To determine which point would be on the residual plot of the data, let us first understand what a residual plot is.
A residual plot shows the residuals on the vertical axis and the corresponding independent variable (x) on the horizontal axis. The residual for each point is calculated as follows:
[tex]\[ \text{Residual} = \text{Given Value} - \text{Predicted Value} \][/tex]
Given the table:
[tex]\[
\begin{tabular}{|c|c|c|c|}
\hline
$x$ & Given & Predicted & Residual \\
\hline
1 & -1.6 & -1.2 & -0.4 \\
\hline
2 & 2.2 & 1.5 & 0.7 \\
\hline
3 & 4.5 & 4.7 & -0.2 \\
\hline
4 & 6.1 & 6.7 & -0.6 \\
\hline
\end{tabular}
\][/tex]
We identified that the residual plot consists of points in the form [tex]\((x, \text{Residual})\)[/tex]. Analyzing each point given in the options:
1. [tex]\((1, -1.6)\)[/tex]: This point does not represent the format [tex]\((x, \text{Residual})\)[/tex]. Instead, it seems to mix the dataset's given value with [tex]\(x\)[/tex].
2. [tex]\((2, 1.5)\)[/tex]: This point uses the predicted value instead of the residual. Therefore, it is not correct.
3. [tex]\((3, 4.5)\)[/tex]: This point uses the given value instead of the residual. It does not fit the residual plot format.
4. [tex]\((4, -0.6)\)[/tex]: This point correctly represents the [tex]\(x\)[/tex] value and the corresponding residual from the table.
Thus, the correct point that would be on the residual plot of the data is:
[tex]\[
(4, -0.6)
\][/tex]
