Professor Z needs to allocate time among several tasks next week to include time for students' appointments.Thus,he needs to forecast the number of students who will seek appointments.He has gathered the following data:
Week # of students
6 weeks ago 83
5 weeks ago 110
4 weeks ago 95
3 weeks ago 80
2 weeks ago 65
Last week 50
-What is the forecast for this year using exponential smoothing with trend if $\alpha$ = 0 5 and $\beta$ = 0 1? Assume the forecast for last week was 65 and the forecast for two weeks ago was 75 ,and that the trend estimate for last years forecast was -5
A)49
B)50
C)52
D)65
E)78

Question

Professor Z needs to allocate time among several tasks next week to include time for students' appointments.Thus,he needs to forecast the number of students who will seek appointments.He has gathered the following data:
Week # of students
6 weeks ago 83
5 weeks ago 110
4 weeks ago 95
3 weeks ago 80
2 weeks ago 65
Last week 50
-What is the forecast for this year using exponential smoothing with trend if $\alpha$ = 0 5 and $\beta$ = 0 1? Assume the forecast for last week was 65 and the forecast for two weeks ago was 75 ,and that the trend estimate for last years forecast was -5 
A)49 
B)50 
C)52 
D)65 
E)78

Quizplus · Accepted Answer

We will use the formula for exponential smoothing with trend:

Ft = α(At-1 + Tt-1) + (1-α)(Ft-1)

where At is the actual value, Tt-1 is the trend estimate, and Ft-1 is the forecast for the previous period.

Given:

α = 0.5
β = 0.1
F1 = 65 (forecast for two weeks ago)
F2 = 75 (forecast for last week)
T1 = -5 (trend estimate for last year's forecast)
F0, T0 are not given, but we can assume they are both 0.

Using this information, we can calculate the forecast for this week:

F3 = α(A2 + T2) + (1-α)(F2)
    = 0.5(110 - 75) + 0.5(65)
    = 52.5

Therefore, the forecast for this week is 52 students seeking appointments. The closest answer choice is (C) 52.

Professor Z Needs to Allocate Time Among Several Tasks Next α\alphaα

Professor Z Needs to Allocate Time Among Several Tasks Next $\alpha$