My ADALINE model using Gradient Descent is increasing error on each iteration
I think something is wrong here.

self.w_ += self.eta * X.T.dot(errors)


You are going to the positive to the gradient while you should be doing is going to the negative direction of it

self.w_ -= self.eta * X.T.dot(errors)


or 

self.w_ += -self.eta * X.T.dot(errors)


see this for more clarification.