Sxx Variance Formula !exclusive! -

[ \widehat\mathrmVar(S_xx) = \frac2 S_xx^2n-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:

[ \mathrmVar(S_xx) = 2(n-1)\sigma_x^4 ] We know: [ \widehat\mathrmVar(S_xx) = \frac2 S_xx^2n-1 ] If (S_xx)

where (s_x^2) is the sample variance of (x). it’s just a constant.

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.