Table 4.13 shows the result of cross classifying a sample of people from the MBTI Step II National Sample (collected and compiled by CPP, Inc.) on whether they report drinking alcohol frequently (1 = yes, 0 = no) and on the four binary scales of the Myers–Briggs personality test:

Extroversion/Introversion (E/I), Sensing/iNtuitive (S/N), Thinking/Feeling

(T/F) and Judging/Perceiving (J/P). The 16 predictor combinations correspond to the 16 personality types: ESTJ, ESTP, ESFJ, ESFP, ENTJ, ENTP, ENFJ, ENFP, ISTJ, ISTP, ISFJ, ISFP, INTJ, INTP, INFJ, INFP.

a. Fit a model using the four scales as predictors of π = the probability of drinking alcohol frequently. Report the prediction equation, specifying how you set up the indicator variables.

b. Find ˆπ for someone of personality type ESTJ.

c. Based on the model parameter estimates, explain why the personality type with the highest ˆπ is ENTP.