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,

**S _{xx }= ∑(X_{i} – X̅)^{2}**.

**S _{xy} = Σ (X_{i }– X̄)(Y_{i} – Ȳ)**.

**S _{yy} = Σ(Y_{i} – Ȳ)^{2}**.

- Here, the sum
**Σ**is taken over all the x_{i}and y_{i}data values from i=1 to i=n. - x
_{i }denotes the given data values of the variable X. **X̅**denotes the mean/average of the X data values.- y
_{i }denotes the given data values of the variable Y. **Ȳ**denotes the mean/average of the x data values.

**S**_{xx} Formula:

_{xx}Formula

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

**S _{xx }= ∑(X_{i} – X̅)^{2}**.

Alternatively, we can also use the following alternative formula,

**S _{xx }= (∑X_{i}^{2}) – n*X̅^{2}.**

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

**S**_{xy} Formula:

_{xy}Formula

The Sxy value can be calculated using the formula,

**Sxy = Σ (X _{i} – X̄)(Y_{i} – Ȳ)**.

Alternatively, we can also use the following alternative formula,

**S _{xy }= (∑ X_{i}Y_{i}) – n*X̅Ȳ.**

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

**S**_{yy} Formula:

_{yy}Formula

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

**S _{yy }= ∑(Y_{i} – Ȳ)^{2}**.

Alternatively, we have

**S _{yy }= (∑Y_{i}^{2}) – n*Ȳ^{2}.**

We summarize the formulas below.

**Related Articles:**

- Sxx, Sxy, and Syy Calculator.
- How to Find Sxx (with Examples & Formula).
- How to Calculate Sxy (Formula & Examples).