# Calculate (Root) Mean Squared Error in R (5 Examples)

In this tutorial you’ll learn how to **compute the mean squared error (MSE) and the root mean squared error (RMSE)** in R programming.

The article consists of five examples for the computation of the MSE and RMSE. More precisely, the page consists of this information:

It’s time to dive into the examples!

## Creating Example Data

As the first step, we have to construct some example data:

set.seed(39756934) # Create example data x <- rnorm(100) y <- rnorm(100) + 0.5 * x my_data <- data.frame(x, y) head(my_data) # Print head of example data

As you can see based on Table 1, our example data is a data frame consisting of the two columns “x” and “y”.

Next, we can estimate a linear regression model using the lm function:

my_mod <- lm(y ~ x, my_data) # Estimate linear model

The previous R code has created a new data object called my_mod, which contains the output of our linear regression. In the following examples, we’ll use this model object to compute the MSE and RMSE.

## Example 1: Calculate MSE Using mean() Function & Residuals

Example 1 illustrates how to calculate the mean squared error based on the mean function and the residuals of our linear regression.

Have a look at the following R code and its output:

mean(my_mod$residuals^2) # Calculate MSE # [1] 0.7643822

As you can see based on the previous output of the RStudio console, the MSE of our analysis is 0.7643822.

## Example 2: Calculate MSE Using mean() & predict() Functions

Example 1 has explained how to compute the MSE using the mean function and the residuals of our model. However, the R programming languages provides alternative ways to calculate the mean squared error.

This example illustrates how to use the mean and predict functions to calculate the MSE of a regression analysis:

mean((my_data$y - predict(my_mod))^2) # Calculate MSE # [1] 0.7643822

The result is exactly the same as in Example 1.

## Example 3: Calculate MSE Using mse() Function of Metrics Package

So far, we have only used the functions provided by the basic installation of the R programming language.

Example 3 explains how to compute the MSE using the mse() function of the Metrics package.

First, we need to install and load the Metrics package.

install.packages("Metrics") # Install & load Metrics package library("Metrics")

Next, we can apply the mse and predict functions to calculate the MSE:

mse(my_data$y, predict(my_mod , my_data)) # Calculate MSE # [1] 0.7643822

Again, the result is 0.7643822. Whether you want to use the Metrics package or one of codes of the previous Examples is a matter of taste!

## Example 4: Calculate RMSE Using mean() & sqrt() Functions

We can easily adjust the previous R codes to calculate the root mean squared error (RMSE) instead of the mean squared error (MSE).

For this task, we can simply apply the sqrt function to the output of one of the previous codes to calculate the square root of this result.

In this example, I’m applying the sqrt function to the R syntax of Example 1:

sqrt(mean(my_mod$residuals^2)) # Calculate RMSE [1] 0.8742895

As you can see, the RMSE of our regression model is 0.8742895.

## Example 5: Calculate RMSE Using rmse() Function of Metrics Package

The Metrics package that we have already used in Example 3 also provides a function to calculate the RMSE. This function is called rmse() and can be applied as shown below:

rmse(my_data$y, predict(my_mod , my_data)) # Calculate RMSE [1] 0.8742895

The result is the same as in the previous example.

## Video & Further Resources

I have recently published a video on my YouTube channel, which explains the examples of the present tutorial. You can find the video below.

In addition, you may want to have a look at the other articles on this website. Please find a selection of related articles below:

In summary: On this page you have learned how to **calculate the (root) mean squared error** in R programming. Tell me about it in the comments section, in case you have further questions and/or comments. Furthermore, please subscribe to my email newsletter in order to get updates on new articles.

## 4 Comments. Leave new

I’m Adrian Keister, who left a comment on your YouTube – which appears to be malfunctioning and not letting me leave my comment. So here’s a MWE:

set.seed(39756934) # Create example data

x = rnorm(100)

y = rnorm(100) + 0.5 * x + 3

my_data = data.frame(x, y)

min(y)

0.6716385

my_mod = glm(y~x, data=my_data, family=Gamma())

mean(my_mod$residuals^2)

0.01388825

mean((my_data$y – predict(my_mod))^2)

6.954654

Hey Adrian,

I’ve just responded to your comment on YouTube. I’ll copy/paste my response here as well:

Thanks for sharing your code. Unfortunately, I don’t have experience in calculating the MSE for Gamma distributions, but I found this function which might be helpful for your case: https://www.rdocumentation.org/packages/DELTD/versions/2.6.5/topics/mseGamma

I hope this helps!

Joachim

Asked on SO.SE, and got the idea that both the residuals and the predict functions need to have type=”response” in order to ensure equality in more general cases.

Please see my response to your other comment.