To find the residual points, we need to subtract the predicted values from the given values for each corresponding \( x \). The residual is calculated as:
[tex]\[ \text{Residual} = \text{Given value} - \text{Predicted value} \][/tex]
Let's go through each point step-by-step:
1. For \( x = 1 \):
[tex]\[
\text{Residual} = -0.7 - (-0.28) = -0.7 + 0.28 = -0.42
\][/tex]
2. For \( x = 2 \):
[tex]\[
\text{Residual} = 2.3 - 1.95 = 2.3 - 1.95 = 0.35
\][/tex]
3. For \( x = 3 \):
[tex]\[
\text{Residual} = 4.1 - 4.18 = 4.1 - 4.18 = -0.08
\][/tex]
4. For \( x = 4 \):
[tex]\[
\text{Residual} = 7.2 - 6.41 = 7.2 - 6.41 = 0.79
\][/tex]
5. For \( x = 5 \):
[tex]\[
\text{Residual} = 8 - 8.64 = 8 - 8.64 = -0.64
\][/tex]
So, the residuals for the data are:
- For \( x = 1 \), Residual = -0.42
- For \( x = 2 \), Residual = 0.35
- For \( x = 3 \), Residual = -0.08
- For \( x = 4 \), Residual = 0.79
- For \( x = 5 \), Residual = -0.64
Updating the table with these residuals:
[tex]\[
\begin{tabular}{|c|c|c|c|}
\hline
[tex]$x$[/tex] & \text{Given} & \text{Predicted} & \text{Residual} \\
\hline
1 & -0.7 & -0.28 & -0.42 \\
\hline
2 & 2.3 & 1.95 & 0.35 \\
\hline
3 & 4.1 & 4.18 & -0.08 \\
\hline
4 & 7.2 & 6.41 & 0.79 \\
\hline
5 & 8 & 8.64 & -0.64 \\
\hline
\end{tabular}
\][/tex]
These points are the residuals based on the given and predicted values.
