The means reparameterization was used on the cabbage data example (Example 9.5) in the text. Define β∗ and X∗ for this model (equation 9.48 using the reparameterization constraints γ 3 = τ 2 = (γ τ...

The means reparameterization was used on the cabbage data example (Example 9.5) in the text. Define β∗ and X∗ for this model (equation 9.48 using the reparameterization constraints γ₃
= τ₂
= (γ_τ)31 = (γ_τ)32 = (γ_τ)12 = (γ_τ)22 = 0. Define K for the reparameterized model so as to obtain the sum of squares for “dates-by-lines” interaction.

Example 9.5

The tests of significance in Example 9.4 assume that the variance of the Example 9.5 errors in the model is the same for all three groups. Estimating the simple linear regression for the three groups separately, we obtain the residual mean squares
1 each with two degrees of freedom. Bartlett’s test statistic in equation 9.36 is 1.596, which is not significant since χ2 (.05;2) = 10.06. Therefore, there is not enough evidence to conclude that the variances are different among the three groups.