Can you provide the responses for below with explanation and R code.

A data set (xi, yi), for i = 1, ...,50, is available in "HW11 data_1.csv" for the logistic regression model; exiBj P(Y; = j | B, i) = j = 1, 2, 3, and 1 P(Yi = 4 | 8, i) = (1) (10 pts) Write down the log-likelihood function n L(B) = log ] [ P(yi | B, xi). i=1 (2) (10 pts) Find the expressions of the partial derivatives OL a2 L and aBi aBjaBK for j = 1, 2, 3 and k = 1, 2, 3. (3) (10 pts) Using the partial derivatives just found, write and run a Newton-Raphson algorithm to obtain the maximum likelihood estimator B. State the algorithm and the final result. (4) (10 pts) Find the predictive probabilities for y with a new predictor at x = T. (5) (10 pts) Hence, what would be the predicted outcome for y at this x