[ \mathrmVar(S_xx) = 2(n-1)\sigma_x^4 ] We know:
[ \mathrmVar\left( \fracS_xx\sigma_x^2 \right) = 2(n-1) ]
If (S_xx) is random (random (x)), the of (\hat\beta 1) involves the expectation of (1/S xx). But conditionally on (x), (S_xx) is constant. 5. Small-Sample Correction If (\sigma_x^2) is unknown, replace with (\hat\sigma x^2 = S xx/(n-1)): sxx variance formula
Thus:
Variance of a chi-squared random variable with (k) df is (2k): [ \mathrmVar(S_xx) = 2(n-1)\sigma_x^4 ] We know: [
Therefore:
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(\hat\beta 1) = \frac\sigma^2S xx ]