这是一份nottingham诺丁汉大学MATH3030作业代写的成功案例

To test the main effect of $A$ with Wilks’ $\Lambda$, we compute
$$
\Lambda_{A}=\frac{|\mathbf{E}|}{\left|\mathbf{E}+\mathbf{H}{A}\right|}=\frac{3602.2}{7600.2}=.474<\Lambda{.05,2,1,24}=.771
$$
and we conclude that velocity has a significant effect on $y_{1}$ or $y_{2}$ or both.
For the $B$ main effect, we have
$$
\Lambda_{B}=\frac{|\mathbf{E}|}{\left|\mathbf{E}+\mathbf{H}{B}\right|}=\frac{3602.2}{5208.6}=.6916>\Lambda{.05,2,3,24}=.591
$$
We conclude that the effect of lubricants is not significant.
For the $A B$ interaction, we obtain
$$
\Lambda_{A B}=\frac{|\mathbf{E}|}{\left|\mathbf{E}+\mathbf{H}{A B}\right|}=\frac{3602.2}{3865.3}=.932>\Lambda{.05,2,3,24}=.591
$$

MATH3030 COURSE NOTES ：

The hypothesis $H_{0}: \mu_{1}=\mu_{2}=\cdots=\mu_{p}=\mu$, say, can also be expressed as
$$
H_{0}: \boldsymbol{\mu}=\mu \mathbf{j},
$$
where $\mathbf{j}=(1,1, \ldots, 1)^{\prime}$. The maximum likelihood estimate of $\mu$ is
$$
\hat{\mu}=\frac{\overline{\mathbf{y}} \mathbf{S}^{-1} \mathbf{j}}{\mathbf{j}^{\prime} \mathbf{S}^{-1} \mathbf{j}}
$$
The likelihood ratio test of $H_{0}$ is a function of
$$
\overline{\mathbf{y}}^{\prime} \mathbf{S}^{-1} \overline{\mathbf{y}}-\frac{\left(\overline{\mathbf{y}}^{\prime} \mathbf{S}^{-1} \mathbf{j}\right)^{2}}{\mathbf{j}^{\prime} \mathbf{S}^{-1} \mathbf{j}}
$$
showed that for any $(p-1) \times p$ matrix $\mathbf{C}$ of rank $p-1$ such that $\mathbf{C j}=\mathbf{0}$