To determine which point would be on the residual plot of the data, let's understand what a residual plot represents. A residual plot shows the residuals on the y-axis and the corresponding x-values on the x-axis. The residual is calculated as the difference between the given value and the predicted value.
From the provided data table:
[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]
The residuals corresponding to each x value are as follows:
- For [tex]\(x = 1\)[/tex], the residual is [tex]\(-0.3\)[/tex]
- For [tex]\(x = 2\)[/tex], the residual is [tex]\(0.3\)[/tex]
- For [tex]\(x = 3\)[/tex], the residual is [tex]\(-0.7\)[/tex]
- For [tex]\(x = 4\)[/tex], the residual is [tex]\(0.1\)[/tex]
The point on a residual plot would be [tex]\((x, \text{residual})\)[/tex]. Now, we can check each of the given points to see which one matches:
1. [tex]\((1, -2.2)\)[/tex] - This point is not correct, because -2.2 is not a residual.
2. [tex]\((2, 1.5)\)[/tex] - This point is not correct, because 1.5 is not a residual.
3. [tex]\((3, 3.7)\)[/tex] - This point is not correct, because 3.7 is not a residual.
4. [tex]\((4, 0.1)\)[/tex] - This point is correct, because it matches the residual value for [tex]\(x = 4\)[/tex].
Therefore, the point [tex]\((4, 0.1)\)[/tex] would be on the residual plot of the data.
