6. (15 pts) In logistic regression, the response variable is sometimes labeled y (-1,+1) rather than y {0, 1). Using a maximum likelihood approach, show that when y (-1, +1}, the logistic regression problem is to m min log (1+ exp(-yax)) (3) where x is the vector of parameters to be estimated (i.e. the regression coefficients) and a, is the vector of predictor variables for observation i (i=1,...,m). Here are the steps. (a) Show that 1 1+exp(-yaa) P(Y=y)= is in fact a valid probability distribution when y {-1, +1}. Here, the subscript i is dropped. (b) Write the log-likelihood function. (e) Show that minimizing the negative of the log-likelihood function leads to the problem (4) shown above.