[ \mathrmVar(S_xx) = 2(n-1)\sigma_x^4 ] We know:
[ \frac(n-1)s_x^2\sigma_x^2 \sim \chi^2_n-1 ]
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. sxx variance formula
[ \mathrmVar(\hat\beta 1) = \frac\sigma^2S xx ]
Variance of a chi-squared random variable with (k) df is (2k): [ \mathrmVar(S_xx) = 2(n-1)\sigma_x^4 ] We know: [
[ \mathrmVar\left( \fracS_xx\sigma_x^2 \right) = 2(n-1) ]
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 . sxx variance formula
[ \mathrmVar(S_xx) = 2(n-1)\sigma_x^4 ] The variance of the slope estimator (\hat\beta_1) in simple linear regression is: