Matlab Polynomial Curve Fitting with Known Relationship [closed]

Question

So, I have this matlab problem, and I'm totally lost. Below, you will find my attempt. We are supposed to fit a polynomial curve to the data, but I'm a bit confused as to how the to get a polynomial to match the known relationship. I've got polyfit solving for the form of y = 1 / (ax + b), but I don't know where to go from there. Any help would be greatly appreciated.

x= 5:5:50;
y= [15 25 32 33 37 35 38 39 41 42];
p= polyfit(x,1 ./ y,1)
a= p(1);
b= p(2);

xFit= 5:50;
yFit= xFit ./ (a * xFit + b)
semilogy(x,y,'o',xFit,yFit,'-');

Answer 1

The trick to this one is at the end there. You took the reciprocal of your y data but what you need is the reciprocal of the entire equation.

Original: $y = a\frac{x}{b+x}$

Reciprocal: $\frac{1}{y}=\frac{1}{a}\frac{b+x}{x}$

So, when you simplify that a little, you'll get: $y^{-1}=\frac{b}{a}x^{-1}+\frac{1}{a}$

Hopefully, you can see that this is a linear equation but your variables are the reciprocals of x and y. So, when you get over to MATLAB, make the same vectors you did, but then get the reciprocals of those. Use polyfit() on those reciprocals and you'll get coefficients for $\frac{b}{a}$ and $\frac{1}{a}$. Solve those for $a$ and $b$ and check your work; you'll see a fit!