Question

I have been toying with some codes to solve this using a Levenberg-Marquardt solver
but I am puzzled by what is given here
http://www.itl.nist.gov/div898/strd/nls/data/LINKS/DATA/Misra1a.dat

When I plug in the certified values and look at the predicted values, they look quite different from the actual Y values… surely I am doing something wrong here – what ?

Y= b1*(1-exp[-b2*X])
b1=238.94212918
b2=0.00055015643181


X       Y       Y-estimate  
10.07   77.6    1.32E+00
14.73   114.9   1.93E+00
17.94   141.1   2.35E+00
23.93   190.8   3.13E+00
29.61   239.9   3.86E+00
35.18   289     4.58E+00
40.02   332.8   5.20E+00
44.82   378.4   5.82E+00
50.76   434.8   6.58E+00
55.05   477.3   7.13E+00
61.01   536.8   7.89E+00
66.4     593.1   8.57E+00
75.47   689.1   9.72E+00
81.78   760     1.05E+01

I thought maybe the base was 10 and tried power(10,…) instead of exp but that does not seem to be the problem.

Answer 1

Your X and Y columns are swapped (really, go look closely at their table again):

238.94212918*(1-e(-0.00055015643181*77.6))
9.98626636447322174420

238.94212918*(1-e(-0.00055015643181*10.07))
1.32009728485679509663

Incidentally, their model also includes a final + e term.