B5=20.0 B6=70.0 B7=178.0 B8=16.5 NONLINEAR LEAST SQUARES ESTIMATION NONLINEAR EQUATION = B1*EXP(-B2*X)+B3*EXP(-(X-B4)**2/B5**2)+B6*EXP(-(X-B7)**2/B8**2) ANALYTIC DERIVATIVES MAXIMUM NUMBER OF DIGITS OF CONVERGENCE OF SUM OF SQUARED RESIDUALS 16. ACTUAL NUMBER OF DIGITS OF CONVERGENCE OF SUM OF SQUARED RESIDUALS 16. MAXIMUM NUMBER OF ITERATIONS 100 ACTUAL NUMBER OF ITERATIONS 6 DEPENDENT VARIABLE IS Y RESULTS OUTPUT # 4 OBSERVATIONS FROM 1 TO 250 USING STARTING VALUES --------------------- B1 97 B2 .009 B3 100 B4 65 B5 20 B6 70 B7 178 B8 16.5 USING ALGORITHM GAUSS-NEWTON NUMBER OF OBSERVATIONS 250 DEGREES OF FREEDOM 242 R**2 .9969623 R**2 ADJ .9968745 UNCENTERED R**2 .9990247 MEAN OF DEP VAR 60.53139 F-TEST MAY BE INVALID-SEE MANUAL F TEST 9928.015 PROB OF F TEST 0 DURBIN-WATSON 2.108397 DURBIN'S H 0 R**2 TIMES N 249.2406 VARIANCE OF ESTIMATE 5.437282 SUM OF SQUARED RESID 1315.822 SEE OR RMSE 2.331798 SUM OF ABS(RES) 451.1702 RHO -5.641498E-02 LOG(LIKELIHOOD) -562.329 SCHWARZ CRITERION -584.4149 AKAIKE CRITERION -570.329 STD DEV OF DEP VAR 41.70884 NAME COEFFICIENT STD. ERR. T-RATIO SIGNIF ---------------------------------------------------------------------- B1 98.77821 .5752732 171.7066 0.000000 B2 1.049728E-02 1.140629E-04 92.03061 0.000000 B3 100.4899 .5883178 170.8089 0.000000 B4 67.48111 .1046059 645.0983 0.000000 B5 23.12977 .1743995 132.6252 0.000000 B6 71.9945 .6262279 114.9653 0.000000 B7 178.998 .1243699 1439.24 0.000000 B8 18.38939 .2013431 91.33358 0.000000 --------------------------------------- NIST - GAUSS1 --------------------------------------- STARTING VALUES CERTIFIED VALUES START 1 START 2 PARAMETER STANDARD DEVIATION B1 = 97.0 94.0 9.8778210871E+01 5.7527312730E-01 B2 = 0.009 0.0105 1.0497276517E-02 1.1406289017E-04 B3 = 100.0 99.0 1.0048990633E+02 5.8831775752E-01 B4 = 65.0 63.0 6.7481111276E+01 1.0460593412E-01 B5 = 20.0 25.0 2.3129773360E+01 1.7439951146E-01 B6 = 70.0 71.0 7.1994503004E+01 6.2622793913E-01 B7 = 178.0 180.0 1.7899805021E+02 1.2436988217E-01 B8 = 16.5 20.0 1.8389389025E+01 2.0134312832E-01 RESIDUAL SUM OF SQUARES: 1.3158222432E+03 RESIDUAL STANDARD DEVIATION: 2.3317980180E+00 DEGREES OF FREEDOM: 242 NUMBER OF OBSERVATIONS: 250