Estimating New Freshmen
Enrollment
Agatha Awuah, Eric Kimmelman, Michael Dillon
Office of Institutional Research
Binghamton University
AIRPO
June 11-13, 2003
Admissions Process
•
•
•
•
•
Set new freshmen targets.
Make offers of admission.
Build wait list.
Collect deposits.
Estimate enrollment based on deposits
received.
• Make offers to the wait list if needed.
Previous Method
Required to estimate enrollment:
1. Yield=last year’s enrollment (1,000) divided by
last year’s offers (3,000).
Est. Yield=1,000/3,000
=.33
2. Target for current year (2,000).
Est. Offers Needed=2,000/.33
=6,000
Previous Method-Results
Fall
Semester
1994
1995
1996
1997
1998
1999
2000
2001
2002
Admits
6384
6496
6497
6633
7004
6765
6761
7787
7479
Prev.
Est. Enr.
Years
Est.
Act.
Yld. Rate Enrollment Enrollment Act. Enr
27.15%
1734
1781
-47
27.90%
1812
1772
40
27.28%
1772
1739
33
26.77%
1775
1798
-23
27.11%
1899
1909
-10
27.26%
1844
1943
-99
28.72%
1942
1834
108
27.13%
2112
2226
-114
28.59%
2138
1899
239
Yield by SAT Score-Fall 2002
SAT Score
Admits
Enrolled
Yield
LE 1150
1433
543
37.89%
1160-1230
1623
481
29.64%
1240- 1280 1321
356
26.95%
1290-1360
1648
325
19.72%
GE 1370
1454
194
13.34%
Total
7479
1899
25.39%
Logistic Regression
• Dichotomous dependent variable.
• Estimates conditional probability of
enrollment controlling for multiple
independent variables-yield.
• Available in most statistical packages.
The Data
• Five fall semesters -1998 to 2002.
• Only matric freshmen admits (35,796)
included.
• Enrollment of admitted applicants: 9,811.
• Yield rate: (9,811/35,796)*100=27.4%.
Steps to Building Model 1
• Estimate baseline model using 5 years of
data (intercept only), estimate enrollment,
then calculate absolute prediction error by
semester.
• Add additional variables and calculate new
absolute prediction error.
Steps to Building Model 2
• Compare prediction errors. If the second
prediction error is smaller than the first,
keep new variable in the model. If not, drop
it from the model.
• Continue process until smallest possible
prediction error is attained.
• Predict enrollment for each year in the
sample with data from other 4 years.
Step One-Baseline Model
Year
Est. Enr. Act. Enr.
Abs. Diff.
1998 7004
1920
1909
11
1999 6765
1854
1943
89
2000 6761
1853
1834
19
2001 7787
2134
2226
92
2002 7479
2049
1899
151
Total
Offers
361
Step Two-Add SAT and HS Avg.
1
Variable
Est.
Coeff.
Std. Dev Chi Sqr.
Pr. > Chi
Sqr.
Intercept 8.730
0.295
878.335
0.001
SAT
-0.003
0.000
1157.089 0.001
HS Avg.
-0.061
0.003
322.130
0.001
Step Two-Add SAT and HS Avg.
2
Year Offers Est.
Enr.
1998 7004
Est.
Act.
Enr.
Yield
1925
27.48% 1909
Act.
Yield
27.26%
1999 6765
1890
27.94% 1943
28.72%
2000 6761
1854
27.42% 1834
27.13%
2001 7787
2171
27.88% 2226
28.59%
2002 7479
1971
26.36% 1899
25.39%
Step Two-Add SAT and HS Avg.
3
Year
Offers
1998
7004
Est. Enr. Act. Enr. Abs.
Diff.
1925
1909
16
1999
6765
1890
1943
53
2000
6761
1854
1834
20
2001
7787
2171
2226
55
2002
7479
1971
1899
72
Total
216
Full Model 1-Academics
Estimated Standard
ChiVariable
Coefficient
Error Square Pr > Chi Sq
Intercept: enr=1
10.798
0.319 1146.18
<.0001
SAT Score
-0.004
0.000 1454.38
<.0001
HS Avg.
-0.071
0.004 403.62
<.0001
Missing SAT
0.172
0.092
3.53
0.0603
Missing HS Avg.
-0.089
0.053
2.87
0.0905
Full Model 2-Inqs/Demo
Estimated Standard
Variable
Coefficient
Error
College Day/Night
0.204
0.035
HS Visit
0.333
0.104
Out of State
-0.456
0.052
Female
-0.229
0.027
Blacks--Non Hisp.
-0.805
0.060
ChiSquare Pr > Chi Sq
33.45
<.0001
10.18
0.0014
77.64
<.0001
72.88
<.0001
181.85
<.0001
Hispanic
216.27
-0.817
0.056
<.0001
Full Model 3-Inst.
Estimated Standard
Variable
Coefficient
Error
School of Mgmt.
0.299
0.041
School of Human
0.572
0.115
Devel.
School of Nursing
0.259
0.101
Engineering
-0.155
0.050
Computer Science
0.239
0.058
ChiSquare Pr > Chi Sq
52.90
<.0001
24.59
<.0001
6.62
9.55
16.85
0.0101
0.002
<.0001
Full Model Performance
Year
Pred.
Enr
Low
95%
High
95%
1998
1880
1807
1952
Act.
Pred.
Enr. - Error
Admits
1909
29
1999
1919
1846
1991
1943
24
2000
1861
1789
1933
1834
27
2001
2191
2113
2268
2226
35
2002
1961
1886
2036
1899
62
Total
177
Full Model Evaluation
Year
1998
1999
2000
2001
2002
Total
Pred.
Enr
1872
1910
1870
2183
1974
Low
95%
1799
1837
1798
2104
1900
High
95%
Act.
Enr.
Diff.
1944
1983
1942
2260
2049
1909
1943
1834
2226
1899
37
33
36
43
75
221
Estimating Quality of Regular
Admits Fall 2002
Estimated
Actual
Prediction
Error
Mean SAT
Score
1231
1238
-7
Mean HS
Average
92
92
0
Additional Applications
•
•
•
•
Predict retention.
Identify “Hot Prospects”.
Identify potential donors.
Evaluate recruitment efforts.
Logistic Regression
Berge, D.A. & Hendel, D.D. (2003, Winter).
Using Logistic Regression to Guide Enrollment
Management at a Public Regional University. AIR
Professional File, 1-11.
Thomas, E, Dawes, W. & Reznik, G. (2001,
Winter). Using Predictive Modeling to Target
Student Recruitment: Theory and Practice. AIR
Professional File, 1-8.
Aldrich, J.H. & Nelson, F.D. (1984). Linear
Probability, Logit and Probit Models. Sage
University Papers: Quantitative Applications in
the Social Sciences, 07-045. Newbury Park, CA:
Sage Publications
Estimating New Freshmen
Enrollment
Agatha Awuah, Eric Kimmelman, Michael Dillon
Office of Institutional Research
Binghamton University
AIRPO
June 11-13, 2003
Website: http://buoir.binghamton.edu