Use the Given Covariance Matrix to Compute the Percentage of the Total

question 24

Multiple Choice

Use the given covariance matrix to compute the percentage of the total variance that is contained in the first principal
component. Round to one decimal place.
- $$\left[ \begin{array} { r r r r } 10 & 13 & 1 & 4 \\6 & 3 & 9 & 6 \\17 & 5 & 5 & 5\end{array} \right]$$

• A)
• \[S = \left[ \begin{array} { r r r r }
• 30 & - 3 & - 15 & - 12 \\
• - 3 & 18 & - 12 & - 3 \\
• - 15 & - 12 & 18 & 9 \\
• - 12 & - 3 & 9 & 2
• \end{array} \right]\]
• B)
• \[S = \left[ \begin{array} { r r r }
• - 30 & 12 & - 12 \\
• 12 & - 6 & 0 \\
• - 12 & 0 & - 36
• \end{array} \right]\]
• C)
• \[S = \left[ \begin{array} { r r r }
• 30 & - 12 & 12 \\
• - 12 & 6 & 0 \\
• 12 & 0 & 36
• \end{array} \right]\]
• D)
• \[S = \left[ \begin{array} { r r r }
• 90 & - 36 & 36 \\
• - 36 & 18 & 0 \\
• 36 & 0 & 108
• \end{array} \right]\]

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