Question

1. Suppose that the Perpetual Help College of Rizal had the following record of its growth of enrollment from 2011-2020. Year Enrolment Year Enrolment 2011 2012 5,200 5,500 2016 2017 7,000 8,800 2013 2014 2015 6,000 6,500 6,800 2018 2019 2020 9,400 9,600 10,500 a) Develop a forecast of enrolment beginning 2014 to 2021 using 3-years moving average forecast model. (8 pts) b) Using weights of .50 for the most recent data, .30 to the second recent data, and .20 to the 3 months old data, develop a forecast beginning 2014 to 2021 using 3 years weighted moving average forecast model. (8 pts) c) Using exponential smoothing and smoothing constant of .30 and 2011 previous forecast of 5200, develop a forecast of enrolment from 2012 to 2021. ( 11 pts) d) Forecast enrollment using Trend line Projection from 2011 to 2021. (15 pts) e) Evaluate forecast accuracy of each forecast model using MSE. Which model should you recommend? ( 8 pts)

Answer 1

a) forecast using 3 year moving average = average of last 3 years enrolment

5200 forecast using Duration year enrolment 3-year moving using weight of exponential smoothing with trend line average 0.5, 0.3 and 0.2 smoothing constant 0.3 projection 1 2011 5200 5200 4789 2 2012 5500 - 5398 3 2013 60001 5290 6007 4 2014 65001 5567 5503 6616 5 2015 6800 6000 6150 5802 7225 6 2016 7000 6433 6550 6101 7835 7 2017 8800 6767 6840 6371 8444 8| 2018 9400 7533 7860 7100 9053 9 2019 9600 8400 8740 7790 9662 10 2020 10500 9267 9380 8333 10271 5690) error square using 3-year moving using weight of exponential smoothing with trend line average 0.5, 0.3 and 0.2 smoothing constant 0.3 projection 0 168846 90000 10367 504100 53 870489 6561001 994009 13540 640000 422500 995804 181012 321489 202500 807356 696466 4133089 3841600 5899900 126995 3485689 2371600 5291287 120598 1440000 739600 3276809 3821 1520289 1254400 4696483 52483 1773006 1355471 22555751 137418 MSE

b) forecast using weighted average method = (0.5 * last month enrolment) + (0.3 * last second month enrolment) + (0.2 * last third month enrolment)

c) forecast using exponential smoothing = 0.3 * last month enrolment + (1-0.3) * last month forecast

d) forecast using trendline = mx + c

where m = slope = 609

x = duration

c = intercept = 4180

e) error square = (actual enrolment - forecast) ^ 2

MSE = average of all error square

since trendline method has least MSE hence it is the most accurate model recommended