-intuition for hypothesis for logistic regression.
approach(asynthosing)  at 1

so as a classification between 0 and 1,
we get hypothesis >= 0.5 for y = 1
and hypothesis < 0.5 for y = 0 so that's for prediction,  next hypothesis calculation to make prediction

the region (purple and blue area)  is set not by training set,  but from the value set by theta (parameters) .  in regards,  the theta are -3, 1,1 respectively,  that are predefined earlier.... when theta are still unknown,  then the training set would set the value of theta... next,  we talk about non-linear decision boundaries....

the first graph determine a non linear regression with  decision boundaries y =1 inside a purple circle...  and everything else ( outside the circle)  y = 0... again the decision boundaries is determined by value set by theta..
the training set may produce the value of parameters,  but the the parameters is the vital part for creating  the decision boundaries... the second graph is more complex parameters with higher order polynomial...
as we can see the boundaries is more complicated than usual... these visualization graphs would give us better understanding about various range of representation... next,  we talk about how automatically choose value of parameters based on training set...s