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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, (1 = admit, 0 = do not admit), is a binary variable. There are three predictor variables: gre, gpa and ivy.league. Institutions which are ivy league schools are considered to have higher prestige. The dependent variable was coded as y = 1 if the student was admitted to the graduate school and coded as y = 0 if not. The three independent variables are: *1 = GRE (Graduate Record Exam) score *2 = GPA (grade point average) if the undergraduate institution is not an ivy league school X3 = if the undergraduate institution is an ivy league school. (a) Write the logistic regression equation relating X1, X2, and x3 to y. elo + P1X1 + $2X2 + 343 E(Y) = 1+elo + *1 + $2X2 + M343 E(y) = elo + 1*1 + 2X2 + N3X3 E(y) = Bo + B1X1 + B2X2 + B3X3 E(y) = 1 + elo + 1*1 + $2X2 + 8383 elo + 1*1 + 2X2 + 8383 (b) What is the interpretation of Ely) when X3 O? For a given GRE score and GPA, it is an estimate of the probability that an applicant who did attend an ivy league school will be admitted to graduate school. For a given GRE score and GPA, it is an estimate of the probability that an applicant who did not attend an ivy league school will be admitted to graduate school. It is an estimate of the GRE score for an applicant with a given GPA that did not attend an ivy league school and has been admitted to graduate school. It is an estimate of the GRE score for an applicant with a given GPA that did attend an ivy league school and has been admitted to graduate school. (c) Use the three independent variables and statistical software to compute the estimated logit. (Round your numerical values to four decimal places.) (*1X2, 3) = (d) What is the estimated probability that an applicant will be admitted to graduate school if they have a GRE score of 600, have a GPA of 3.20, and whose undergraduate institution is not an league school? (Round your answer to four decimal places.) What is the estimated probability that an applicant will be admitted to graduate school if they have a GRE score of 600, have a GPA of 3.20, and whose undergraduate institution is an ivy league school? (Round your answer to four decimal places.)

(e) What is the estimated odds ratio for ivy league schools? (Round your answer to four decimal places.) Interpret the estimated odds ratio. (Round your answer to four decimal places.) times greater than for applicants who did not attend an The odds of an applicant being accepted to graduate school if they did attend an ivy league school are ivy league school. (f) Based on the answers found in parts (d) and (e), it appears that applicants that --Select--- Aare more likely to be admitted to graduate school.