In statistics, the **mean absolute error** (MAE) is a way to measure the accuracy of a given model. It is calculated as:

MAE = (1/n) * Σ|y_{i} – x_{i}|

where:

**Σ:**A Greek symbol that means “sum”**y**The observed value for the i_{i}:^{th}observation**x**The predicted value for the i_{i}:^{th}observation**n:**The total number of observations

We can calculate the mean absolute error in R by using the **mae(actual, predicted)** function from the **Metrics** package.

This tutorial provides two examples of how to use this function in practice.

**Example 1: Calculate Mean Absolute Error Between Two Vectors**

The following code shows how to calculate the mean absolute error between a vector of observed values and a vector of predicted values:

library(Metrics) #define observed and predicted values observed <- c(12, 13, 14, 15, 15, 22, 27, 29, 29, 30, 32) predicted <- c(11, 13, 14, 14, 16, 19, 24, 30, 32, 36, 30) #calculate mean absolute error between vectors mae(observed, predicted) [1] 1.909091

The mean absolute error (MAE) turns out to be **1.909**.

This tells us that the average absolute difference between the observed values and the predicted values is 1.909.

**Example 2: Calculate Mean Absolute Error for a Regression Model**

The following code shows how to fit a regression model in R and then calculate the mean absolute error between the predictions made by the model and the actual observed response values:

library(Metrics) #create data df <- data.frame(x1=c(1, 3, 3, 4, 4, 6, 6, 8, 9, 3), x2=c(7, 7, 4, 10, 13, 12, 17, 19, 20, 34), y=c(17, 18, 19, 20, 24, 28, 25, 29, 30, 32)) #view first six rows of data head(df) x1 x2 y 1 1 7 17 2 3 7 18 3 3 4 19 4 4 10 20 5 4 13 24 6 6 12 28 #fit regression model model <- lm(y~x1+x2, data=df) #calculate MAE between predicted values and observed values mae(df$y, predict(model)) [1] 1.238241

The mean absolute error (MAE) turns out to be **1.238**.

This tells us that the average absolute difference between the observed values and the predicted values is 1.238.

In general, the lower the value for the MAE the better a model is able to fit a dataset. When comparing two different models, we can compare the MAE of each model to know which one offers a better fit to a dataset.

**Additional Resources**

Mean Absolute Error Calculator

How to Calculate Mean Absolute Error in Excel

How to Calculate Mean Absolute Error in Python