I started to read this yesterday but I immediately saw y and x both dependent?
and don't you mean X1,i>xo not X1,1>xo?
You need to type this more carefully.
This is just curve fitting, not stats.
You want to incorporate both models using an indicator function .
You want , when
and you want , when , don't worry about the .
But, I'm concerned about using the same y-intercept here, a.
BUT it is the same a.
When , we have the same intercept.
So I would go with (b).