2. (5.5) Exercise 4.12 introduced four scales of the Myers-Briggs personality test. Table 5.6 shows SAS output for fitting a model using the four scales as predictors of whether a subject drinks alcohol frequently. Table 5.6 SAS output for fitting model to Myers-Briggs personality scales data of Exercise 4.12. Criterion DF Value Deviance 11 11 . 1491 Standard Like-ratio 958 Chi- Parameter Estimate Error Conf Limits Square Intercept -2.4668 0. 2429 -2. 9617 -2. 0078 103 .10 EI e 0. 5550 0 . 2170 0. 1314 0. 9843 6.54 SN -0. 4292 0. 2340 -0 . 8843 0. 0353 3.36 TF 0. 6873 0.2206 0 . 2549 1. 1219 9. 71 JP -0. 2022 0.2266 -0. 6477 0. 2426 0 . 80 a. Con duct a model goodness-of-fit test and interpret. If you were to simplify the model by removing a predictor, which would you remove? Why? b. Software reports AIC values of 642.1 for the model with the four main effects and the six interaction terms, 637.5 for the model with only the four binary main effect terms, and 648.8 for the model with no predictors. According to this criterion, which model is preferred? Explain the rational for using AIC. c. 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. d. Using the MBTI data file at the website www.stat.ufl.edu/~aa/introcda/data, use model- building methods to select a model for this alcohol response variable. Use R