SOLUTION
Given the question in the image, the following are the solution steps to complete the table
STEP 1: Write the equation of the line
[tex]y=0.25x+29[/tex]
STEP 2: Calculating the residual when x=10
[tex]\begin{gathered} y=0.25x+29 \\ x=10 \\ By\text{ substitution,} \\ y=0.25(10)+29=2.5+29=31.5 \\ \text{ To get Residual} \\ 31.3-31.5=-0.2 \end{gathered}[/tex]
STEP 3: Calculating the residual when x=20
[tex]\begin{gathered} y=0.25x+29 \\ x=20 \\ By\text{ substitution,} \\ y=0.25(20)+29=5+29=34^{\square} \\ \text{ To get Residual} \\ 34-34=0 \end{gathered}[/tex]
STEP 4: Calculating the residual when x=30
[tex]\begin{gathered} y=0.25x+29 \\ x=30 \\ By\text{ substitution,} \\ y=0.25(30)+29=7.5+29=36.5 \\ \text{ To get Residual} \\ 36.5-36.5=0 \end{gathered}[/tex]
STEP 5: Calculating the residual when x=40
[tex]\begin{gathered} y=0.25x+29 \\ x=40 \\ By\text{ substitution,} \\ y=0.25(40)+29=10+29=39 \\ \text{ To get Residual} \\ 38.2-39=-0.8 \end{gathered}[/tex]
STEP 6: Plotting the quality of fit graph
A residual plot has the Residual Values on the vertical axis; the horizontal axis displays the independent variable. A residual plot is typically used to find problems with regression. A residual is a measure of how well a line fits an individual data point. This vertical distance is known as a residual. For data points above the line, the residual is positive, and for data points below the line, the residual is negative. The closer a data point's residual is to 0, the better the fit.
We have the table below:
This table for plotting the residuals gives the graph below:
