The president of State University wants to forecast student enrollments for this academic year based on the following historical data: $$\begin{array} { l l }
\text { Year } & \text { Enrollments } \
\hline \text { 5 years ago } & 15,000 \
4 \text { years ago } & 16,000 \
\text { 3 years ago } & 18,000 \
2 \text { years ago } & 20,000 \
\text { Last year } & 21,000
\end{array}$$ 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: $$\begin{array} { l l } 
\text { Year } & \text { Enrollments } \
\hline \text { 5 years ago } & 15,000 \
4 \text { years ago } & 16,000 \
\text { 3 years ago } & 18,000 \
2 \text { years ago } & 20,000 \
\text { Last year } & 21,000
\end{array}$$ 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

First, we need to find the level estimate (LT) and the trend estimate (TT) using the given values of alpha and beta for trend-adjusted smoothing. 
LT = alpha x (latest enrollment) + (1 - alpha) x (LT + TT) 
TT = beta x (LT - previous LT) + (1 - beta) x TT

Using the values given in the problem, we can calculate: 
LT = 0.05 x 21,000 + 0.95 x (21,000 + 1,500) = 21,075 
TT = 0.3 x (21,075 - 20,000) + 0.7 x 1,500 = 895.5

The forecast for this year using trend-adjusted smoothing is calculated as follows: 
Forecast = LT + 2 x TT 
= 21,075 + 2 x 895.5 = 22,866

Therefore, the answer is D) 22,650.

The President of State University Wants to Forecast Student Enrollments