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The Mean Absolute Error (MAE) is a commonly used metric for evaluating the accuracy of a regression model in R. It measures the average absolute difference between the actual and predicted values of a variable. The calculation for MAE involves taking the average of the absolute differences between the predicted and actual values. This metric is useful in assessing the overall performance of a model, as it gives equal weight to all errors, regardless of their direction. In R, the MAE is calculated by taking the sum of the absolute differences and dividing it by the total number of observations. A lower MAE value indicates a better fit between the model and the data.
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 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.