How to Calculate Sxx in Statistics (With Example)


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(xix)2

where:

  • Σ: A symbol that means “sum”
  • xi: The ith 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(xix)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:

ssx calculator for linear regression

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

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