Solve to completion

(a) Give an example of a logistic regression model which would be an ap- propriate use of some (or all) of these variables. Explain why logistic regression is an appropriate choice. (b) Give an example of a Poisson regression model which would be an appropriate use of some (or all) of these variables. Explain why Poisson regression is an appropriate choice. True or False: The Poisson regression is used to improve over a linear functional form for continuous data. True O False For which of the following dependent variables would it be appropriate to use the Poisson regression model? Check all that apply. The number of children ever born to a woman ) The economic status of a mother at the time she had her first child The number of accidents for a given intersection in a given time period O) Goals scored for each game in a season ) The gender of criminal offenders Suppose in a Poisson quasi-maximum likelihood estimation (QMLE) the variance is proportional to the mean: Var(yx) = a"E(yx), where a? >> 0 is an unknown parameter. Which of the following ensures that the Poisson variance assumption holds? Oo'=1(30%)Q2 (Poisson regression): We collected n = 15 independent count observations {yi : i = 1, ..., 15} and their corresponding covariates {r; : i = 1, ..., 15}. Assume the relationship between y; and x; (for i = 1, ..., 15) is y; ~ Poisson(X,) and log(M) = a + Br;. Please 1) write down the likelihood function L(o, B|x, y) of the Poisson regression model; 2) derive the Newton method for maxmizing L(a, B|x, y); 3) implement the Newton method using R to get MLE of (a, B). -0.30 0.32 0.41 0.62 -0.21 0.31 0.41 0.81 yi 2 10 11 22 0 6 9 34 Ti 0.50 -0.21 -0.20 0.70 0.10 0.13 0.69 yi 5 0 21 3 2 29