The School of Continuing Studies has grown rapidly to match the steady rise in demand for learning opportunities. Annual enrollments have increased by 78% over the past five years and are approaching 30,000. The School’s success presents both opportunities and challenges as we seek to expand our programming, improve access, and deepen our impact. The ability to understand enrolment trends and develop accurate forecasting models will strengthen our efforts to expand access to a diverse learner community. These techniques will also strengthen our ability to anticipate growth, improve planning, and provide indicators useful in evaluating School operations. This presentation explores the accuracy and validity of various statistical techniques used in understanding and predicting enrolment and how these are used in developing and planning strategic enrolment management activities.

1. Strategic Enrolment Management and
Predictive Analytics

2. 1. Strategic importance of forecasting enrolments
2. Introduction to auto-regressive integrated moving average
models (ARIMA)
3. Overview of the forecasting process
4. Background on business and foreign language programs at
the School
5. Modelling and Forecasts
6. Methods to quantify accuracy and gauge uncertainty
7. Application: enrolment planning
Agenda

3. Why Forecast and the Relationship to Budgeting?
Detect Problems/Challenges Early

4. More than 75 professional
development certificates
and over 400 courses
taught by industry leading experts.

5. More than 20 languages for all
learner levels from absolute
beginner to expert. 1 on 1 or
group learning. 40% of language
learners each year are new.

6. Annual Enrolment

7. Our Learners

8. Overview of Forecasting Process

9. Enrolment Time Series
Spring
Fall
Winter

10. ARIMA Models
• Auto-Regressive Integrated Moving Average
• Are an adaptation of discrete-time filtering
methods developed in 1930’s-1940’s by
electrical engineers (Norbert Wiener et al.)
• Statisticians George Box and Gwilym Jenkins
developed systematic methods for applying
them to business & economic data in the 1970’s
(hence the name “Box-Jenkins models”)

11. What AR-I-MA stands for
• A series which needs to be differenced to be
made stationary is an “integrated” (I) series
• Lags of the stationarized series are called
“autoregressive” (AR) terms
• Lags of the forecast errors are called “moving
average” (MA) terms

12. A) Business
Decomposition of enrolment for trend, seasonality, and residuals for (A) Business and (B) Language - Foreign
B) Foreign Languages

13. ARIMA(1,0,0)(0,1,0)3 - First order
auto-regressive model with one
seasonal difference. (AIC = 350)
ARIMA(0,1,1)3 - Third order moving
average model with one seasonal
difference. (AIC = 269)

14. Accuracy and Uncertainty Analysis
Is the Model Valid? The Ljung-Box statistic (Q*) tests the model adequacy
by comparing with the corresponding Chi-square distribution. In the figure
below all the p-values are greater than 0.05 suggesting that the models are
adequate. The greater the p values are, the stronger the evidence is for
model adequacy.

15. Accuracy and Uncertainty Analysis
Is the Model Valid? Residual Analysis: The autocorrelation function and the partial
autocorrelation function of the residuals are within two standard errors. the QQ-plot in Figure 8
nearly fits a straight line, which both serve as indications for model adequacy. Therefore, we
can conclude that both model fits are adequate from residual diagnostics.

16. Accuracy and Uncertainty Analysis
Are the results accurate? Equality of Variance and Difference of Means:
Non-Parametric Tests Difference in Populations
Are the results accurate? Measures of Forecasting Accuracy and Bias
ME: Mean Error
MPE: Mean Percentage Error
RMSE: Root Mean Square Error
MAPE: Mean Absolute Percentage Error
MAE: Mean Absolute Error
RMSE, MAPE , MAE and R2 are scale-
independent and can be used to
compare forecast accuracy between
different data sets

17. Application of Forecasts in Developing
Enrolment Budgets:

18. School Programming (Product Mix)
Steps:
1. For each semester, course-
sections, are aggregated at a
course level based on
location, and method of
instruction
2. The number of sections,
total and average enrolment
per/section was calculated.
3. Year over Year percent
changes were calculated.
4. Enrolment for each unique
course/ moi /location were
calculated based on average
enrolment and an increment
defined by the variance of
year over year enrolment
changes.
5. Revenue projections
completed.

19. Scheduling/Sequencing: Art + Science
Annual Enrolments

20. Enrolment: 361
Forecast: 379
Budget: 341
Enrolment: 4,407
Forecast: 5,279
Budget: 4,586
As of May 16, 2017
25% of Sections
(111 Classes) still open
for enrolment.

21. Future Enrolment Planning Initiatives
Strategic Activity Enrolment
Target
Base
Enrolment
Target
Stretch
Academic/Career Advising 200 300
Enhanced Front Line Sales Function 150 200
Retention and Learner Loyalty Initiative 300 400
New Partnership Agreement 50 100

22. Q and A