Solution:
Given the scatterplot below:
where the equation of the line of best fit is expressed as
[tex]y=1.82x+11.36[/tex]
A) Predicted increase in the amount of money spent on entertainment, for an increase of one hour in time worked.
Recall that the line equation is expressed as
[tex]\begin{gathered} y=mx+c \\ where \\ m=slope \\ slope=\frac{increase\text{ in y}}{increase\text{ in x}} \end{gathered}[/tex]
By comparison with the equation of line of best fit, we see that
[tex]\begin{gathered} slope=1.82 \\ where \\ slope=\frac{increase\text{ in amout of money spent}}{increase\text{ in the number of hours worked}} \end{gathered}[/tex]
Thus, we have
[tex]\begin{gathered} 1.82=\frac{increase\text{ in amount of money spent}}{1} \\ \Rightarrow predicted\text{ increase in amount of money spent on entertainment = \$1.82} \end{gathered}[/tex]
B) Predicted amount of money spent on entertainment for a student with no number of hours worked
This implies that from the equation of the line of best fit, the value of x is zero.
By substitution, we have
[tex]\begin{gathered} y=1.82(0)+11.36 \\ =0+11.36 \\ \Rightarrow y=\$11.36 \end{gathered}[/tex]
C) Predicted amount of money spent on entertainment for a student with8 hours of work.
Thus, we have the value of x to be 8 from the equation of the line of best fit.
By substitution, we have
[tex]\begin{gathered} y=1.82\left(8\right)+11.36 \\ =14.56+11.36 \\ \Rightarrow y=\$25.92 \end{gathered}[/tex]
