Question

During the past five months the emergency room at the new district Hospital has observed the number of patients during the weekend (Friday through Sunday). They typically experience greater patient traffic on weekends than during the week. Week No of Patients 105 119 122 128 117 136 141 126 143 140 a) Compute a weighted three-period moving average forecast, using weights of 3, 2, and 1 for the most recent, next recent, and most distant data. (4 marks) b) What are the MAD, MSE and the MPE for this method? (6 marks) c) If the company decided to forecast using exponential smoothing with value of alpha = 3, what is the forecast in month 11? (use 2 decimal places) (4 marks) d) Using the MAD, is the exponential method an improvement over the previous method? (2 marks) e) Compute the linear regression equation given the following: EX=55.0, EY=1277, EXY=7304, EX2=385 and forecast sales for month. (4 marks)

Answer 1

(a)

Forecast
112.5
121.5
123.1667
125.6667
127.3333
136
136.3333

(b)

8.595238	103.504	06.41%
MAD	MSE	MAPE

(c)

134.58

(d)

10.44092

MAD

No

(e)

Forecast

146.4

The calculations are:

Data		Weighted moving averages - 3 period moving average	Forecasts and Error Analysis
Period	Demand	Weights		Forecast	Error	Absolute	Squared	Abs Pct Err
Period 1	105	0.5	3 periods ago
Period 2	119	0.33	2 periods ago
Period 3	122	0.166667	1 periods ago
Period 4	128			112.5	15.5	15.5	240.25	12.11%
Period 5	117			121.5	-4.5	4.5	20.25	03.85%
Period 6	136			123.1667	12.83333	12.83333	164.6944	09.44%
Period 7	141			125.6667	15.33333	15.33333	235.1111	10.87%
Period 8	126			127.3333	-1.33333	1.333333	1.777778	01.06%
Period 9	143			136	7	7	49	04.90%
Period 10	140			136.3333	3.666667	3.666667	13.44444	02.62%
				Total	48.5	60.16667	724.5278	44.84%
				Average	6.928571	8.595238	103.504	06.41%
					Bias	MAD	MSE	MAPE
						SE	12.03767
Next period	134

Alpha	0.3	Exponential Smoothing
Data			Forecasts and Error Analysis
Period	Demand		Forecast	Error	Absolute	Squared	Abs Pct Err
Period 1	105		105	0	0	0	00.00%
Period 2	119		105	14	14	196	11.76%
Period 3	122		109.2	12.8	12.8	163.84	10.49%
Period 4	128		113.04	14.96	14.96	223.8016	11.69%
Period 5	117		117.528	-0.528	0.528	0.278784	00.45%
Period 6	136		117.3696	18.6304	18.6304	347.0918	13.70%
Period 7	141		122.9587	18.04128	18.04128	325.4878	12.80%
Period 8	126		128.3711	-2.3711	2.371104	5.622134	01.88%
Period 9	143		127.6598	15.34023	15.34023	235.3226	10.73%
Period 10	140		132.2618	7.738159	7.738159	59.87911	0.0552726
			Total	98.61096	104.4092	1557.324	79.03%
			Average	9.861096	10.44092	155.7324	07.90%
				Bias	MAD	MSE	MAPE
					SE	13.95226
Next period	134.58

Data		Simple linear regression	Forecasts and Error Analysis
Period	Demand (y)	Period(x)		Forecast	Error	Absolute	Squared	Abs Pct Err
Period 1	105	1		112.4	-7.4	7.4	54.76	07.05%
Period 2	119	2		115.8	3.2	3.2	10.24	02.69%
Period 3	122	3		119.2	2.8	2.8	7.84	02.30%
Period 4	128	4		122.6	5.4	5.4	29.16	04.22%
Period 5	117	5		126	-9	9	81	07.69%
Period 6	136	6		129.4	6.6	6.6	43.56	04.85%
Period 7	141	7		132.8	8.2	8.2	67.24	05.82%
Period 8	126	8		136.2	-10.2	10.2	104.04	08.10%
Period 9	143	9		139.6	3.4	3.4	11.56	02.38%
Period 10	140	10		143	-3	3	9	02.14%
				Total	0	59.2	418.4	47.23%
Intercept	109			Average	0	5.92	41.84	04.72%
Slope	3.4				Bias	MAD	MSE	MAPE
						SE	7.231874
Forecast	146.4	11
						Correlation	0.833706
						Coefficient of determination	0.695066

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