I have data for $x,y$ where $y=[0,0,0.016,0.65,0.97,0.99,1]$ and $x=[1,2,3,4,5,6,7]$. For this data I fitted a sigmoid type function as $f(x)=a/(1+exp(-b*x)+c)$. I fitted this using matlab cftool, and the obtained parameter values are:
a = 1.748e-07 (-5.743e-07, 9.238e-07)
b = 4.047 (2.914, 5.18)
c = -1 (-1, -1)
But the issue is, say I try to interpolate values at $x=5$ using the above estimated values, then for $x=5$, $f(x)=230$ but $f(x)$ should result in values between 0 and 1.
Is this an issue in the used function form for $f(x)$? Or is it because estimated value of $a$ has a large confidence interval?
How can I resolve this issue?