TUTORIAL Chapter 15

TUTORIAL Chapter 15 EXAPMLE 1.(34) The following data represents enrollment in a major in one university for the past 6 semesters. Semester 12 3 4 5 6 Enrollment87 110123127145160 a) Construct a graph of the time series of the enrollment. b) Does it appear a trend in the enrollment data? c) Prepare a simple exponential smoothing forecast for semester 7 using alpha=0.35 and Y = 87. 1d) Prepare a double exponential smoothing forecast using alpha=0.20 and beta=0.25. e) Calculate MAD for both forecasts. Which model appears to be doing better? a) b. Yes it does appear that trend is present. c. %Which Equation do we use? FF=+ α()y−Ftt+1 tt Absolute Actual Forecast Forecast Forecast Semester Enrollment Enrollment Error Error 1 87 87.00 0.00 0.00 211087.0023.0023.003 123 95.05 27.95 27.95 4127104.8322.1722.175 145 112.59 32.41 32.41 6160123.9332.0732.077 136.56 Sum 139.67 Alpha0.35MAD 23.599 d. Which Equations do we use? Cy=+α (1−α )(C+T ) TC= β()−+C(1−β)T tt t−−11tttt−11t− FC= +Ttt+1 t Absolute Actual Forecast Forecast Forecast Semester Enrollment Constant Trend Enrollment Error Error Initial Values 77.93 13.54 1 87 90.58 13.32 91.48 -4.48 4.48 2 110 105.12 13.62 103.90 6.10 6.10 3 123 119.60 13.84 118.74 4.26 4.26 4 127 132.15 13.52 133.43 -6.43 6.43 5 145 145.53 13.48 145.66 0.66 0.66 6 160 159.21 13.53 159 ...