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

Step 1: Calculate the Three-Period Weighted Moving Average Forecast

Let's assign weights to the most recent three months' data. Suppose the weights are as follows:

• Weight for the most recent month: 0.5
• Weight for the second most recent month: 0.3
• Weight for the third most recent month: 0.2

Using these weights, the forecast for a given month can be calculated as: $\text{Forecast}_{n} = (0.5 \times \text{Profit}_{n-1}) + (0.3 \times \text{Profit}_{n-2}) + (0.2 \times \text{Profit}_{n-3})$

Step 2: Calculate the Forecasts for Each Month (starting from Apr-12)

• Apr-12 Forecast = $(0.5 \times 5,064) + (0.3 \times 5,503) + (0.2 \times 5,750)$
• May-12 Forecast = $(0.5 \times 4,757) + (0.3 \times 5,064) + (0.2 \times 5,503)$
• Jun-12 Forecast = $(0.5 \times 5,200) + (0.3 \times 4,757) + (0.2 \times 5,064)$
• Jul-12 Forecast = $(0.5 \times 5,678) + (0.3 \times 5,200) + (0.2 \times 4,757)$
• Aug-12 Forecast = $(0.5 \times 6,619) + (0.3 \times 5,678) + (0.2 \times 5,200)$
• Sep-12 Forecast = $(0.5 \times 6,195) + (0.3 \times 6,619) + (0.2 \times 5,678)$

Step 3: Calculate MAD, MSE, and MAPE

MAD (Mean Absolute Deviation)

$\text{MAD} = \frac{1}{n} \sum_{i=1}^{n} |\text{Actual}_i - \text{Forecast}_i|$

MSE (Mean Squared Error)

$\text{MSE} = \frac{1}{n} \sum_{i=1}^{n} (\text{Actual}_i - \text{Forecast}_i)^2$

MAPE (Mean Absolute Percentage Error)

$\text{MAPE} = \frac{100\%}{n} \sum_{i=1}^{n} \left| \frac{\text{Actual}_i - \text{Forecast}_i}{\text{Actual}_i} \right|$

I'll now perform the calculations based on the steps above.The calculated values for the three-period weighted moving average forecast are as follows:

• MAD (Mean Absolute Deviation): 520.0
• MSE (Mean Squared Error): 415,895.4
• MAPE (Mean Absolute Percentage Error): 8.9%

These values are rounded to one decimal place as required.

Would you like to go into more detail on any of these calculations?

Here are five related questions that might expand your understanding:

1. How would the results differ if we used equal weights instead of the weighted moving average?
2. What would the forecasts look like if you used a four-period moving average?
3. How does MAD compare to MSE in terms of sensitivity to outliers?
4. Can you calculate the same metrics (MAD, MSE, MAPE) using exponential smoothing?
5. How do changes in the weights affect the accuracy of the moving average forecast?

Tip: When using MAPE, remember that it tends to be less effective when actual values are very close to zero, as this can result in disproportionately large percentage errors.