--------------------------------------- BETA - GAUSS2 --------------------------------------- NLS Y B1*EXP( -B2*X )+B3*EXP( -(X-B4)**2/B5**2 )+B6*EXP(-(X-B7)**2/B8**2 ) / INPUTB B1=96.0 B2=0.009 B3=103.0 B4=106.0 B5=18.0 B6=72.0 B7=151.0 B8=18.0 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 # 3 OBSERVATIONS FROM 1 TO 250 USING STARTING VALUES --------------------- B1 96 B2 .009 B3 103 B4 106 B5 18 B6 72 B7 151 B8 18 USING ALGORITHM GAUSS-NEWTON NUMBER OF OBSERVATIONS 250 DEGREES OF FREEDOM 242 R**2 .9964865 R**2 ADJ .9963849 UNCENTERED R**2 .9990185 MEAN OF DEP VAR 60.53188 F-TEST MAY BE INVALID-SEE MANUAL F TEST 8579.494 PROB OF F TEST 0 DURBIN-WATSON 2.223151 DURBIN'S H 0 R**2 TIMES N 249.1216 VARIANCE OF ESTIMATE 5.155075 SUM OF SQUARED RESID 1247.528 SEE OR RMSE 2.270479 SUM OF ABS(RES) 439.1254 RHO -.112675 LOG(LIKELIHOOD) -555.6668 SCHWARZ CRITERION -577.7527 AKAIKE CRITERION -563.6668 STD DEV OF DEP VAR 37.76226 NAME COEFFICIENT STD. ERR. T-RATIO SIGNIF ---------------------------------------------------------------------- B1 99.01833 .5374877 184.2244 0.000000 B2 1.099495E-02 1.333531E-04 82.44989 0.000000 B3 101.8802 .5921732 172.0446 0.000000 B4 107.031 .150068 713.2164 0.000000 B5 23.57858 .226956 103.8906 0.000000 B6 72.04559 .6172197 116.726 0.000000 B7 153.2701 .1946667 787.3461 0.000000 B8 19.52597 .2641655 73.91568 0.000000 --------------------------------------- NIST - GAUSS2 --------------------------------------- STARTING VALUES CERTIFIED VALUES START 1 START 2 PARAMETER STANDARD DEVIATION B1 = 96.0 98.0 9.9018328406E+01 5.3748766879E-01 B2 = 0.009 0.0105 1.0994945399E-02 1.3335306766E-04 B3 = 103.0 103.0 1.0188022528E+02 5.9217315772E-01 B4 = 106.0 105.0 1.0703095519E+02 1.5006798316E-01 B5 = 18.0 20.0 2.3578584029E+01 2.2695595067E-01 B6 = 72.0 73.0 7.2045589471E+01 6.1721965884E-01 B7 = 151.0 150.0 1.5327010194E+02 1.9466674341E-01 B8 = 18.0 20.0 1.9525972636E+01 2.6416549393E-01 RESIDUAL SUM OF SQUARES: 1.2475282092E+03 RESIDUAL STANDARD DEVIATION: 2.2704790782E+00 DEGREES OF FREEDOM: 242 NUMBER OF OBSERVATIONS: 250