Sxx Variance Formula [best] (2026)

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

This is unbiased if (x) is normal. | Case | Formula for (\mathrmVar(S_xx)) | |------|--------------------------------------| | (x) fixed | 0 | | (x) random, normal | (2(n-1)\sigma_x^4) | | (x) random, normal, estimated | (\frac2S_xx^2n-1) | sxx variance formula

It seems you’re looking for a paper or derivation related to the term — a common notation in statistics, particularly in simple linear regression and sum of squares decomposition . [ \mathrmVar(S_xx) = 2(n-1)\sigma_x^4 ] The variance of

But if we treat (x_i) as (e.g., in observational studies, random sampling from a bivariate population), then (S_xx) is a statistic with a sampling distribution. It measures the total corrected sum of squares

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.

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

Thus: