Sure, let's find the residual points for each given pair of Given and Predicted values. The residual is calculated as the difference between the Given value and the Predicted value.
Here are the step-by-step calculations for the residuals:
1. For [tex]\( x = 1 \)[/tex]:
[tex]\[
\text{Given} = -0.7, \quad \text{Predicted} = -0.28
\][/tex]
[tex]\[
\text{Residual} = \text{Given} - \text{Predicted} = -0.7 - (-0.28) = -0.7 + 0.28 = -0.42
\][/tex]
2. For [tex]\( x = 2 \)[/tex]:
[tex]\[
\text{Given} = 2.3, \quad \text{Predicted} = 1.95
\][/tex]
[tex]\[
\text{Residual} = \text{Given} - \text{Predicted} = 2.3 - 1.95 = 0.35
\][/tex]
3. For [tex]\( x = 3 \)[/tex]:
[tex]\[
\text{Given} = 4.1, \quad \text{Predicted} = 4.18
\][/tex]
[tex]\[
\text{Residual} = \text{Given} - \text{Predicted} = 4.1 - 4.18 = -0.08
\][/tex]
4. For [tex]\( x = 4 \)[/tex]:
[tex]\[
\text{Given} = 7.2, \quad \text{Predicted} = 6.41
\][/tex]
[tex]\[
\text{Residual} = \text{Given} - \text{Predicted} = 7.2 - 6.41 = 0.79
\][/tex]
5. For [tex]\( x = 5 \)[/tex]:
[tex]\[
\text{Given} = 8.0, \quad \text{Predicted} = 8.64
\][/tex]
[tex]\[
\text{Residual} = \text{Given} - \text{Predicted} = 8.0 - 8.64 = -0.64
\][/tex]
Now, let's fill in the table with the residuals:
[tex]\[
\begin{array}{|c|c|c|c|}
\hline
x & \text{Given} & \text{Predicted} & \text{Residual} \\
\hline
1 & -0.7 & -0.28 & -0.42 \\
\hline
2 & 2.3 & 1.95 & 0.35 \\
\hline
3 & 4.1 & 4.18 & -0.08 \\
\hline
4 & 7.2 & 6.41 & 0.79 \\
\hline
5 & 8.0 & 8.64 & -0.64 \\
\hline
\end{array}
\][/tex]
