(Multivariate logistic regression) Consider the following multivariate version of logistic regression. Suppose that we are given n pairs of data (,Y;) where I; = (1, til. ..., Tik) Rk+1 and Yi Ber (texto) independently for i = 1,..., n. Here 3 = (30, B1, ..., 8x) E Rk+1 is the vector of coefficients (i.e., parameters). Suppose that we are given the following dataset: 21: 9 5 9 7 3 5 9 5 22: 43 98 73 48 51 5 71 92 37 42 63 20 Y: 1 1 0 0 1 1 1 0 1 0 0 8 1 8 1 0 (a) (3 pts) Fit the logistic regression model to the data to compute the maximum likelihood estimators Bo, 1 and 32. This should be similar to what you have done for a problem in Homework 11, except that there are two covariates rather than one (c.f. multiple linear regression v.s. simple linear regression). (b) (4 pts) Produce one plot in the 21-22 plane consisting of the following three things: (i) A scatter plot of (2,1,1,2) for which Y; = 0; (ii) A scatter plot of (0:1, 1:2) for which Y; = 1; (iii) The line 12 = -Bo/82 - (1/B2).21. Distinguish (i) and (ii) using different colors or styles of points, and indicate the two parts clearly. Use the limits 0