Question 2. A researcher is interested in how variables, such Exam scores), GPA (grade point average) and prestige of the undergraduate institution, effect admission into raduate 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 Institutions with a rank of 1 have the highest prestige, while those with a rank of 4 Gave the lowest

Using R output above, answer the following questions: a- Interpret the coefficients for "ranklowes", "gpa" and "intercept"? b- Assume that you want to check if model fit will improve when you include the ethnicity 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 bei admitted into college?

Call: glm (formula = admit_re- gre + gpa + rank, family = binomial(link = "probit"), data = prob_data) Deviance Residuals: Min 10 Median 30 Max -2.1035 -1.1560 0.6389 0.8710 1.6163 Coefficients: Estimate Std. Error z value Pr(>121) (Intercept) 2.386836 0.673946 3.542 0.000398 *** gre -0.001376 0.000650 -2.116 0.034329 * gpa -0.477730 0.197197 -2.423 0.015410 * rankhigh 0.415399 0.194977 2.131 0.033130 * ranklow 0.812138 0.208358 3.898 9.71e-05 *** rank lowest 0.935899 0.245272 3.816 0.000136 *** Signif. codes: '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1'' 1