# Math 6020-001 HOMEWORK 3 Multilinear Models

• 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.

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