# How to Calculate Mean Absolute Error in R

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|yi – xi|

where:

• Σ: A Greek symbol that means “sum”
• yi: The observed value for the ith observation
• xi: The predicted value for the ith 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

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.