The president of State University wants to forecast student enrollment for this academic year based on the following historical data:
$$\begin{array} { | c | c | }
\hline \text { Year } & \text { Enrollnents } \
\hline 5 \text { years ago } & 15,000 \
\hline 4 \text { years ago } & 16,000 \
\hline 3 \text { years ago } & 18,000 \
\hline \text { 2 years ago } & 20,000 \
\hline \text { Luast year } & 21,000 \
\hline
\end{array}$$
What is the forecast for this year using exponential smoothing with ? = 0.5, if the forecast for two years ago was 16,000?
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 enrollment for this academic year based on the following historical data:
$$\begin{array} { | c | c | } 
\hline \text { Year } & \text { Enrollnents } \
\hline 5 \text { years ago } & 15,000 \
\hline 4 \text { years ago } & 16,000 \
\hline 3 \text { years ago } & 18,000 \
\hline \text { 2 years ago } & 20,000 \
\hline \text { Luast year } & 21,000 \
\hline
\end{array}$$
What is the forecast for this year using exponential smoothing with ? = 0.5, if the forecast for two years ago was 16,000?
A) 18,750
B) 19,500
C) 21,000
D) 22,650
E) 22,800

Quizplus · Accepted Answer

The exponential smoothing formula is: $ F_t = \alpha A_{t-1} + (1-\alpha) F_{t-1} $. For last year: $ F_{last} = 0.5 \times 20,000 + 0.5 \times 16,000 = 18,000 $. For this year: $ F_{this} = 0.5 \times 21,000 + 0.5 \times 18,000 = 19,500 $.

The President of State University Wants to Forecast Student Enrollment