Predictive Hacks

# RMSE MAE and MAPE in R

In this tutorial, we will show you how to calculate the RMSE, MAE, and MAPE in R. For all metrics, we will consider the following $$y$$ and $$\hat{y}$$ and we will verify that we derive the right results by using the Metrics library.

library(Metrics)

y<-c(10, 20, 30, 40, 50, 60)
y_pred<-c(9, 22, 28, 34, 55, 58)



## RMSE

The formula of the RMSE (Root Mean Square Error) is given by:

$$RMSE = \sqrt{\sum_{i=1}^{n}\frac{(\hat{y_i} – y_i)^2}{n}}$$

Let’s apply the formula and verify the results using the library:

sqrt(sum((y_pred-y)^2)/length(y))


[1] 3.511885
rmse(y, y_pred)


[1] 3.511885

## MAE

The formula of the MAE (Mean Absolute Error) is given by:

$$MAE = \sum_{i=1}^{n}\frac{\mid\hat{y_i} – y_i\mid}{n}$$

Let’s apply the formula and verify the results using the library:

sum(abs(y_pred-y))/length(y)


[1] 3
mae(y, y_pred)


[1] 3

## MAPE

The formula of the MAPE (Mean Absolute Percentage Error) is given by:

$$MAPE = \frac{1}{n}\sum_{i=1}^{n}\mid\frac{y_i – \hat{y_i}}{y_i}\mid$$

Let’s apply the formula and verify the results using the library:

mean(abs((y_pred-y)/y))


[1] 0.09166667
mape(y, y_pred)


[1] 0.09166667

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