Sxx - Variance Formula

[ \fracS_xx\sigma_x^2 \sim \chi^2_(n-1) ]

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 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. [ \fracS_xx\sigma_x^2 \sim \chi^2_(n-1) ] This is unbiased