To determine which point would be on the residual plot of the data, we need to consider the residual plot definition.
In a residual plot, we plot the independent variable [tex]\( x \)[/tex] against the corresponding residuals. The residual is defined as the difference between the given value and the predicted value.
Given the table:
[tex]\[
\begin{tabular}{|c|c|c|c|}
\hline
$x$ & Given & Predicted & Residual \\
\hline
1 & -2.5 & -2.2 & -0.3 \\
\hline
2 & 1.5 & 1.2 & 0.3 \\
\hline
3 & 3 & 3.7 & -0.7 \\
\hline
4 & 5 & 4.9 & 0.1 \\
\hline
\end{tabular}
\][/tex]
We can create a list of the pairs [tex]\((x, \text{Residual})\)[/tex] for each entry:
1. When [tex]\( x = 1 \)[/tex], the residual is -0.3. So the point is [tex]\((1, -0.3)\)[/tex].
2. When [tex]\( x = 2 \)[/tex], the residual is 0.3. So the point is [tex]\((2, 0.3)\)[/tex].
3. When [tex]\( x = 3 \)[/tex], the residual is -0.7. So the point is [tex]\((3, -0.7)\)[/tex].
4. When [tex]\( x = 4 \)[/tex], the residual is 0.1. So the point is [tex]\((4, 0.1)\)[/tex].
The only point that matches a pair [tex]\((x, \text{Residual})\)[/tex] from the residual plot is [tex]\((4, 0.1)\)[/tex].
Thus, the correct point on the residual plot is:
[tex]\((4, 0.1)\)[/tex]
