The principal of Green Valley High School has been tracking the number of new student enrollments over the past few years to plan for classroom space and teacher hiring. The data for new enrollments is shown below:
Year 1 2 3 4 5 6
Enrollments 40 42 38 42 41
Six years ago, the school district projected that enrollment in year 1 would be 38 students.
(a) Use exponential smoothing, first with a smoothing constant of $\alpha$=0.3, and then with $\alpha$=0.8, to develop forecasts for years 2 through 6.
(b) Determine which smoothing constant provides a better forecast using MAD, MSE, and MAPE.