MATLAB curve-fitting with a custom equation

Question

I'm working on curve-fitting data which consists of two arrays:

t: 1, 3, 4, 7, 8, 10

P: 2.1, 4.6, 5.4, 6.1, 6.4, 6.6

The relationship between the two variables is given by P = mt/(b+t). I'm told to determine the constants m and b by curve-fitting the equation to the data points. This should be done by writing the reciprocal of the equation and using a first-order polynomial. Here is my code:

t = [1 3 4 7 8 10];
P = [2.1 4.6 5.4 6.1 6.4 6.6];

p = polyfit(t, t./P, 1);


m = 1/p(1)
b = p(2)*m

tm = 1:0.01:10;
Pm = (m*tm)./(b+tm);

plot(t,P, 'o', tm, Pm)

The answer in the book is m = 9.4157 and b = 3.4418. The code above yields m = 8.4807 and b = 2.6723. What is my mistake? Any suggestions would be greatly appreciated. Thank you for your time.

Could the answers in the book be wrong? I plotted m and b from the answers: hold on,plot(tm,(9.4157*tm)./(3.4418+tm),'r'); and at least just eyeballing it, I'd suggest your solution is closer to fitting. — David_G
I'm wondering the same. I will leave my answer as is. Thank you very much for your response, David_G. — scimaks

Huguenot Huguenot · Accepted Answer · 2013-05-24T10:40:56

To follow up on the comment made by @David_G, it looks like you have a better answer. In fact, if you run the data through Curve Fitting Toolbox in MATLAB you get:

General model:
  f(t) = m*t/(b+t)
Coefficients (with 95% confidence bounds):
   b =       2.587  (1.645, 3.528)
   m =       8.448  (7.453, 9.443)

Goodness of fit:
  SSE: 0.1594
  R-square: 0.9888
  Adjusted R-square: 0.986
  RMSE: 0.1996

Your solution is almost as good:

Goodness of fit:
  SSE: 0.1685
  R-square: 0.9881
  Adjusted R-square: 0.9852
  RMSE: 0.2053

And both of them are better than the one in the book:

Goodness of fit:
  SSE: 0.404
  R-square: 0.9716
  Adjusted R-square: 0.9645
  RMSE: 0.3178

MATLAB curve-fitting with a custom equation

1 Answers