Convert the matrix of observations to mean-deviation form, and construct the sample covariance matrix.
-$$\mathrm { S } = \left[ \begin{array} { r c c }
30 & - 12 & 12 \
- 12 & 6 & 0 \
12 & 0 & 36
\end{array} \right]$$
A) $79.1 \%$
B) $41.7 \%$
C) $34.4 \%$
D) $65.0 \%$

Question

Convert the matrix of observations to mean-deviation form, and construct the sample covariance matrix.
-$$\mathrm { S } = \left[ \begin{array} { r c c } 
30 & - 12 & 12 \
- 12 & 6 & 0 \
12 & 0 & 36
\end{array} \right]$$
A) $79.1 \%$
B) $41.7 \%$
C) $34.4 \%$
D) $65.0 \%$

Quizplus · Accepted Answer

The mean-deviation form of a matrix involves centering the data by subtracting the mean of each variable from each observation. However, the given matrix S appears to be a covariance matrix rather than raw data observations. To construct the sample covariance matrix from S, we don't need to convert it to mean-deviation form because it already represents covariances between variables. The question seems to be misstated or lacks the necessary data for conversion to mean-deviation form. Therefore, without additional context or clarification, the task as described (converting to mean-deviation form and then constructing the sample covariance matrix from the already given covariance matrix) is not applicable. The percentages provided as options do not directly relate to the process of converting a matrix to mean-deviation form or constructing a covariance matrix from given data.

Convert the Matrix of Observations to Mean-Deviation Form, and Construct S=[30−1212−126012036]\mathrm { S } = \left[ \begin{array} { r c c } 30 & - 12 & 12 \\- 12 & 6 & 0 \\12 & 0 & 36\end{array} \right]S=​30−1212​−1260​12036​​

Convert the Matrix of Observations to Mean-Deviation Form, and Construct $\mathrm { S } = \left[ \begin{array} { r c c } 30 & - 12 & 12 \\- 12 & 6 & 0 \\12 & 0 & 36\end{array} \right]$