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:

False Consensus

The cognitive bias to overestimate the extent to which others share one's beliefs, attitudes, and behaviors.

Ingroup

A group to which an individual identifies as being a member, often viewed in contrast to an "outgroup".

Self-Focus

The act of directing attention inward, towards one's own thoughts, feelings, and experiences, which can influence self-awareness and personal growth.

Form Impressions

The process of forming opinions or beliefs about others based on the initial information presented to us.