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

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

Outline Problem Definition Predicting Student Enrollment at Time ‘t’ Using Historical Data 1.Enrollment Process - For Newly Enrolled 2.The predictive problem 3.Logistic Prediction Model a. Data Issues and programming Solutions 4.Quadratic Prediction Model a. Exploratory analysis to Identify Patterns 5.Combine for overall Prediction: Results

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

All Prospective Students Applicants FTIC Transfer Graduate Others Admitted to TWU New12 th Day Enrolled New StudentsEnrollment Process New Students: Enrollment Process

Idea Behind Enrollment Prediction at 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’ Predict Timet Begin Prediction Fall 12 th Day

Weekly Partition of Prediction Interval Predict Week0517  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’

Enroll_t  P t = {1, 2, …, N t } -- Finite set of applicants at week = t  k  P t Enrollment is a dichotomous response variable – y k  y k = 1 (student enrolled), y k = 0 (student did not enroll)  Enrollment of all applicants at week = t,

Model Dichotomous Variable For each y k, k  P t  let θ k represent the probability that y k = 1  There exists applicant information for each individual:  x k = (x 1k, x 2k, …, x pk ) = (Distance k, SAT k,…, Major_Ratio k ) Use Logistic Regression to model θ k

Logistic Regression Model The probability of student k enrolling is L k = β 0 + β 1 Distance k + β 2 SAT k +…+ β p Major_Ratio k These are predictor variables

Predict Enroll_t Estimated Enroll_t is …  Let Y be the random vector of responses:  Thus, Note: 1 is a N t x 1 vector of ones

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

 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. Programming and Variable Selection Start Saturated Model Drop Predictor Stop Fitted Model No Yes SAS Programming: Exploratory and Variable Creation

FTIC Variable Selection Variable NameVariable TypeVariable Description TwelveResponse1 if enrolled; 0 otherwise Distance♦ExplanatoryContinuous variable SAT_M, SAT_V, ACTExplanatoryContinuous Variable; SAT Math score, SAT Verbal score, Act Score Give ACT♦Explanatory1 if score provided; 0 otherwise Program Ratio♦ExplanatoryContinuous variable Major Ratio♦ExplanatoryContinuous variable Date of BirthExplanatoryContinuous variable Gender♦Explanatory1 if female; 0 for male Apply Early♦Explanatory1 if apply before January 1; 0 otherwise E1, E2, E3, E4, E5, E6, E7 ExplanatoryDummy variables for Ethnicity Personal♦ExplanatoryDiscrete Variable; Number of key information available for a student

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

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

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?

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

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

Cumulative FTIC Enrollment by Week Notice the parallel lines, which implies equal slopes! Enroll_tTotal Enrollment 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

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

Enroll_t’ Model Use 2003 Enroll_t’ Model to predict Enroll_t’ for 2004  Estimate of Enroll_t’: (R 2 = )

Predict 2004 Enroll_t’

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

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

- END - Thank you! Any Questions?