# Sxx, Sxy, and Syy Equations

-

The Sxx, Sxy, and Syy equations are given below. These formulas can be used to calculate the values of Sxx, Sxy, and Syy which are very useful quantities.

## Sxx, Sxy, and Syy Equations (Formula):

The Sxx, Sxy, and Syy Equations are,

Sxx = ∑(Xi – X̅)2.

Sxy = Σ (Xi – X̄)(Yi – Ȳ).

Syy = Σ(Yi – Ȳ)2.

• Here, the sum Σ is taken over all the xi and yi data values from i=1 to i=n.
• xi denotes the given data values of the variable X.
• denotes the mean/average of the X data values.
• yi denotes the given data values of the variable Y.
• Ȳ denotes the mean/average of the x data values.

#### Sxx Formula:

As stated above the Sxx value can be calculated using the formula,

Sxx = ∑(Xi – X̅)2.

Alternatively, we can also use the following alternative formula,

Sxx = (∑Xi2) – n*X̅2.

The proof of the fact that both these formulas are equal can be found here.

#### Sxy Formula:

The Sxy value can be calculated using the formula,

Sxy = Σ (Xi – X̄)(Yi – Ȳ).

Alternatively, we can also use the following alternative formula,

Sxy = (∑ XiYi) – n*X̅Ȳ.

It is a fact that both these formulas give the same result.

#### Syy Formula:

The Syy formula is the same as the Sxx formula with the variable Y in place of the variable X.

Syy = ∑(YiȲ)2.

Alternatively, we have

Syy = (∑Yi2) – n*Ȳ2.

We summarize the formulas below.

#### Related Articles:

Summary
Article Name
Sxx, Sxy, and Syy Equations
Description
The Sxx, Sxy, and Syy Equations are: Sxx = ∑(Xi - X̅)^2 Sxy = Σ (Xi – X̄)(Yi - Ȳ) Syy = Σ(Yi - Ȳ)^2.