To determine which point would be on the residual plot of the data, we need to understand the concept of a residual plot. A residual plot graphs the residual values on the y-axis and the x values on the x-axis. The residuals are the differences between the given values and the predicted values.
Let's analyze the given table and the information it provides:
[tex]\[
\begin{array}{|c|c|c|c|}
\hline
x & \text{Given} & \text{Predicted} & \text{Residual} \\
\hline
1 & -2.5 & -2.2 & -0.3 \\
\hline
2 & 1.5 & 1.2 & 0.3 \\
\hline
3 & 3 & 3.7 & -0.7 \\
\hline
4 & 5 & 4.9 & 0.1 \\
\hline
\end{array}
\][/tex]
Now, let's focus on creating the points for the residual plot. Each point on the residual plot is represented as [tex]\((x, \text{Residual})\)[/tex]:
- For [tex]\(x = 1\)[/tex], the residual is [tex]\(-0.3\)[/tex], so the point is [tex]\((1, -0.3)\)[/tex].
- For [tex]\(x = 2\)[/tex], the residual is [tex]\(0.3\)[/tex], so the point is [tex]\((2, 0.3)\)[/tex].
- For [tex]\(x = 3\)[/tex], the residual is [tex]\(-0.7\)[/tex], so the point is [tex]\((3, -0.7)\)[/tex].
- For [tex]\(x = 4\)[/tex], the residual is [tex]\(0.1\)[/tex], so the point is [tex]\((4, 0.1)\)[/tex].
Given these points: [tex]\((1, -0.3)\)[/tex], [tex]\((2, 0.3)\)[/tex], [tex]\((3, -0.7)\)[/tex], and [tex]\((4, 0.1)\)[/tex], we need to select the correct point from the provided multiple-choice options.
The correct point that would appear on the residual plot is [tex]\((4, 0.1)\)[/tex].
Therefore, the correct answer is:
[tex]\((4, 0.1)\)[/tex]
