Please provide comprehensive responses to the following:

 (a) In the use of a categorical variable with n possible values, explain the following:
    1. Why only n – 1 binary variables are necessary
    2. Why using n variables would be problematic

(b) Describe how logistic regression can be used as a classifier.

(c) Discuss how the ROC curve can be used to determine an appropriate threshold value for a classifier

(d) If the probability of an event occurring is 0.4, then

    1. What is the odds ratio?
    2. What is the log odds ratio?