Suppose you fit a logistic regression classifier to a dataset comprise of observations ?=[?1 ?2] where your threshold is 0.5 so any new observation is classified as ?=1 if ?(?=1|?;?)0.5. Now assume you decide to apply a basis function expansion so ?(?)=[1 ?1 ?12 ?2 ?22] and aftertraining you obtain the following parameters ??=[21 6 1 8 1]. Consequently, the decision boundary obtained is a circle.

Hint: The equation of a circle centered at (?,?) is (?1?)2+(?2?)2=?2, where r is the radius of the circle.

1. (a)Is the point (4,0) inside or outside the circle? Justify analytically

O

Inside

O

Outside

(b)If we increase the threshold to 0.8, the radius of the circle will increase. Justify analytically

(c)If we increase the bias term ?0, the radius of the circle will increase. Justify analytically

O

True

O

False

(d)Increasing or decreasing the radius based on ?0, produces the region for ?=1 to growth orshrink in size. How is the last related to what the bias term ?0 represents? Justify