But then you may decide that your quadratic model doesn’t really make sense because a quadratic function eventually comes back down. Well, we wouldn’t really expect housing prices to go down when the size increases.
f (w,b,x) = w1 * x + w2 * x^2 + b should always increasing eventually unless w2 is negative. am I right?
Yes, as you are saying this is dependent on the weights: if w_2 is negative: then for {x\to\infty}: f will decrease.
Yes, I agree with you. It seems this polynomial fit with a negative w_2 is used to model the “flattening out” effect, meaning that from a certain size on a further increase in size does not lead to a strong increase of the price anymore.
It is fair to question if the model is valid for certain ranges of x, and especially extrapolation characteristics for high x as you are pointing out this is questionable. So, I am totally with you on your conclusion.
And I believe it’s exactly these thoughts and questions like this one that the learners are supposed to ask themselves to get the most out of the lessons.
Also in practice, it’s always important to give some thought about the model limitations!
Best regards
Christian
Thank you
