LogitRegData:

"x" "y" "1" 1.04 1 "2" -1.09 0 "3" 1.14 1 "4" 0.67 1 "5" -1.45 0 "6" 0.23 1 "7" 1.2 1 "8" 0.47 1 "9" 0.45 1 "10" -1.33 0 "11" -0.21 1 "12" -0.33 1 "13" -0.62 1 "14" 1.5 0 "15" -0.7 1 "16" 0.61 1 "17" 1.4 1 "18" 0.13 1 "19" -1.02 1 "20" 1.49 1 "21" 0.37 1 "22" -0.19 0 "23" -1.37 1 "24" 1.57 1 "25" -0.99 0 "26" 1.88 1 "27" 0.66 1 "28" -1.22 0 "29" -1.78 0 "30" -1.62 1 "31" -0.93 0 "32" -0.13 0 "33" 1.8 1 "34" -1.63 0 "35" 0.63 0 "36" -1.7 1 "37" 0.49 1 "38" 0.72 1 "39" 0.2 1 "40" -0.64 0 "41" 0.41 1 "42" 1.13 1 "43" -0.44 0 "44" -0.53 0 "45" -0.32 1 "46" -0.5 1 "47" 1.12 1 "48" 1.81 1 "49" -1.85 1 "50" -1.2 0

(20%)Q3 (Logistic regression): We collected n = 50 independent binary observations {yi : i = 1, ...,n} and their corresponding covariates {li: i = 1, ...,n}. Assume the relationship between Yi and X; (for i = 1, ..., n) is yi ~ Bernoulli(Pi) and logit(Pi) = a + Bri, where logit(t) = log it. Please 1) write down the likelihood function La,b|x, y) of the logistic regression model; 2) derive the Newton method for maximizing L(a,b|x,y); 3) implement the Newton method using R to get MLE of (a,). (The data set {(xi, Yi) :15isn} is stored in Logit Reg Data.txt.) (20%)Q3 (Logistic regression): We collected n = 50 independent binary observations {yi : i = 1, ...,n} and their corresponding covariates {li: i = 1, ...,n}. Assume the relationship between Yi and X; (for i = 1, ..., n) is yi ~ Bernoulli(Pi) and logit(Pi) = a + Bri, where logit(t) = log it. Please 1) write down the likelihood function La,b|x, y) of the logistic regression model; 2) derive the Newton method for maximizing L(a,b|x,y); 3) implement the Newton method using R to get MLE of (a,). (The data set {(xi, Yi) :15isn} is stored in Logit Reg Data.txt.)