Calls to a college emergency hotline for the past 29 months are as follows (with the earliest month shown first): 50, 35, 25, 40, 45, 35, 20, 30, 35, 20, 15, 40, 55, 35, 25, 55, 55, 40, 35, 60, 75, 50, 40, 42, 51, 22, 38, 45, and 65.
(a) Assuming an initial forecast of 55 calls for month 1, use exponential smoothing with a = 0.15, 0.65, and 0.95 to forecast calls for each month. What is the forecast for the 30th month in each case?
(b) Actual calls during the 30th month were 85. Which smoothing constant provides a superior forecast?