Question

Consider the following data:

Monthly Profit of a Gym Month Jan-12 Feb-12 Mar-12 Apr-12 May-12 Jun-12 Jul-12 Aug-12 Sep-12

Profit ($) 5,350 5,103 4,824 4,437 5,080 5,358 5,819 6,091 5,837

Step 2 of 5 : What are the MAD, MSE and MAPE scores for the three-period moving average? Round any intermediate calculations, if necessary, to no less than six decimal places, and round your final answer to one decimal place.

Answer 1

First We will Calculate Moving Averages.

Month	Profit	Total of moving period	Moving average
January	5350
February	5103
March	4824
April	4437	15277	5092.333333
May	5080	14364	4788
June	5358	14341	4780.333333
July	5819	14875	4958.333333
August	6091	16257	5419
September	5837	17268	5756
October		17747	5915.666667
Total
Total of moving period (1) = 5350+5103+4824
Moving average (1) = Total of moving period (1) /3

e.g. 3 period moving avg is calculated for calulated for the next corresponding 4th period estimated value

For MAD we need the absolute error

Month	Profit	Total of moving period	Moving average	Error Moving Avg - Profit	Absolute error
January	5350
February	5103		0
March	4824		0
April	4437	15277	5092.333333	-655.3333333	655.3333333
May	5080	14364	4788	292	292
June	5358	14341	4780.333333	577.6666667	577.6666667
July	5819	14875	4958.333333	860.6666667	860.6666667
August	6091	16257	5419	672	672
September	5837	17268	5756	81	81
October		17747	5915.666667
Total					3138.666667

MAD = =

MAD = 523.11

For MSE we need Square of error

Month	Profit	Total of moving period	Moving average	Error Moving Avg - Profit	Absolute error	Error^2
January	5350
February	5103		0
March	4824		0
April	4437	15277	5092.333333	-655.3333333	655.3333333	429461.8
May	5080	14364	4788	292	292	85264
June	5358	14341	4780.333333	577.6666667	577.6666667	333698.8
July	5819	14875	4958.333333	860.6666667	860.6666667	740747.1
August	6091	16257	5419	672	672	451584
September	5837	17268	5756	81	81	6561
October		17747	5915.666667
Total					3138.666667	2047317

MSE = =

MSE = 341219.5

For MPSE we need % error which is calculate 'error / actual * 100'

Month	Profit	Total of moving period	Moving average	Error Moving Avg - Profit	Absolute error	Error^2	% Absolute Error
January	5350
February	5103		0
March	4824		0
April	4437	15277	5092.333333	-655.3333333	655.3333333	429461.8	14.769739%
May	5080	14364	4788	292	292	85264	5.748031%
June	5358	14341	4780.333333	577.6666667	577.6666667	333698.8	10.781386%
July	5819	14875	4958.333333	860.6666667	860.6666667	740747.1	14.790628%
August	6091	16257	5419	672	672	451584	11.032671%
September	5837	17268	5756	81	81	6561	1.387699%
October		17747	5915.666667
Total					3138.666667	2047317	58.510156%

MPSE = =

MPSE = 9.75%

Final ANS: MAD = 523.11

MSE = 341219.5

  MPSE = 9.75%