Sxx Variance Formula May 2026

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

Thus:

Therefore:

Variance of a chi-squared random variable with (k) df is (2k):

Here’s a concise paper-style explanation, including the formula, its derivation, and its role in variance estimation. 1. Definition of SXX In the context of simple linear regression: sxx variance formula

It measures the total corrected sum of squares for the predictor variable (x). If (x_i) are fixed constants (standard regression assumption), (S_xx) is not a random variable — it has no variance; it’s just a constant.

[ \mathrmVar(S_xx) = 2(n-1)\sigma_x^4 ] The variance of the slope estimator (\hat\beta_1) in simple linear regression is: [ S_xx = \sum_i=1^n (x_i - \barx)^2 ]

[ \mathrmVar(S_xx) = 2(n-1)\sigma_x^4 ] We know: