1. Data file "data/drinking. Rdata" has 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: Extro- version/Introversion (E/I), Sensing/iNtuitive (S/N), Thinking/Feeling (T/F) and Judging/Perceiving (J/P). You can load the data by R code below: load (file = "data/drinking. Rdata") 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) (5 points) Fit a model using the four scales as predictors of = the probability of drinking alcohol frequently. Report the prediction equation, specifying how you set up the indicator variables. (b) (5 points) Find for someone of personality type ESTJ. (c) (5 points) Based on the model parameter estimates, explain why the personality type with the highest is ENTP. (d) (5 points) Conduct a model goodness-of-fit test, and interpret. (e) (5 points) If you were to simplify the model by removing a predictor, which would you remove? Why? (f) (5 points) When six interaction terms are added, the deviance decreases to 3.74. Show how to test the hypothesis that none of the interaction terms are needed, and interpret. 2. A model fit predicting preference for President (Democrat, Republican, Independent) using x = annual income (in $10,000 dollars) is log (d/) = 3.3 0.2x and log (^R/^1) = 1.0+0.3x (a) (5 points) State the prediction equation for log (^R/^D). Interpret its slope. (b) (5 points) Find the range of x for which R > D. (c) (5 points) State the prediction equation for I. > drinking F1 F2 F3 F4 Yes No 1 E S T J 10 67 2 E S TP 8 34 345 3 E S F J 5 101 4 5 6 E S FP 7 72 E NT J 3 20 E N TP 2 16 7 EN F J 4 27 8 E N F P 15 65 9 H S T J 17 123 10 I S TP 3 49 11 I S F J 6 132 12 I S F P 4 102 13 I NT J 1 12 14 I N 15 16 TP5 39 I N F J 1 30 INFP 673