In statistics, **Sxx** represents the sum of squared deviations from the mean value of x.

This value is often calculated when fitting a simple linear regression model by hand.

We use the following formula to calculate Sxx:

**Sxx = Σ(x _{i} – x)^{2}**

where:

**Σ**: A symbol that means “sum”**x**: The i_{i}^{th}value of x**x**: The mean value of x

The following example shows how to use this formula in practice.

**Example: Calculating Sxx by Hand**

Suppose we would like to fit a simple linear regression model to the following dataset:

Suppose we would like to calculate Sxx, which represents the sum of squared deviations from the mean value of x.

First, we must calculate the mean value of x:

- x = (1 + 2 + 2 + 3 + 5 + 8) / 6 = 3.5

Next, we can use the following formula to calculate the value for Sxx:

- Sxx = Σ(x
_{i}– x)^{2} - Sxx = (1-3.5)
^{2}+(2-3.5)^{2}+(2-3.5)^{2}+(3-3.5)^{2}+(5-3.5)^{2}+(8-3.5)^{2} - Sxx = 6.25 + 2.25 + 2.25 + .25 + 2.25 + 20.25
- Sxx = 33.5

The value for Sxx turns out to be **33.5**.

This tells us that the sum of squared deviations between the individual x values and the mean x value is 33.5.

Note that we could also use the Sxx Calculator to automatically calculate the value of Sxx for this model as well:

The calculator returns a value of **33.5**, which matches the value that we calculated by hand.

Note that we use the following formulas to perform simple linear regression by hand:

y = a + bx

where:

- a = y – bx
- b = Sxy / Sxx

The calculation for Sxx is just one calculation that we must perform in order to fit a simple linear regression model.

**Related:** How to Calculate Sxy in Statistics

**Additional Resources**

The following tutorials explain how to perform other common tasks in statistics:

How to Perform Simple Linear Regression by Hand

How to Perform Multiple Linear Regression by Hand