Calculate Sum of Squared Deviations in R (2 Examples)

This tutorial explains how to compute the sum of squares (also called sum of squared deviations) in the R programming language.

Letâ€™s get started.

Example Data

Consider the following example data:

```x <- 11:20                          # Create example vector
x                                   # Print example vector
#  [1] 11 12 13 14 15 16 17 18 19 20```

The previous output of the RStudio console shows that our example data is a numeric vector containing a range from 11 to 20.

Example 1: Compute Sum of Squares Using sum() & mean() Functions

The following R programming syntax illustrates how to calculate the sum of squared deviations of a numeric vector in R.

For this task, we can apply the sum and mean functions as shown in the following R code:

```ss_1 <- sum((x - mean(x))^2)        # Calculate sum of squares
ss_1                                # Print sum of squares
# [1] 82.5```

The previous output of the RStudio console shows the result: The sum of squares of our input vector is 82.5.

Example 2: Compute Sum of Squares Using var() & length() Functions

In Example 2, Iâ€™ll show an alternative to the mean and sum functions that we have used in Example 1. In this example, weâ€™ll use the var and length functions instead.

Have a look at the following R code:

```ss_2 <- var(x) * (length(x) - 1)    # Calculate sum of squares
ss_2                                # Print sum of squares
# [1] 82.5```

As you can see, the RStudio console returns exactly the same result as the code in Example 1. For that reason, the code of Example 2 provides a good way to double-check your results.

Video, Further Resources & Summary

In case you need more explanations on the R programming codes of this tutorial, you may want to have a look at the following video on the Statistics Globe YouTube channel. In the video, Iâ€™m explaining the R code of this article in a live session:

Furthermore, you may have a look at some of the related articles on statisticsglobe.com. You can find a selection of tutorials below.

In summary: You have learned on this page how to calculate the sum of squared deviations in the R programming language. Let me know in the comments section, in case you have additional questions.

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