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Question 2. A researcher is interested in how variables, such as GRE (Graduate Record Exam scores), GPA (grade point average) and prestige of the undergraduate institution, effect admission into graduate school. The response variable, admit/don't admit, is a binary variable, . "admit_re" for this study is the dependent variable which is equal to 0 if the individual was admitted to graduate school, and 1 otherwise. There are three predictor variables: GRE, GPA, and rank. We will treat the variables GRE and GPA as continuous. The variable rank takes on the values 1 through 4. Institutions with a rank of I have the highest prestige, while those with a rank of 4 have the lowest. . Call: glm( formula - admit_re-gre + gpa + rank, family = binonial(link - "probit"). data prob_data) 3. Max Deviance Residuals: Min 10 Median -2.1035 -1.1560 8.6389 30 8.8710 1.6163 3 Coefficients: Estimate Std. 'Error z value Pr(>12) (Intercept) 2.386836 8.673946 3.542 8.688398 *** gre -0.001376 0.000650 -2.116 0.034329 * gpa -0.477730 8.197197 -2.423 0.015410 * * rankhigh 0.415399 @.194977 2.131 0.033138. ranklow 0.812138 @.208358 3.898 9.71e-05 *** ranklowest 8.935899 0.245272 3.816 0.000136 *** 2.131 gre, 2.3868 36 apa 0.000650 ront high ronk Low 388 and lowed a 5232 3 0,001 Kool Os 0.1 - Signif. codes: '***' 0.001 ***' 0.01 '' 0.05 '.' 0.1'' 1 @ Using R output above, answer the following questions: a- Interpret the coefficients for "ranklowest", "gpa" and "intercept? b- Assume that you want to check if model fit will improve when you include the ethnicit variable into this regression. How can you check this statistically in a probit model? c- If the odds of getting into a college is found to be 0.6, what is the probability of not be admitted into college? *