Q4 [6 pts] The Basics of Logistic Regression [a] (2 pts) Let y = 14.(0.6+2.3 be logistic function of x, show that both y and 1 -y are values between 0 and 1 if x=2. [b] (2 pts) Produce S-shape curve (or the so called Sigmoidal curve), use the y defined in (a), complete the following R code and produce a S-shape curve for the given x. What you should learn from this question is that we could map X on an interval [-4, 4] to the interval [0,1]. The core idea of logistic regression is that we could model the odds ratio of a success in the following form: log = Bo + BIX1 + 3212 + ... + BpIp set . seed (310311) x = seq (-4, 4, length. out =100) # find y and plot(x, y, type="l") [c] [2 pts] Odds ratio is the ratio of the probability of an event occurring to the probability of the event not occurring. Let us assume that the probability of winning a lottery is 0.01. Then, what is the probability of not winning? What is the odds of winning the lottery