To determine which point would be on the residual plot of the given data, we need to understand the structure and the meaning of the residual plot.
A residual plot displays the residuals on the vertical axis and the x-values on the horizontal axis. The residual is the difference between the given value and the predicted value (Residual = Given - Predicted).
From the table provided:
[tex]\[
\begin{array}{|c|c|c|c|}
\hline
x & \text{Given} & \text{Predicted} & \text{Residual} \\
\hline
1 & -1.6 & -1.2 & -0.4 \\
\hline
2 & 2.2 & 1.5 & 0.7 \\
\hline
3 & 4.5 & 4.7 & -0.2 \\
\hline
4 & 6.1 & 6.7 & -0.6 \\
\hline
\end{array}
\][/tex]
We need to identify which one from the provided answer options corresponds to an entry on the residual plot. The residual plot includes pairs [tex]\((x, \text{Residual})\)[/tex]. Based on our table, the [tex]\((x, \text{Residual})\)[/tex] pairs are:
- (1, -0.4)
- (2, 0.7)
- (3, -0.2)
- (4, -0.6)
Let's compare these pairs with the provided answer options:
1. [tex]\((1, -1.6)\)[/tex]
2. [tex]\((2, 1.5)\)[/tex]
3. [tex]\((3, 4.5)\)[/tex]
4. [tex]\((4, -0.6)\)[/tex]
Among the options, the correct pair, [tex]\((x, \text{Residual})\)[/tex] which fits the residual plot from the table, would be [tex]\((4, -0.6)\)[/tex].
Therefore, the point [tex]\((4, -0.6)\)[/tex] is the one that would be on the residual plot of the data.
