Let $A = \left[ \begin{array} { c c } 1 & 0 \\- 2 & 2 \\6 & 5\end{array} \right]$

question 161

Multiple Choice

Let $A = \left[ \begin{array} { c c } 1 & 0 \\- 2 & 2 \\6 & 5\end{array} \right]$ and $B = \left[ \begin{array} { c c } 7 & - 2 \\4 & 12 \\9 & - 2\end{array} \right]$ , evaluate $- 2 A + B$ .

• A) \(\left[ \begin{array} { c c }
• - 5 & 2 \\
• - 8 & 2 \\
• 6 & 5
• \end{array} \right]\)
• B) \(\left[ \begin{array} { c c }
• 8 & - 2 \\
• 2 & 14 \\
• 15 & 3
• \end{array} \right]\)
• C) \(\left[ \begin{array} { c c }
• - 8 & 2 \\
• - 2 & - 14 \\
• - 15 & 3
• \end{array} \right]\)
• D) \(\left[ \begin{array} { c c }
• 5 & - 2 \\
• 3 & - 12 \\
• 8 & 8
• \end{array} \right]\)
• E) \(\left[ \begin{array} { c c }
• 5 & - 2 \\
• 8 & 8 \\
• - 3 & - 12
• \end{array} \right]\)

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Definitions:

Residual

The difference between the observed value and the value predicted by a model, indicating the error in prediction for that specific point.

Least-squares Line

A line of best fit determined by the least squares method, which minimizes the sum of squared vertical distances between the actual data points and the predicted points on the line.

Unbiased Estimator

A statistical estimator whose expected value exactly equals the parameter it estimates.

Intercept

The value of the dependent variable when all independent variables in a regression model are set to zero, representing the model’s starting point.