Create a sample report to analyze admission and enrollment decisions at the school of arts & letters in a selective four-year college in North America. For predictor variables, include the applicant’s sex, ethnicity, grade point average, and SAT scores. Make predictions for the admission probability and the enrollment probability using typical values of the predictor variables.

College admission can be stressful for both students and parents as there is no magic formula when it comes to admission decisions. Two important factors considered for admission are the student’s high school record and performance on standardized tests. According to the National Association for College Admission Counseling (NACAC), a student’s high school record carries more weight than standardized test scores. Just as prospective students are anxious about receiving an acceptance letter, most colleges are concerned about meeting their enrollment targets. The number of acceptances a college sends out depends on its enrollment target and admissions yield, defined as the percentage of students who enroll at the school after being admitted. It is difficult to predict admissions yield as it depends on the college’s acceptance rate as well as the number of colleges to which students apply. As the number of applications for admission and the number of acceptances increase, the yield decreases. In this report, we analyze factors that affect the probability of college admission and enrollment at a school of arts & letters in a selective four-year college in North America. Predictors include the applicant’s high school GPA, SAT score,1 and the Male, White, and Asian dummy variables capturing the applicant’s sex and ethnicity. In Table 7.29, we present the representative applicant profile.

TABLE 7.29 Applicant Profile for the School of Arts & Letters 

Of the 6,964 students who applied to the school of arts & letters, 30.76% were males; in addition, the percentages of white and Asian applicants were 55.59% and 12.42%, respectively, with about 32.00% from other ethnicities. The average applicant had a GPA of 3.50 and an SAT score of 1146. Table 7.29 also shows that 1,739 (or 24.97%) applicants were granted admission, of which 401 (23.06%) decided to enroll. As expected, the average GPA and SAT scores of admitted applicants are higher than those who applied and those who enrolled, but to a lesser extent.

Two logistic regression models are estimated using the same predictor variables, one for predicting the admission probability and the other for predicting the enrollment probability. The entire pool of 6,964 applicants is used for the first regression, whereas 1,739 admitted applicants are used for the second regression. The results are presented in Table 7.30. With accuracy rates of 81% and 77%, respectively, both models do a good job with predicting probabilities. It seems that the sex of the applicant plays no role in the admission or enrollment decisions. 

1 The higher of SAT and ACT scores is included in the data where for comparison, ACT scores on reading and math are first converted into SAT scores.

TABLE 7.30 Logistic Regressions for College Admission and Enrollment 

Interestingly, both white and Asian applicants have a lower probability of admission than those from other ethnicities. Perhaps this is due to affirmative action, whereby colleges admit a proportionally higher percentage of underrepresented applicants. As expected, quality applicants, in terms of both GPA and SAT, are pursued for admission. 

On the enrollment side, admitted applicants who are white are more likely to enroll than all other admitted applicants. Finally, admitted applicants with high GPA and high SAT scores are less likely to enroll at this college. This is not surprising because academically strong applicants will have many offers, which lowers the probability that an applicant will accept the admission offer of a particular college. 

In order to further interpret the influence of SAT scores on college admission and enrollment, we compute predicted admission and enrollment probabilities for representative males from all ethnicities with a GPA of 3.8 and SAT scores varying between 1000 and 1600. The results are shown in Figures 7.18 and 7.19.

FIGURE 7.18 Predicted Admission Probability 

Consider the case of a representative male applicant with an SAT score of 1300. For a white male, the predicted probabilities of admission and enrollment are 47% and 24%, respectively. The corresponding probabilities are 45% and 13%, respectively, for Asians and 55% and 13%, respectively, for all other ethnicities. The probabilities get closer as SAT scores increase.

FIGURE 7.19 Predicted Enrollment Probability 

Higher admission rate for underrepresented applicants is consistent with the admission practices at other colleges that believe that diversity enriches the educational experience for all. 

Unfortunately, despite a higher admission rate, the lower admission yield at this college for underrepresented applicants makes the percentage of those who actually enroll even lower than the percentage of those who apply. As we can observe in Table 7.18, about 23% of underrepresented applicants applied for admission, but the percentage of those who enrolled dropped to 21.45%. This is consistent with an article in The New York Times (August 24, 2017) that found that black and Hispanic students are more underrepresented at the nation’s top colleges and universities than they were 35 years ago. The yield for Asian applicants is the lowest at 8.73%. It is advised that the college explore the reasons for the especially low admission yield of nonwhite applicants and finds ways to raise it.

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Variable Male Applicant (%) White Applicant (%) Asian Applicant (%) Other Applicant (%) High School GPA (Average) SAT Score (Average) Number of Applicants Applied 30.76 55.59 12.42 31.99 3.50 1,146 6,964 Admitted 27.37 61.13 11.73 27.14 3.86 1,269 1,739 Enrolled 26.68 69.83 8.73 21.45 3.74 1,229 401