To determine which point from the provided table would be on the residual plot, we need to understand what a residual plot represents. A residual plot shows the residuals (i.e., errors between the given values and the predicted values) on the y-axis versus the corresponding [tex]\( x \)[/tex]-values on the x-axis.
The table given is:
[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 consider the residual plot points as [tex]\((x, \text{residual})\)[/tex]:
- For [tex]\( x = 1 \)[/tex], the residual is [tex]\(-0.4\)[/tex], so the point is (1, -0.4).
- For [tex]\( x = 2 \)[/tex], the residual is [tex]\( 0.7 \)[/tex], so the point is (2, 0.7).
- For [tex]\( x = 3 \)[/tex], the residual is [tex]\(-0.2\)[/tex], so the point is (3, -0.2).
- For [tex]\( x = 4 \)[/tex], the residual is [tex]\(-0.6\)[/tex], so the point is (4, -0.6).
Now we match these points with the provided options:
- (1, -1.6)
- (2, 1.5)
- (3, 4.5)
- (4, -0.6)
After examining the options, the correct point that appears on the residual plot is [tex]\((4, -0.6)\)[/tex].
Therefore, the point that would be on the residual plot of the data is [tex]\((4, -0.6)\)[/tex].
