Sxx Variance Formula [OFFICIAL]

This method is preferred for hand calculations because you do not have to subtract the mean from every single data point. It yields the exact same result but is usually faster.

$$S_xx = \sum x_i^2 - \frac(\sum x_i)^2n$$

In regression and multivariate statistics, the notation ( S_xx ) comes from the idea of sums of squares and cross-products.

This notation system (often attributed to the “corrected sums of squares” approach) is standard in regression textbooks. The “S” stands for “Sum” (or sometimes “Corrected Sum”), and the subscript indicates which variables are involved. Sxx Variance Formula

Thus, Sxx is the most basic building block: the corrected sum of squares for a single variable.

Here’s the critical insight: Sxx is the numerator of the sample variance.

Recall the formula for sample variance ( s_x^2 ): This method is preferred for hand calculations because

[ s_x^2 = \frac\sum_i=1^n (x_i - \barx)^2n - 1 ]

Therefore:

[ S_xx = (n - 1) \cdot s_x^2 ]

This is the fundamental relationship. Sxx is just the total squared deviation before dividing by degrees of freedom.

Why is this important? Because:

So, if you know Sxx, you can instantly find the variance. Conversely, if you know the variance, you can find Sxx. In regression and multivariate statistics, the notation (