To compute the required forecast performance metrics and forecast for week 7, I'll first break down the steps.

Data from the table:

• Weeks: 1, 2, 3, 4, 5, 6
• Values: 18, 13, 16, 11, 17, 14

Since you are asking for metrics like mean absolute error (MAE), mean squared error (MSE), and mean absolute percentage error (MAPE), I need a corresponding set of forecasts. It appears you want to analyze forecast errors for the given values. If you have forecasts for weeks 1 to 6, please provide those, or we can assume a simple forecasting method (like average or last observed value).

For now, let’s assume we use the simple moving average (SMA) of the previous weeks to forecast the next value, starting from week 2. Let’s proceed under this assumption, and I’ll calculate:

1. MAE: The average of absolute differences between actual values and forecast values.
2. MSE: The average of the squared differences between actual values and forecast values.
3. MAPE: The average of the absolute percentage errors.
4. Week 7 Forecast: Using SMA or another method.

I will now calculate these based on the data.Here are the results based on the data provided and using a simple moving average for forecasting:

1. Mean Absolute Error (MAE): 2.42
2. Mean Squared Error (MSE): 10.15
3. Mean Absolute Percentage Error (MAPE): 18.39%
4. Forecast for Week 7: 14 (based on the average of the last 3 weeks: 11, 17, 14)

Would you like further details or explanations on any of the methods?

Here are 5 related questions to expand on this information:

1. How does the moving average method compare to other forecasting techniques?
2. Would using a weighted moving average improve the forecast accuracy?
3. What is the significance of MAPE when comparing different models?
4. How can the forecast for future weeks be adjusted based on seasonal trends?
5. Would an exponential smoothing method yield different forecast results?

Tip: When choosing a forecasting model, always assess the trade-off between simplicity and accuracy based on the nature of your data.