 Exercise Set 2.10, page 60. #2.1, 2.5, 2.6.
 Exercise Set 4.8, page 132. #4.1.
 Body weight (in grams) for n=150 female mice were obtained
immediately after the birth of their first four liters.
The sample mean vector and the sample correlation matrix
were, in this order,
\[
\bar{\mathbf{X}} = \begin{bmatrix}
39.88\\45.08\\48.11\\49.95
\end{bmatrix}
\quad\text{and}\quad
\mathbf{R}=\begin{bmatrix}
1&0.75&0.63&0.64\\
&1&0.69&0.74\\
& &1&0.66\\
& & &1
\end{bmatrix}.
\]
Perform a principle components analysis on this [sample] correlation
matrix. Can the data be effectively summarized in fewer than 4 dimensions?
Identify as many of the principle components as possible.
Justify your assertion[s] very carefully using a detailed analysis and
careful discussion.
