# Nonlinear model fit: not getting correct numerical values from model [closed]

I tried to nonlinear fit a set of data as described below. However, it appears to yield a fit solution that in appearance looks good with the plotted data set, 'dat1', however, actual fit solution answers don't appear to represent the fit curve in the plot. (Note, I could not copy over the plot image itself.) Here's what I did,

I have a set of data:

dat1 = {{.1, .1010}, {.04, 0.1192}, {.02, 0.1555}, {.01, 0.1777}, {.004, 0.1789}};


to which I have fit a model using the nonlinear fit model function:

nlm =
NonlinearModelFit[dat1, a + b Log10[x] + c Log10[x]^2, {a, b, c}, x];
Normal[nlm]


gives

FittedModel[-0.0298908 - 0.0662938 Log[x] - 0.00502002 Log[x]^2 ]


When the fit model, nlm and the data set, 'dat1' are plotted:

Plot[nlm[x], {x, 0.004, 0.1},
Epilog -> {Red, PointSize[Medium], Point@dat1}]


it gives a plot containing the combined fit curve and red dot point curve for dat1 data. (Note: can't get graphic to insert here.)

I tested the fitted model:

Clear[x];
d + e Log10[x] + f Log10[x]^2 /.
{x -> .04, d -> -0.0298908, e -> -0.0662938, f -> -0.00502002}


and it gave the answer:

0.0529737

However if you look at the plot, this answer is nowhere near the value estimate in the plot.

I also tried:

d + e Log10[x] + f Log10[x]^2 /. {x -> .004, d -> -0.0298908,
e -> -0.0662938, f -> -0.00502002}


and it's answer was:

0.100212

Am I missing something or what? Please advise.

Edit

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## closed as off-topic by m_goldberg, Sjoerd C. de Vries, Kuba, Yves Klett, ArtesAug 18 '13 at 19:54

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question arises due to a simple mistake such as a trivial syntax error, incorrect capitalization, spelling mistake, or other typographical error and is unlikely to help any future visitors, or else it is easily found in the documentation." – m_goldberg, Sjoerd C. de Vries, Kuba, Yves Klett, Artes
If this question can be reworded to fit the rules in the help center, please edit the question.

You are mixing up Log and Log10. The values you are entering for e and f are the coefficients of Log not Log10. –  bobthechemist Aug 17 '13 at 22:04
As bobthechemist has pointed out, you probably require d + e Log[x] + f Log[x]^2 /. {x -> .04, d -> -0.0298908, e -> -0.0662938, f -> -0.00502002} => 0.131487 –  TomD Aug 17 '13 at 22:15
Why don't you use nlm["Function"][.04] which gives 0.131487. –  m_goldberg Aug 17 '13 at 23:26

As pointed out in the comments to the question, the OP made a simple mistake of confusing Log with Log10. However, the OP could have saved himself a lot of grief by using NonlinearModelFit as Stephan Wolfram intended him to :-)

data = {{.1, .1010}, {.04, 0.1192}, {.02, 0.1555}, {.01, 0.1777}, {.004, 0.1789}};
nlm = NonlinearModelFit[data, a + b Log10[x] + c Log10[x]^2, {a, b, c}, x];

nlmF = nlm["Function"]

0.0298908 - 0.0662938 Log[#1] - 0.00502002 Log[#1]^2 &

nlmF /@ {.004, .04}

{0.183105, 0.131487}

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Thanks very much, a very obvious point I overlooked. –  user9102 Aug 18 '13 at 0:06