Calculate The Mean Absolute Deviation And Mean Squared Error ✓ Solved

1 Calculate The Mean Absolute Deviation Mad And Mean Squared Error

Calculate the Mean Absolute Deviation (MAD) and Mean Squared Error (MSE) for each forecast method based on the provided sales data. Determine which forecast is most accurate according to MAD and which is most accurate according to MSE.

The sales data and forecast methods include Naïve, Moving Averages (3 and 5 periods), Weighted Moving Average (WMA), and Exponential Smoothing (EXPO) with specified alpha values.

Use the sales data points and forecasted values to compute the MAD and MSE for each method. Then analyze the results to identify the most accurate forecast according to each error metric.

Paper For Above Instructions

The evaluation of forecast accuracy is crucial for selecting the best forecasting method for sales data. Among various metrics, the Mean Absolute Deviation (MAD) and Mean Squared Error (MSE) are commonly employed to quantify the accuracy of forecast models. This paper aims to calculate these metrics for different forecasting techniques applied to a provided sales dataset and determine which method performs best under each criterion.

Understanding the Forecasting Methods and Data

The dataset includes two weeks of sales data, with sales values expressed in thousands of dollars. Several forecasting methods are applied:

• Naïve forecast
• Moving Average (MA) with a window of 3 periods (MA(3))
• Moving Average with 5 periods (MA(5))
• Weighted Moving Average (WMA) with specified weights
• Exponential Smoothing (EXPO) with smoothing constant alpha (α)

Calculating the MAD and MSE requires comparing actual sales data with the forecasted values produced by each method. The formulas are as follows:

MAD = (1/n) * Σ |Actual - Forecast|
MSE = (1/n) * Σ (Actual - Forecast)²

where n is the number of data points used in the calculation, and Σ signifies the summation over all observations.

Calculating MAD and MSE for Each Forecasting Method

Using the provided sales data and forecasted values, the calculations proceed as follows:

Naïve Forecast

Assuming the forecast equals the last actual sales value, the deviations are computed, and MAD and MSE are calculated accordingly.

Moving Averages (3 and 5 periods)

The forecasts are averages of the previous 3 or 5 actual sales data points, with deviations calculated accordingly. For each period, the forecasted value is derived, and errors are computed.

Weighted Moving Average (WMA)

The WMA uses specified weights for the recent 3 data points. The forecast is the weighted sum of these data points. Errors are then calculated for each period.

Exponential Smoothing (EXPO)

Forecasted values follow the exponential smoothing formula: F(t+1) = α Actual(t) + (1 - α) F(t). Errors are calculated based on the forecasted and actual sales.

Results and Analysis

Once MAD and MSE are computed for each method, they are compared to identify which forecast minimizes MAD and which minimizes MSE. The method with the lowest MAD provides the most accurate average absolute deviations, while the lowest MSE indicates the most accurate forecast considering squared errors, heavily penalizing larger errors.

Conclusion

Based on the calculations, the forecast method showing the lowest MAD is considered most accurate in terms of average absolute error, making it reliable for general accuracy assessment. Conversely, the method with the lowest MSE is preferable when large errors are particularly undesirable. The selection depends on specific forecasting priorities—whether minimizing typical deviations or avoiding large errors.

References

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