This is with reference with Andrew Ng's video on Logistic Regression, I just want to confirm a small doubt I have.
I get the basic idea of Logistic Regression that $z=\theta^Tx$
Where $\theta$= Parameters of our model and $x$= observations of the dataset.
And the $z$ is then used as an input for our sigmoidal function, which is,
Where this function will give us the probability of our "Y-Variable" taking a value 0 or 1.
The part I don't get is that when representing this $f(z)$ in a graphical form as a function of z, the curve of the sigmoid is shown to intersect the y axis at a value of 0.5, implying that when
$z=0$, then $f(z)=0.5$ && $z>0$, then $f(z)>0.5$ && $z<0$, then $f(z)<0.5$
My doubt is whether this always has to be the case. Because it's perfectly possible that when we get the $\theta$ paramters, the $z$ values that we calculate can never take on negative values.