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(xi – x)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(xi – 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
