Mark Hamner

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

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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
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New Students Enrollment Process
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Idea Behind Enrollment Prediction at Time t

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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

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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
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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 ,

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Model Dichotomous Variable

• For each yk, k ? Pt
• ? let ?k 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 ?k

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Logistic Regression Model

• The probability of student k enrolling is
• Lk ß0 ß1 Distancek ß2 SATk ßp
  Major_Ratiok

These are predictor variables
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Predict Enroll_t

• Let Y be the random vector of responses
• ? Thus,

Note 1 is a Nt x 1 vector of ones
Estimated Enroll_t is
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Logistic Model

• Predictor variables Distance, DOB,
  Major_Ratio, SAT_M, SAT_V, Gender, Personal,
  etc.
• What variables will get picked for model
  building?

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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.

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FTIC Variable Selection
Variable Name Variable Type Variable Description
Twelve Response 1 if enrolled 0 otherwise
Distance? Explanatory Continuous variable
SAT_M, SAT_V, ACT Explanatory Continuous Variable SAT Math score, SAT Verbal score, Act Score
Give ACT? Explanatory 1 if score provided 0 otherwise
Program Ratio? Explanatory Continuous variable
Major Ratio? Explanatory Continuous variable
Date of Birth Explanatory Continuous variable
Gender? Explanatory 1 if female 0 for male
Apply Early? Explanatory 1 if apply before January 1 0 otherwise
E1, E2, E3, E4, E5, E6, E7 Explanatory Dummy variables for Ethnicity
Personal? Explanatory Discrete Variable Number of key information available for a student
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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

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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

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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?
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Applicant Yield By Strata

• Enrollment is yield from applicant data is
  decreasing for each strata
• How does this affect yearly increase in
  enrollment?

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Percent Increase Applicant Vs. Enrolled

• Applicant increase is not a viable indicator of
  enrollment increase

• What patterns are reliable to model?

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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
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Relationship Between Enrollment Total
Enrollment
By definition, (Total Enroll Enroll_t)
Enroll_t

Model Enroll_t and smooth out the consistent
patterns by week
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Enroll_t Model
Use 2003 Enroll_t Model to predict Enroll_t
for 2004 ? Estimate of Enroll_t
(R2 0.9857)
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Predict 2004 Enroll_t
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Predict 2004 FTIC Total Enroll

• ? Total Enrollment Enroll_t Enroll_t
  Note 2004 FTIC Actual Total is 687

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Predict 2005 FTIC Total Enroll

• ? Total Enrollment Enroll_t Enroll_t
  Note 2005 FTIC Actual Total is 765

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- END -
Thank you! Any Questions?