Sxx Variance Formula ((better)) -

Here’s a concise paper-style explanation, including the formula, its derivation, and its role in variance estimation. 1. Definition of SXX In the context of simple linear regression:

If (x_i \sim \texti.i.d. N(\mu_x, \sigma_x^2)):

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

where (s_x^2) is the sample variance of (x).

[ \mathrmVar\left( \fracS_xx\sigma_x^2 \right) = 2(n-1) ] Here’s a concise paper-style explanation

[ \mathrmVar(\hat\beta 1) = \frac\sigma^2S xx ]

Therefore:

Thus: