Question

The president of State University wants to forecast student enrollment for this academic year based on the following historical data: Year Enrollments 5 years ago 15,000 4 years ago 16,000 3 years ago 18,000 2 years ago 20,000 Last year 21,000 What is the forecast for this year using exponential smoothing with alpha = 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. None of the above

Answer 1

Answer:

Option (b) 19,500

Explanation:

Data provided in the question:

Year                 Enrollments ($A_t$)

5 years ago         15,000

4 years ago         16,000

3 years ago         18,000

2 years ago         20,000

Last year              21,000

α = 0.5

Forecast for two years ago  = 16,000

Now,

Forecast for last year

i.e year 5

F₅ = (1 - α ) F₄ + α (A₄)

here,

= ((1 - 0.5 ) × 16,000 ) + ( 0.5 × 20,000  )

= 8,000 + 10,000

= 18,000

Thus,

Forecast for this year

F₆ = (1 - α)F₅ + α(A₅)

= ( (1 - 0.5 ) × 18, 000 ) + ( 0.5 × 21,000 )

= 9,000 + 10,500

= 19,500

Hence,

Option (b) 19,500