[ \mathrmVar(\hat\beta 1) = \frac\sigma^2S xx ]
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
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)): [ \mathrmVar(\hat\beta 1) = \frac\sigma^2S xx ] It
Thus:
[ S_xx = \sum_i=1^n (x_i - \barx)^2 ]