Mark Hamner Texas Woman’s University Department of Mathematics and Computer Science

1. Predicting Real-Time Percent Enrollment Increase__________________ Mark Hamner Texas Woman’s University Department of Mathematics and Computer Science Preet Ahluwalia Credit Risk Analyst-AmeriCredit

2. Texas Woman’s University Denton . Dallas . Houston Year 2005 Facts Total Enrollment – 11,344 Undergrad – 6,266 Graduate (Masters) – 4,369 Doctoral - 709 • Campus Enrollment • Denton –9,157 • Dallas – 921 • Houston – 1,266 • Female – 10,368 • Male – 976 59 academic programs (19 doctoral)

3. Outline Problem Definition Predicting Student Enrollment at Time ‘t’ Using Historical Data • Enrollment Process - For Newly Enrolled • The predictive problem • Logistic Prediction Model • a. Data Issues and programming Solutions • Quadratic Prediction Model • a. Exploratory analysis to Identify Patterns • Combine for overall Prediction: Results

4. Enrollment • Enrollment predictions can be broken into two fundamental pieces: • The focus of this paper is the prediction of Newly Enrolled students. Newly Enrolled Students Re-Enrolling/ Continuing Students

5. All Prospective Students Applicants FTIC Transfer Graduate Others Admitted to TWU New12th Day Enrolled New Students: Enrollment Process

6. Idea Behind Enrollment Prediction at Time = t

7. Predict Predict Fall 12th Day Begin Prediction Time t Enrollment Prediction at Time ‘t’ •  Let Time = t denote the prediction date • For Applicants Before t , we will have data • For Applicants after time t (denoted by t’) , we will not have data Total Enrollment = Enroll_t + Enroll_t’

8. Predict Predict Week 0 5 17 Weekly Partition of Prediction Interval • The prediction interval will be broken up into weekly Intervals • The diagram below illustrates prediction at Week = 5 • At Week = 5 we have 35 more days of applicant data than at Week = 0 Total Enroll = Enroll_t + Enroll_t’

9. Enroll_t • Pt= {1, 2, …, Nt} -- Finite set of applicants at week = t • kPt Enrollment is a dichotomous response variable – yk • yk= 1 (student enrolled), yk= 0 (student did not enroll) • Enrollment of all applicants at week = t ,

10. Model Dichotomous Variable For each yk, k Pt  let θk represent the probability that yk = 1 • There exists applicant information for each individual: • xk = (x1k, x2k, …, xpk) = (Distancek, SATk,…, Major_Ratiok) Use Logistic Regression to model θk

11. Logistic Regression Model • The probability of student k enrolling is • Lk = β0+ β1 Distancek + β2 SATk +…+ βp Major_Ratiok These are predictor variables

12. Predict Enroll_t • Let Y be the random vector of responses: •  Thus, Note: 1is a Nt x 1 vector of ones Estimated Enroll_t is …

13. Current Year Prediction Year Prior Applicant Data Logistic Model • Predictor variables: Distance, DOB, Major_Ratio, SAT_M, SAT_V, Gender, Personal, etc. • What variables will get picked for model building?

14. SAS Programming: Exploratory and Variable Creation Start Saturated Model Yes Drop Predictor No Stop Fitted Model Programming and Variable Selection •  Use SAS to create possibly significant variables • and dummy code categorical variables • Example: Major_Ratio, Ethnic, etc. •  Backward Selection • Slightly different variables are selected for: FTIC, Transfer, and Graduate.

15. FTIC Variable Selection

16. Case Study-Logistic Model Prediction  Applicant data for 2003 to predict 2004 FTIC by weekly time intervals • The Logistic Model does not predict after week = t

17. Enrollment after Week = t • Total Enrollment = Enroll_t + Enroll_t’ • At any week = t, we need to predict Enroll_t’ • Identify historical relationships that may be helpful

18. Applicant Versus Enrolled by Year • Both applications and enrollment have been increasing • Notice enrollment yield is decreasing  Is the % increase in enrollment matching the % increase in apply?

19. Applicant Yield By Strata • Enrollment is yield from applicant data is decreasing for each strata • How does this affect yearly increase in enrollment?

20. Percent Increase Applicant Vs. Enrolled • Applicant increase is not a viable indicator of enrollment increase • What patterns are reliable to model?

21. Cumulative FTIC Enrollment by Week • Notice the parallel lines, which implies equal slopes! • At any week = t, we can relate Enroll_t to Total Enrollment(Week = 17) • Thus, (Total Enroll – Enroll_t) should be very similar from year to year

22. Relationship Between Enrollment & Total Enrollment • By definition, (Total Enroll – Enroll_t) = Enroll_t’ • Model Enroll_t’ and smooth out the consistent patterns by week

23. Enroll_t’ Model • Use 2003 Enroll_t’ Model to predict Enroll_t’ for 2004  Estimate of Enroll_t’: (R2 = 0.9857)

24. Predict 2004 Enroll_t’

25. Predict 2004 FTIC Total Enroll  Total Enrollment = Enroll_t + Enroll_t’ Note: 2004 FTIC Actual Total is 687

26. Predict 2005 FTIC Total Enroll  Total Enrollment = Enroll_t + Enroll_t’ Note: 2005 FTIC Actual Total is 765

27. - END - Thank you! Any Questions?