Question

Professor Very Busy needs to allocate time next week to include time for office hours. He needs to forecast the number of students who will seek appointments. He has gathered the following data:
week #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 this week's forecast using the least squares trend line for these data?(show me the detail)

Answer 1

Solution:

Smooth the pattern as well as the arrangement to get the outlook this year.

S(Week 5) = TAF(Week 5) + alpha*(Actual(Week 5) - TAF(Week 5))

                 = 75 + 0.5(65 - 75) = 70

S(Week 6) = TAF(Week 6) + alpha*(Actual(Week 6) - TAF(Week 6))

                 = 65 + 0.5(50 - 65) = 57.5

T(Week 6) = T(Week 5) + beta*(TAF(Week 6) - TAF(Week 5) - T(Week5))

                = -5 + 0.1(65 - 75 - (-5)) = -5 + (-0.5) = -5.5

Therefore, TAF(Week 7) = S(Week 6) + T(Week 6) = 57.5 + (-5.5) = 52.0