Sxx Variance Formula: |best|

Under the :

[ \mathrmVar(S_xx) = 2(n-1)\sigma_x^4 ] The variance of the slope estimator (\hat\beta_1) in simple linear regression is:

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

[ \frac(n-1)s_x^2\sigma_x^2 \sim \chi^2_n-1 ]

Thus:

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) |

[ \mathrmVar(S_xx) = 2(n-1)\sigma_x^4 ] We know: Under the : [ \mathrmVar(S_xx) = 2(n-1)\sigma_x^4 ]

But if we treat (x_i) as (e.g., in observational studies, random sampling from a bivariate population), then (S_xx) is a statistic with a sampling distribution.