The observed values are given in the table shown in the question. The line of best fit is given to be:
[tex]y=-1.1x+90.31[/tex]
where x is the average monthly temperature and y is the heating cost.
A residual is a difference between the observed y-value (from scatter plot) and the predicted y-value (from regression equation line). The formula will be:
[tex]Residual=Observed\text{ }y\text{ }value-Predicted\text{ }y\text{ }value[/tex]
QUESTION A
The average monthly temperature is 24.9:
[tex]x=24.9[/tex]
Observed cost:
[tex]y=51.00[/tex]
Predicted cost:
[tex]\begin{gathered} y=-1.1(24.9)+90.31=-27.39+90.31 \\ y=62.92 \end{gathered}[/tex]
Residual:
[tex]\begin{gathered} R=51.00-62.92 \\ R=-11.92 \end{gathered}[/tex]
QUESTION B
The average monthly temperature is 35.9:
[tex]x=35.9[/tex]
Observed cost:
[tex]y=67.00[/tex]
Predicted cost:
[tex]\begin{gathered} y=-1.1(35.9)+90.31=-39.49+90.31 \\ y=50.82 \end{gathered}[/tex]
Residual:
[tex]\begin{gathered} R=67.00-50.82 \\ R=16.18 \end{gathered}[/tex]
