Aresearcher is interested in how variables, such (graduate record exam gpa (grade point average) and prestige of the undergraduate institution, effect admission into graduate school. a set of hypothetical data is given at htt nal csv to investigate this problem. these data are also attached a probl data. csv. this dataset consists of results from 400 applications to various universities. the following variable are recorded: admit: ao/1 variable (1 admitted, o denied admission) gre: gre score of the applicant gpa: gpa of the applicant rank: a value1 through 4, indicating school's prestige. institutions with a rank of 1 have the highest prestige, while those with a rank of 4 have the lowest. note: ordinarily you would consider the variable rank as a categorical variable in analyzing these data however, on this exam, treat the variable rank as continuous (a) note the observed values of the admit variable by yi yn and assume that yl bernouli with the probability of success wi (the probability that a student is admitted). moreover model by the logit function exp (x b) (b) for 1, 1 exp (x b) (1) where xt (1, u, x12,x13) is a vector of p observed covariates for case i where 1 indicates the intercept, xt1 gre, x12 gpa and x13 rank, with b (b,,b2, b3, r being the four corresponding parameters to be estimated. i. [5 points] use the data given and glm function in r to fit the above logit model to the ii. the given data. here use the summary function in r to show the result of the fitted model. [5 points] draw four curves on the same plot, corresponding to ranks 1 through 4, where the x-axis is gre values ranging from 220 to 800 and the y-axis is the probability of admission, as predicted by the fitted logistic regression model for gpa value fixed at 3.8. use a different color for each plot and include a legend. briefly explain what you see on the plot