The president of State University wants to forecast student enrollments for this academic year based on the following historical data: $$\begin{array} { | c | c | }
\hline \text { Year } & \text { Enrollments } \
\hline \text { 5 Years ago } & 15,000 \
\hline \text { 4 Years ago } & 16,000 \
\hline \text { 3 Years ago } & 18,000 \
\hline \text { 2 Years ago } & 20,000 \
\hline \text { Last Year } & 21,000 \
\hline
\end{array}$$
What is the forecast for this year using trend-adjusted (double) smoothing with alpha = .05 and beta = .3, if the forecast for last year was 21,000, the forecast for two years ago was 19,000, and the trend estimate for last year's forecast was 1,500?
A) 18,750
B) 19,500
C) 21,000
D) 22,650
E) 22,800

Question

The president of State University wants to forecast student enrollments for this academic year based on the following historical data: $$\begin{array} { | c | c | } 
\hline \text { Year } & \text { Enrollments } \
\hline \text { 5 Years ago } & 15,000 \
\hline \text { 4 Years ago } & 16,000 \
\hline \text { 3 Years ago } & 18,000 \
\hline \text { 2 Years ago } & 20,000 \
\hline \text { Last Year } & 21,000 \
\hline
\end{array}$$
What is the forecast for this year using trend-adjusted (double) smoothing with alpha = .05 and beta = .3, if the forecast for last year was 21,000, the forecast for two years ago was 19,000, and the trend estimate for last year's forecast was 1,500?
A) 18,750
B) 19,500
C) 21,000
D) 22,650
E) 22,800

Quizplus · Accepted Answer

The trend-adjusted forecast is calculated using the formula: $ F_{t+1} = S_t + T_t $, where $ S_t $ is the smoothed level and $ T_t $ is the trend estimate. The smoothed level $ S_t $ is updated as $ S_t = \alpha \times \text{Actual}_{t} + (1-\alpha) \times (S_{t-1} + T_{t-1}) $, and the trend $ T_t $ is updated as $ T_t = \beta \times (S_t - S_{t-1}) + (1-\beta) \times T_{t-1} $. Using these formulas with the given data, the forecast for this year is 22,650.

The President of State University Wants to Forecast Student Enrollments