MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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**Consider the data given below.**

\[
\begin{array}{c|cccccc}
x & -2 & -1 & 0 & 1 & 2 \\
\hline
y & 3 & 3 & 7 & 9 & 10 \\
\end{array}
\]

**Calculate the coefficient of determination, \( r^2 \). (Round your answer to four decimal places.)**

\[ r^2 = \_\_\_\_ \]

**What information does this value give about the usefulness of the linear model?**

- ○ The value of \( r^2 \) is quite large which suggests that the median of the \( y \) data is very close to the median of the \( x \) data.

- ○ The value of \( r^2 \) is quite large which suggests that the average of the \( y \) data is very close to the average of the \( x \) data.

- ○ The value of \( r^2 \) is very close to 0 which suggests that the average of the \( y \) data is very different from the average of the \( x \) data.

- ○ The value of \( r^2 \) is quite large which suggests that a large proportion of the variation in \( y \) can be explained by the variable \( x \).

- ○ The value of \( r^2 \) is very close to 0 which suggests that a small proportion of the variation in \( y \) can be explained by the variable \( x \).

**Note:** The prompt includes a submission area labeled "Submit Answer."
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Transcribed Image Text:**Consider the data given below.** \[ \begin{array}{c|cccccc} x & -2 & -1 & 0 & 1 & 2 \\ \hline y & 3 & 3 & 7 & 9 & 10 \\ \end{array} \] **Calculate the coefficient of determination, \( r^2 \). (Round your answer to four decimal places.)** \[ r^2 = \_\_\_\_ \] **What information does this value give about the usefulness of the linear model?** - ○ The value of \( r^2 \) is quite large which suggests that the median of the \( y \) data is very close to the median of the \( x \) data. - ○ The value of \( r^2 \) is quite large which suggests that the average of the \( y \) data is very close to the average of the \( x \) data. - ○ The value of \( r^2 \) is very close to 0 which suggests that the average of the \( y \) data is very different from the average of the \( x \) data. - ○ The value of \( r^2 \) is quite large which suggests that a large proportion of the variation in \( y \) can be explained by the variable \( x \). - ○ The value of \( r^2 \) is very close to 0 which suggests that a small proportion of the variation in \( y \) can be explained by the variable \( x \). **Note:** The prompt includes a submission area labeled "Submit Answer."
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