Mean Absolute Error (MAE) is a measure of prediction accuracy in regression analysis. It is calculated by taking the average of the absolute differences between the predicted values and the actual values.

For example, if a model predicts the values 3, 4, 5, and 6 for a set of actual values 2, 3, 4, and 5, the MAE would be calculated as:

MAE = (|3-2| + |4-3| + |5-4| + |6-5|) / 4 = 1.5

In this case, the model has an average error of 1.5, indicating that its predictions are generally off by that amount.

Another example of MAE can be seen in a model that predicts stock prices. If the model predicts a stock will have a price of $100, but the actual price is $105, the error would be |100-105| = 5. If the model also predicts a stock will have a price of $90, but the actual price is $95, the error would be |90-95| = 5. In this case, the MAE would be calculated as:

MAE = (5 + 5) / 2 = 5

This indicates that the model has an average error of 5 dollars per prediction, suggesting that its predictions are not very accurate.

MAE is commonly used in regression analysis because it is easy to interpret and understand. Unlike other error measures, such as mean squared error, MAE is not affected by large errors or outliers. This makes it a more robust measure of accuracy, as it can provide a more reliable estimate of the model’s performance.

Additionally, MAE is relatively insensitive to the distribution of the data. This means that it can be used with data that has a variety of shapes, including skewed or non-normal distributions. This makes MAE a versatile measure that can be applied to a wide range of regression problems.

Overall, MAE is a valuable tool for evaluating the accuracy of regression models. It provides a simple, interpretable measure of prediction error that can be used to compare the performance of different models and identify areas for improvement.