Question

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 5,200 2016 7,000

2012 5,500 2017 8,800

2013 6,000 2018 9,400

2014 6,500 2019 9,600

2015 6,800 2020 10,500

a) Develop a forecast of enrolment beginning 2014 to 2021 using 3-years moving average forecast model.

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.

c) Using exponential smoothing and smoothing constant of .30 and 2011 previous forecast of 5200, develop a forecast of enrolment from 2012 to 2021.

d) Forecast enrollment using Trend line Projection from 2011 to 2021.

e) Evaluate forecast accuracy of each forecast model using MSE . Which model should you

recommend?

Answer 1

Answer :

Forecast using

Duration	Year	Enrolment	3 Year moving average	Using weigh of 0.5,0.3 and 0.2	Exponential smoothing with smooting contant 0.3	Trend line projection
1	2011	5200	-	-	5200	4789
2	2012	5500	-	-	5200	5398
3	2013	6000	-	-	5290	6007
4	2014	6500	5567	5690	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

Error square using

-	3 Year moving average	Using weight of 0.5,0.3 and 0.2	Exponential smoothing with smoothing constant 0.3	Trend line projection
-	-	-	0	168846
-	-	-	90000	10367
-	-	-	504100	53
-	870489	656100	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
MSE	1773006	1355471	2255575	137418

(a). Forcast using 3 years moving average = average fo last 3 years enrolment

(b). Forcast using weighted average menthod = (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 + (10.3)*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.

Kindly Up-vote Thank You !!!