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

question 21

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.
- $\left[ \begin{array} { l l l l l l } 26 & 31 & 26 & 31 & 11 & 31 \\ 10 & 40 & 55 & 25 & 50 & 30 \end{array} \right]$

• A)
• \[S = \left[ \begin{array} { r r }
• 60 & - 55 \\
• - 55 & 280
• \end{array} \right]\]
• B)
• \[\mathrm { S } = \left[ \begin{array} { r r }
• 50 & - 45 \frac { 5 } { 6 } \\
• - 45 \frac { 5 } { 6 } & 233 \frac { 1 } { 3 }
• \end{array} \right]\]
• C)
• \[S = \left[ \begin{array} { r r }
• - 60 & 55 \\
• 55 & - 280
• \end{array} \right]\]
• D)
• \[\mathrm { S } = \left[ \begin{array} { r r }
• 300 & - 275 \\
• - 275 & 1400
• \end{array} \right]\]

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Definitions:

Successful Mergers

The combining of two or more companies in a way that results in increased value generation, efficiency gains, and enhanced competitiveness in the market.

Rapid Growth

This denotes a phase where a company or economy experiences an above-average increase in revenue, production, or other significant measures over a short time.

Acquisitions

The process of obtaining control of another corporation by purchasing or exchanging equity interests or assets.

Horizontal Merger

A horizontal merger is a business consolidation that occurs between firms operating in the same industry or producing similar products, aimed at increasing market share.