Developing an Enrollment Projection Model IAIR Presentation November 5 th , 2010

1. Developing an Enrollment Projection ModelIAIR PresentationNovember 5th, 2010 Alex J. Caffarini David Rudden President – Analysights, LLC Elgin Community College

2. Introduction • ECC wanted to develop a predictive model to forecast enrollment for future terms at ECC • Any requests for enrollment projections would follow the “master plan” rule of thumb: • Average rate of growth of 2%/year • Written in 1999 • Nobody knew where that growth rate came from • Document predicted that enrollments would double to 20,000 students per term by 2020 • Neglects the fact that this is mathematically impossible with only a 2% growth rate over 20 years!

3. A BetterApproach: Predictive Modeling • We wanted a forecasting method based upon: • The realities and trends in the enrollment environment • Objective, replicable processes • Two models built: • Regression • Long-term Forecasting (up to 6 terms out) • Predictive/Causal • Exponential smoothing • Short-term Forecasting (best for term-to-term projection) • More trend-based/Intuitive

4. Methodology Enrollment data provided for 53 consecutive terms (Summer 1992 through Fall 2009) Data adjusted for seasonal variation Fall 2009 observation withheld from model construction, to see how well model would predict for that term

5. Methodology (continued) • Began with simple time-series regression model; autocorrelation detected • Adjusted data for autocorrelation, re-ran regression model on adjusted data • Improved model’s explanatory power • Improved model’s forecast accuracy • Tried adding additional variables to model; no further improvement

6. Methodology (continued) Ended up with a two-variable regression model that explained 57% of variation in enrollment Also developed exponential smoothing model for shorter-term forecasting

7. Key Findings • Enrollment on a long-term upward trend: • Passage of time alone associated with rising enrollment • Previous term enrollment strongly influences current term’s enrollment • Tuition per credit hour not a significant predictor, as you’ll see later

8. Seasonal Adjustment of Data • Because enrollment headcount varies depending on Fall, Spring, or Summer, data had to be adjusted for seasonality: • 3-period moving average used; • A term’s actual data divided by its 3-period moving average to determine its seasonal ratio; • Ratios averaged for each season, to determine seasonal adjustment factor; • Actual enrollment divided by its season’s adjustment factor; and • Model run on adjusted data; results then multiplied by season’s adjustment factor

9. Summer Ratio has Large Variance! Note that there was a large variance with Summer, compared to other terms, which made it difficult to forecast Summer enrollment as precisely as the other terms

10. Regression Analysis • Statistical method to assess relationship between one or more predictor (independent) variables and a single (dependent) variable. • Equation generated to show how changes in independent variables explain changes in dependent variable • Ŷ=α + β1X1+ β2X2+…+ βnXn + ε • Equation used to forecast dependent variable

11. Regression Model • Started with a simple one-variable model: • Time Period (time period #) as independent variable • Each sequential term numbered from 1 to 51 (Fall 1992 as period #1; Summer 2009 as period #51); • Baseline Enrollment(seasonally-adjusted baseline enrollment) as dependent variable • Resulting model • R2=46.6% • T-values and intercept (α) inflated • Analysis of regression errors revealed presence of autocorrelation

12. Correcting Autocorrelation Found that the regression errors for each term were correlated with those of subsequent terms Used common remedy: lagging B_ENROLL by one period:

13. Correcting Autocorrelation (continued) • Ran regression using just Lagged Baseline Enrollment as independent variable; • Updated model: • R2=47.6% • T-statistics for Lagged Enrollment and intercept more reasonable • Autocorrelation almost entirely eliminated • This lagged model predicted Fall 2009 enrollment within 3.2%; could we do better?

14. Reinstating PERIOD variable • Still thought Time Period could add explanatory and predictive power to model: • Renumbered each remaining observation from 1 to 50 (Spring 1993=1; Summer 2009=50); • Two independent variables: • Lagged Baseline Enrollment • Time Period • Revised Model • R2=56.9% • t-statistics reasonable and significant • Closer forecast to Fall 2009: within 2.3%

15. Could the model be improved further? • Additional variables were added to model: • Tuition per credit hour (inflation-adjusted); • Promotional catalogs mailed; and • Kane County Unemployment Rate • No added value to model • Tuition increased at same rate as national average, so no effect on overall enrollment; • Promotional catalogs mailed not significant. • Unemployment rate did increase R2 to 61% and was significant but its wide variation reduced forecast accuracy (off by 8.1%).

16. Original Two-Variable Model Selected • Seasonality aside, of 100 students enrolled last term, an average of 45 return this term. • Again, adjusting for seasonality, each new period brings an additional 26.5 students over the prior period. • Multiply forecast result by seasonal weight to get forecast for actual enrollment. • A prediction interval consistent with a 95% confidence level was constructed for forecasts.

17. Exponential Smoothing • Statistical method which assumes that demand for the following period is some weighted average of demand for the past periods. • Exponentially decreasing weights assigned to older observations so recent observations have more weight in forecasting. • Uses a smoothing constant, “alpha” (α), a number between 0 and 1: • Near 1 means more weight on most recent observation; • Near 0 means more weight on less recent observations.

18. Final Exponential Smoothing Model Enrollment data exhibited a slight upward trend, so double exponential smoothing used. Model built on seasonally adjusted enrollment from Spring 1993 through Summer 2009 (same as with regression). Set up equations in Excel; used Solver tool to generate optimal values for α and β. Multiply forecast result by seasonal weight to get forecast for actual enrollment. A prediction interval consistent with a 95% confidence level was constructed for forecasts.

19. How Well Did Each Model Forecast Fall 2009 Enrollment? Both models came within 3% of actual enrollment for Fall 2009 ECC’s Master Plan projection wasn’t bad for this particular term, but would have failed to predict any of the enrollment decreases in terms prior to this

20. Final Notes Models should aid – not replace – planning and decision process; The further into the future you try to predict, the less accurate your forecasts will be; and Models’ forecast accuracy degrades over time; always keep track of what the model forecasted and actual enrollment, so that you can identify when it’s time to remodel.