Logistic Regression

Assume we have two features x = (x1, x2). Each sample is (X), x) with associated label y(i) that is either 1 or 0. P(y=112,0) - (a) Decision boundary. [5 pts) Logistic regression assumes log ( Py=0) 03) = + 0121 + 02X2. Let's define the prediction threshold as p, such that if P(y = 1\x, 0) > p, where 0 log Lm (b) Decision boundary, cont. [5 pts] The line defined by 10 + 01x1 + 02x2 = log ( - ) is called the decision boundary of the logistic regression model, since it splits the plane in two regions of different predictions. What is the decision boundary when we fairly set p = 0.5? Describe, in plain language, what happens to the decision boundary when p is changed