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  3. consider the following data: monthly profit of a

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 ($) 6,500 6,253 5,514 5,357 5,425 6,278 8,119 6,390 6,090 Step 1 of 5: Determine the three-period moving...

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Statistics

Consider the following data:

Monthly Profit of a Gym
MonthJan-12Feb-12Mar-12Apr-12May-12Jun-12Jul-12Aug-12Sep-12
Profit ($)6,5006,2535,5145,3575,4256,2788,1196,3906,090

Step 1 of 5:

Determine the three-period moving average for the next timeperiod. If necessary, round your answer to one decimal place.

Step 2 of 5:

What are the MAD, MSE and MAPE scores for the three-periodmoving average? Round any intermediate calculations, if necessary,to no less than six decimal places, and round your final answer toone decimal place.

Step 3 of 5:

Determine the exponentially smoothed forecast for the next timeperiod using a smoothing constant, αα, of 0.350.35. If necessary,round your answer to one decimal place.

Step 4 of 5:

What are the MAD, MSE and MAPE scores for the exponentiallysmoothed forecast? Round any intermediate calculations, ifnecessary, to no less than six decimal places, and round your finalanswer to one decimal place.

Step 5 of 5:

Based on the MAPE scores, which forecast is best?

Answer & Explanation Solved by verified expert
4.1 Ratings (814 Votes)

for 3 period moving average:

3 week
Time period Actual Value(A) Moving avg. Forecast(F) Forecast error E=|A-F| Squared Forecast Error MAPE
1 6500
2 6253
3 5514
4 5357 6089.00 732.00 535824.00 0.1366
5 5425 5708.00 283.00 80089.00 0.0522
6 6278 5432.00 846.00 715716.00 0.1348
7 8119 5686.67 2432.33 5916245.44 0.2996
8 6390 6607.33 217.33 47233.78 0.0340
9 6090 6929.00 839.00 703921.00 0.1378
Total 5349.6667 7999029.2222 0.7949
Average 891.61 1333171.54 13.25%
MAD MSE MAPE

for exponential smoothing:

Time period Actual Value(A) Forecast(F) Forecast error E=A-F Squared Forecast Error MAPE
1 6500
2 6253 6500.00 247.00 61009.00 0.0395
3 5514 0.00 5514.00 30404196.00 1.0000
4 5357 1929.90 3427.10 11745014.41 0.6397
5 5425 3129.39 2295.62 5269848.23 0.4232
6 6278 6413.55 135.55 18373.80 0.0216
7 8119 6366.11 1752.89 3072632.12 0.2159
8 6390 6979.62 589.62 347651.60 0.0923
9 6090 6773.25 683.25 466834.55 0.1122
Total 14645.03 51385559.71 2.54
Average 1830.63 6423194.96 31.80%
MAD MSE MAPE

Step 1 of 5: three-period moving average for the next time period =6866.3

Step 2 of 5:

MAD =891.6

MSE=1333171.5

MAPE =13.2%

Step 3 of 5

exponentially smoothed forecast for the next time period =6534.1

Step 4 of 5:

MAD =1830.6

MSE=6423194.9

MAPE =31.8%

Step 5 of 5:

three-period moving average is best
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