correct answer please Consider the following data:


Monthly Profit of a GymMonth

Jan-12

Feb-12

Mar-12

Apr-12

May-12

Jun-12

Jul-12

Aug-12

Sep-12

Profit ($)

5,7505,750

5,5035,503

5,0645,064

4,7574,757

5,2005,200

5,6785,678

6,6196,619

6,1956,195

5,9255,925

Step 4 of 5 :  

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




To calculate the Mean Absolute Deviation (MAD), Mean Squared Error (MSE), and Mean Absolute Percentage Error (MAPE) for the three-period weighted moving average, we'll follow these steps:

### Step 1: Calculate the Three-Period Weighted Moving Averages
First, we'll calculate the three-period weighted moving averages using the weights 33, 22, and 11 for each month from April-12 to September-12.

The formula is:

\[
\text{Weighted Moving Average} = \frac{(P_{\text{Month3}} \times 33) + (P_{\text{Month2}} \times 22) + (P_{\text{Month1}} \times 11)}{33 + 22 + 11}
\]

where $ P_{\text{Month3}} $, $ P_{\text{Month2}} $, and $ P_{\text{Month1}} $ are the profits for the most recent, second recent, and third recent months, respectively.

Let's calculate these:

1. **April-12**:  
   \[
   \text{Weighted Moving Average} = \frac{(5064 \times 33) + (5503 \times 22) + (5750 \times 11)}{66} = \frac{167112 + 121066 + 63250}{66} = \frac{351428}{66} = 5324.666667
   \]
2. **May-12**:  
   \[
   \text{Weighted Moving Average} = \frac{(4757 \times 33) + (5064 \times 22) + (5503 \times 11)}{66} = \frac{156981 + 111408 + 60533}{66} = \frac{328922}{66} = 4983.666667
   \]
3. **June-12**:  
   \[
   \text{Weighted Moving Average} = \frac{(5200 \times 33) + (4757 \times 22) + (5064 \times 11)}{66} = \frac{171600 + 104654 + 55704}{66} = \frac{331958}{66} = 5030.575758
   \]
4. **July-12**:  
   \[
   \text{Weighted Moving Average} = \frac{(5678 \times 33) + (5200 \times 22) + (4757 \times 11)}{66} = \frac{187374 + 114400 + 52327}{66} = \frac{354101}{66} = 5365.166667
   \]
5. **August-12**:  
   \[
   \text{Weighted Moving Average} = \frac{(6619 \times 33) + (5678 \times 22) + (5200 \times 11)}{66} = \frac{218427 + 124916 + 57200}{66} = \frac{400543}{66} = 6061.287879
   \]
6. **September-12**:  
   \[
   \text{Weighted Moving Average} = \frac{(6195 \times 33) + (6619 \times 22) + (5678 \times 11)}{66} = \frac{204435 + 145618 + 62458}{66} = \frac{412511}{66} = 6257.742424
   \]

### Step 2: Calculate the Errors

The errors are calculated as the difference between the actual profit and the weighted moving average.

\[
\text{Error for Apr-12} = 4757 - 5324.666667 = -567.666667
\]
\[
\text{Error for May-12} = 5200 - 4983.666667 = 216.333333
\]
\[
\text{Error for Jun-12} = 5678 - 5030.575758 = 647.424242
\]
\[
\text{Error for Jul-12} = 6619 - 5365.166667 = 1253.833333
\]
\[
\text{Error for Aug-12} = 6195 - 6061.287879 = 133.712121
\]
\[
\text{Error for Sep-12} = 5925 - 6257.742424 = -

Learn how to calculate Mean Absolute Deviation (MAD), Mean Squared Error (MSE), and Mean Absolute Percentage Error (MAPE) for a three-period weighted moving average forecast using gym profit data. Detailed step-by-step solution with formulas and calculations provided.

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