In statistics, **Sxy** represents the sum of the product of the differences between x values and the mean of x and the differences between y values and the mean of y.

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

We use the following formula to calculate Sxy:

**Sxy = Σ(x _{i} – x)(y_{i} – y)**

where:

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

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

**Example: Calculating Sxy by Hand**

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

Suppose we would like to calculate Sxy for this dataset.

First, we must calculate the mean value of x:

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

Then, we must calculate the mean value of y:

- y = (8 + 12 + 14 + 19 + 22 + 21) / 6 = 16

Using these values, the following screenshot shows how to calculate the value for Sxy:

The value for Sxy turns out to be **59**.

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

The calculator returns a value of **59**, 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 Sxy is just one calculation that we must perform in order to fit a simple linear regression model.

**Related:** How to Calculate Sxx 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