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