这是一份试验设计与方差分析作业代写的成功案

In this equation $c_{i 1}$ is the coefficient of $\bar{X}{i . .}$ when testing for a linear trend, and $c{i 2}$ is the coefficient for the quadratic trend.

The value of $a_{1}^{}$ is estimated from $C_{1}$ for the $A$ main effect just as in Chapter 10: $$ \hat{a}{1}^{}=C{1} / \Sigma_{i} c_{i 1}^{2}=100 / 20=5 .
$$
To estimate $a^{}\left(b_{j}\right){2}$, we use the same formula (substituting $C{2}$ for $C_{1}$ and $C_{i 2}$ for $C_{i 1}$, but we use a different $C_{2}$ for each level of $B$. The values we use are in the quadratic column in Table 11.3:
$$
\begin{aligned}
&\hat{a}^{}\left(b_{1}\right){2}=-2 / \Sigma{i} c_{i 2}^{2}=-2 / 4=-.50 \
&\hat{a}^{}\left(b_{2}\right){2}=-13 / \Sigma{i} c_{i 2}^{2}=-13 / 4=-3.25 \
&\hat{a}^{}\left(b_{3}\right){2}=-19 / \Sigma{i} c_{i 2}^{2}=-19 / 4=-4.75 .
\end{aligned}
$$
The estimate of $\mu_{11}$ would then be $\hat{\mu}{11}=45.00+5(-3)-.50(1)=29.50$. The estimate of $\mu{12}$ would be $\mu_{12}=52.75+54(-3)-3.25(1)=34.50$. The other estimates shownand plotted in are obtained similarly.

MSTAT 502/STAT 316/MTH 513A/MATH 321/STAT210/STA 106 COURSE NOTES ：

Sometimes addition, subtraction, or multiplication of matrices is possible after one or both matrices have been transposed. To transpose a matrix, we simply exchange rows and columns. For example, the transpose of $C$ is
$$
C^{t}=\left|\begin{array}{rr}
3 & 4 \
-2 & 2 \
1 & 0
\end{array}\right|
$$
One important use of transposing is to enable the multiplication of a matrix by itself. We cannot write $A A$ unless $A$ is a square matrix, but we can always write $A^{t} A$ and $A A^{t}$. For the matrix above,
$$
C^{t} C=\left|\begin{array}{rr}
3 & 4 \
-2 & 2 \
1 & 0
\end{array}\right|\left|\begin{array}{rrr}
3 & -2 & 1 \
4 & 2 & 0
\end{array}\right|=\left|\begin{array}{rrr}
25 & 2 & 3 \
2 & 8 & -2 \
3 & -2 & 1
\end{array}\right| .
$$