3. (Multivariate logistic regression) Consider the following multivariate version of logistic regression. Suppose that we are given n pairs of data (C,Y) where 2; = (1,7i... Zit) RE+and Y: Ber tea) independently for i = 1,...,.. Here 8 = (20.81... B) RA+1 is the vector of evefficients (ie, parameters). Suppose that we are given the following dataset: 8 43 98 73 1 45 0 42 51 5 71 92 0 1 1 1 5 20 D 0 (a) (3 pts) Fit the logistic regression model to the data to compute the maximum likelihood estimators o.1 and 82. This should be similar to what you have done for a problem in Homework 11, cxcxpt that there are two covarintes rather than one (cf. multiple linear regression vs. simple linear regression). (b) (4 pts) Produce one plot in the plane consisting of the following three things: (i) A scatter plot of (311,12) for which Y = 0; (ii) A scatter plot of (141,12) for which Y=l(i) The line Solo: /B)x1 Distinguish (i) and (ii) using different colors or styles of points, and indicate the two parts clearly. Use the limits 05:21