use r if needed

data for the question:

EI SN TF JP smoke drink n

e s t j 13 10 77

e s t p 11 8 42

e s f j 16 5 106

e s f p 19 7 79

e n t j 6 3 23

e n t p 4 2 18

e n f j 6 4 31

e n f p 23 15 80

i s t j 32 17 140

i s t p 9 3 52

i s f j 34 6 138

i s f p 29 4 106

i n t j 4 1 13

i n t p 9 5 35

i n f j 4 1 31

i n f p 22 6 79

Q. 4 (30 points) We are using the same MBTI dataset. We fit a model using the four scales as predictors of whether a subject drinks alcohol frequently. Answer the following questions. (a) (10 pts) Conduct a model goodness-of-fit test, and interpret. If you were to sim- plify the model by removing a predictor, which would you remove? Why? (b) (10 pts) Report AIC values for the model with the four main effects and the six interaction terms; the model with only the four main effect; the model with no predictors. According to this criterion, which model is preferred? Explain the rationale for using AIC. (c) (10 pts) Using the MBTI data set, use model-builing mehtods to select a model for this alcohol response variable. Q. 4 (30 points) We are using the same MBTI dataset. We fit a model using the four scales as predictors of whether a subject drinks alcohol frequently. Answer the following questions. (a) (10 pts) Conduct a model goodness-of-fit test, and interpret. If you were to sim- plify the model by removing a predictor, which would you remove? Why? (b) (10 pts) Report AIC values for the model with the four main effects and the six interaction terms; the model with only the four main effect; the model with no predictors. According to this criterion, which model is preferred? Explain the rationale for using AIC. (c) (10 pts) Using the MBTI data set, use model-builing mehtods to select a model for this alcohol response variable