FindFit problem

Questions
1

Good day. I have been using Findfit over a set of data to find two unknown of an equation. What I used for input was:

y=249-(1-a)/2.86* (b* 34.21)/a/(b-0.03)(Exp(b x-0.03* x)-1)

data={{0, 249}, {0, 243}, {0.13, 241}, {0.25, 237}, {0.25, 237}, {0.38, 229}, {0.5, 217}, {0.5, 217}, {0.63, 208}, {0.75, 198}, {0.75, 200}}

FindFit[data, 249-(1-a)/2.86* (b* 34.21)/a/(b-0.03)(Exp(b x-0.03* x)-1), {a,b}, x]

However the results i got is “FindFit::nrjnum: The Jacobian is not a matrix of real numbers at {a, b} = {1., 1.}.”. Does it means: the trend can’t not fit into that equation? Or did I make a mistake somewhere in my syntax?

Many thanks

2

It would be easier if you posted in <> format. You had some typos x*b needs to have a space in between x b and functions like Exp[] need square brackets […]

In[6]:= data = {{0, 249}, {0, 243}, {0.13, 241}, {0.25, 237}, {0.25, 
   237}, {0.38, 229}, {0.5, 217}, {0.5, 217}, {0.63, 208}, {0.75, 
   198}, {0.75, 200}}

Out[6]= {{0, 249}, {0, 243}, {0.13, 241}, {0.25, 237}, {0.25, 
  237}, {0.38, 229}, {0.5, 217}, {0.5, 217}, {0.63, 208}, {0.75, 
  198}, {0.75, 200}}

In[7]:= fit = 
 FindFit[data, 
  249 - (1 - a)/
     2.86 (b 34.21)/a/(b - 0.03) (Exp[b x - 0.03*x] - 1), {a, b}, x]

Out[7]= {a -> 0.170384, b -> 0.84151}

In[8]:= y = 
 243 - (1 - a)/2.86 (b 34.21)/a/(b - 0.03) (Exp[b x - 0.03*x] - 1) /. 
  fit

Out[8]= 243 - 60.3948 (-1 + E^(0.81151 x))
3

del

4

Ah, many thanks. I thought i just hit the wall in this.

Much appreciate!!!

5

No problem. Also, define equation once makes it easier:

In[8]:= data = {{0, 249}, {0, 243}, {0.13, 241}, {0.25, 237}, {0.25, 
   237}, {0.38, 229}, {0.5, 217}, {0.5, 217}, {0.63, 208}, {0.75, 
   198}, {0.75, 200}}

Out[8]= {{0, 249}, {0, 243}, {0.13, 241}, {0.25, 237}, {0.25, 
  237}, {0.38, 229}, {0.5, 217}, {0.5, 217}, {0.63, 208}, {0.75, 
  198}, {0.75, 200}}

y = 249 - (1 - a)/2.86 (b 34.21)/a/(b - 0.03) (Exp[b x - 0.03 x] - 1)

Out[9]= 243 - (11.9615 (1 - a) b (-1 + E^(-0.03 x + b x)))/(
 a (-0.03 + b))

In[10]:= FindFit[data, y, {a, b}, x]

Out[10]= {a -> 0.430225, b -> 1.81015}

In[11]:= Simplify[y /. %]

Out[11]= 259.108 - 16.1084 E^(1.78015 x)