As with many other construction materials, the price of gravel (per ton) depends on the quantity of material ordered. The following table presents the unit cost (dollars/ton) for gravel for various order sizes (in tons).
$\begin{array} { c c }
\hline \text { Tons of Gravel } & \text { Unit Cost(dollars/ton) } \
\hline 10 & 29.60 \
20 & 22.06 \
30 & 19.88 \
40 & 19.05 \
50 & 17.84 \
60 & 16.93 \
70 & 17.86 \
80 & 17.36 \
90 & 16.74 \
\hline
\end{array}$
Which of the following graphs is the correct residual plot for the data set? (Hint: create your own residual plot
And compare it to those shown below.)

Question

As with many other construction materials, the price of gravel (per ton) depends on the quantity of material ordered. The following table presents the unit cost (dollars/ton) for gravel for various order sizes (in tons). 
$\begin{array} { c c } 
\hline \text { Tons of Gravel } & \text { Unit Cost(dollars/ton) } \
\hline 10 & 29.60 \
20 & 22.06 \
30 & 19.88 \
40 & 19.05 \
50 & 17.84 \
60 & 16.93 \
70 & 17.86 \
80 & 17.36 \
90 & 16.74 \
\hline
\end{array}$
 Which of the following graphs is the correct residual plot for the data set? (Hint: create your own residual plot
And compare it to those shown below.)

Quizplus · Accepted Answer

A residual plot is a graph that shows the differences between the predicted values and the actual values. The horizontal axis represents the independent variable (in this case, tons of gravel), and the vertical axis represents the residual (the difference between the predicted and actual values). A good residual plot should have no pattern and should have points scattered randomly around the horizontal axis. It should also have an almost equal distribution of the points above and below the horizontal axis.

Option A shows a residual plot with a clear pattern, which indicates that the model is not fitting the data well. 
Option C shows a residual plot with a fan-like pattern, which indicates that the variance is not constant across the range of the independent variable, violating a key assumption of linear regression. 
Option D shows a residual plot with most of the points concentrated at the bottom, which indicates that the model is underestimating the values.

Option B shows a residual plot with no clear pattern, with points scattered randomly around the horizontal axis, and an almost equal distribution of the points above and below the horizontal axis. This is the best choice and indicates that the model is fitting the data well with no major issues.

As with Many Other Construction Materials, the Price of Gravel