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 ($)

6,3006,300

6,0536,053

5,3945,394

5,1975,197

5,3655,365

6,1186,118

7,7197,719

6,3386,338

6,0456,045

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.

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

### 1. Three-Period Moving Averages
First, calculate the three-period moving averages for each month starting from Mar-12. These moving averages will be compared to the actual profits.

### 2. Errors Calculation
For each period, calculate:
- **Absolute Error** for MAD: $ \text{Absolute Error} = |\text{Actual Profit} - \text{Forecasted Profit}| $
- **Squared Error** for MSE: $ \text{Squared Error} = (\text{Actual Profit} - \text{Forecasted Profit})^2 $
- **Percentage Error** for MAPE: $ \text{Percentage Error} = \left|\frac{\text{Actual Profit} - \text{Forecasted Profit}}{\text{Actual Profit}}\right| \times 100 $

### 3. Aggregation
- MAD: Average of absolute errors
- MSE: Average of squared errors
- MAPE: Average of percentage errors

Let's calculate the three-period moving averages, and then compute the MAD, MSE, and MAPE.The calculated scores for the three-period moving average are as follows:
- **Mean Absolute Deviation (MAD):** 767.1
- **Mean Squared Error (MSE):** 1,052,752.1
- **Mean Absolute Percentage Error (MAPE):** 11.8%

These values give a quantitative measure of the forecast accuracy based on the three-period moving average.

Would you like more details on how these values were derived, or do you have any further questions?

Here are five related questions:
1. How would these values change if we used a four-period moving average instead?
2. What does a high MSE value indicate about the accuracy of the moving average?
3. How does MAPE help in comparing forecast accuracy across different datasets?
4. Can you calculate the MAD, MSE, and MAPE

Learn how to calculate Mean Absolute Deviation (MAD), Mean Squared Error (MSE), and Mean Absolute Percentage Error (MAPE) for a three-period moving average with a detailed solution. This problem involves analyzing monthly profit data and evaluating forecast accuracy metrics. Suitable for professionals and analysts.

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