Look ahead at the scenario described in Prob. 20.7-3. Notice the steady trend upward in the number of applications over the past three years-from 4,600 to 5,300 to 6,000. Suppose now that the admissions office of Ivy College had been able to foresee this kind of trend and so had decided to use exponential smoothing with trend to do the forecasting. Suppose also that the initial estimates just over three years ago had been expected value = 3,900 and trend = 700. Then, with any values of the smoothing constants, the forecasts obtained by this forecasting method would have been exactly correct for all three years. Illustrate this fact by doing the calculations to obtain these forecasts when the smoothing constant is α = 0.25 and the trend smoothing constant is ß = 0.25. (Use hand calculations rather than an Excel template)

Probs. 20.7-3

Three years ago, the admissions office for Ivy College began using exponential smoothing with a smoothing constant of 0.25 to forecast the number of applications for admission each year. Based on previous experience, this process was begun with an initial estimate of 5,000 applications. The actual number of applications then turned out to be 4,600 in the first year. Thanks to new favorable ratings in national surveys, this number grew to 5,300 in the second year and 6,000 last year. (Use hand calculations below rather than an Excel template)

(a) Determine the forecasts that were made for each of the past three years.

(b) Calculate MAD for these three years.

(c) Calculate MSE for these three years.

(d) Determine the forecast for next year.