The calculators below calculate the value of Sxx, Sxy, and Syy on the basis of the x data values and y data values entered. Simply enter the values of the x and y variables in the calculators below to find the Sxx, Sxy, and Syy values.

**Sxx Calculator:**

The S_{xx} value is calculated by adding up the squared deviations of the data values from the mean. The calculator below finds the value of S_{xx} on the basis of the x values entered.

**Sxx: 49.71429**

**Sxy Calculator:**

The S_{xy} variance can be found by taking the sum of the product of deviations of the x and y values from their means. We need to enter both the x and y data values in order to calculate the S_{xy} value.

**x values:**

**y values:**

**Sxy = -291.00000**

**Syy Calculator:**

The sum of squares due to Y, that is, S_{yy} can be calculated using the formula,

S_{yy} = Σ(Y_{i} - Ȳ)^{2}.

We can directly obtain the S_{yy} value using the calculator below.

**Syy: 317.42857**

**Example Calculation:**

The Sxx value is an important quantity that is useful during calculations in both regression and correlation analysis. It is calculated using the formula,

S_{xx} = Σ (X_{i} - X̄)^{2}

For instance, if the x values are 1, 2, 2, 3, 5, 8, and 9. Then,

**Step 1**: We first calculate the mean X̄,

X̄ = (2 + 3 + 6 + 8 + 3 + 8 + 9)/7 = 39/7 = 5.5714

**Step **2: Then we calculate the x variance by subtracting the data values from the mean, squaring the differences, and then adding them up,

S_{xx} = Σ (Xi - X̄)^{2} = (2 - 5.5714)^{2} + (3 - 5.5714)^{2} + (6 - 5.5714)^{2}+ (8 - 5.5714)^{2} + (3 - 5.5714)^{2} + (8 - 5.5714)^{2} + (9 - 5.5714)^{2} = **49.71429**

As we see above, the calculations can be long and tiresome to perform by hand. We recommend that you use the S_{xx} calculator above to calculate the value directly without any manual calculations.