Show that V(s 2 ) = 2 4 /(n - 2). The result follows from Theorem 10.1

Show that V(s²) = 2σ⁴/(n - 2). The result follows from Theorem 10.1 and the fact that V(x²) = 2v.

Transcribed Image Text:

THEOREM 10.1 Let s = SSE/(n – 2). Then, when the assumptions of Section 10.2 are satisfied, the %3D statistic SSE x = (n – 2)s possesses a chi-square distribution with v = (n – 2) degrees of freedom. From Theorem 10.1, it follows that s2 = n-2 Then E(s?) %3D n - 2 E(x) where E(X) = v = (n - 2). Therefore, E(s) (n - 2) %3D = o? and we conclude that s is an unbiased estimator of o?. The procedure used in Table 10.3 to calculate SSE can lead to large rounding errors. The formula for s' and an appropriate method for calculating SSE are shown in the box below. We will illustrate the calculation of s' with Example 10.3. Estimation of o? SSE SSE Degrees of freedom for error where E(vi - î) = SSy - BISSy (Ex.)? SS.y = E0 - 5 = Ey?- SSE = Warning: When performing these calculations, you may be tempted to round the calculated values of SS., B1, and SS. Be certain to carry at least six significant figures for each of these quantities to avoid substantial errors in the calculation of SSE.