Solution:
Given the table below:
whose line of best fit is expressed as
[tex]y=0.9x+18.56[/tex]
The observed amount spent on entertainment is the value of y for a corresponding value of x in the table of value.
The predicted amount spent on entertainment is the value of y for a corresponding value of x in the equation of line of best fit.
The residual is the difference between the observed amount and predicted amount spent on entertainment.
Thus, given:
[tex]\begin{gathered} When\text{ x=7.9,} \\ Observed\text{ amount spent on entertainment \lparen in dollars\rparen=28.50} \\ Predicted\text{ amount spent on entertainment=0.9\lparen7.9\rparen+18.56} \\ =25.67 \\ Residual(in\text{ dollars\rparen =28.50-25.67} \\ =2.83 \end{gathered}[/tex][tex]\begin{gathered} when\text{ x=12.0,} \\ Observed\text{ amount spent on entertainment \lparen in dollars\rparen=29.36} \\ Predicted\text{ amount spent on entertainment \lparen in dollars\rparen=0.9\lparen12.0\rparen+18.56} \\ =29.36 \\ Residual\text{ \lparen in dollars\rparen=29.36-29.36} \\ =0 \end{gathered}[/tex]
Hence,
