Fitting a function

Question

I defined and evaluated a function

Max2[t_?NumericQ] := Log[Abs[-1 + First[Maximize[sol1[[2]][x, t], 0 <= x <= L, x]]]];

Now, I expect this to be close to a straight line as a function of $t$, so I would like to get the best slope from a fit.

Looking at the reference website, I don't understand how to linearly fit a function.

You have provided incomplete information. How come on earth we will know what sol1[[2]][x, t] or the value of x are? Without this info no one can address the problem here. — PlatoManiac
– PlatoManiac, Commented Nov 17, 2013 at 15:11
One way to find a linear fit to a function is by taking the derivative. — bill s
– bill s, Commented Nov 17, 2013 at 15:19

wxffles · Accepted Answer · 2013-11-17 22:17:03Z

Let's take a vaguely straight function like you say yours is:

Plot[Log[t], {t, 50, 100}]

logplot

You could fit a line to it by sampling a bunch of points:

data = Table[{t, Log[t]}, {t, 50, 100}];

And fitting a line through those:

fit = Fit[data, {1, t}, t] (* 3.2732 + 0.0136576 t *)

Or you could minimise the integral of the square difference (i.e. least squares) directly yourself:

fit2 = a + b t /. Last@NMinimize[Integrate[(a + b t - Log[t])^2, {t, 50, 100}], {a, b}] (* 3.27497 + 0.0136447 t *)

They both give similar results:

Plot[{Log[t], fit, fit2}, {t, 50, 100}]

logfit

Thanks a lot! How can I extract the slope from the output fit, without making the derivative? — usumdelphini
– usumdelphini, Commented Nov 17, 2013 at 23:41
You could use a rule fit /. m_ t + c_ :> m or pick out the right part fit[[2, 1]] — wxffles
– wxffles, Commented Nov 18, 2013 at 1:47

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