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).
$\begin{array} { c c }
\hline \text { Tons of Gravel } & \text { Unit Cost (dollars/ton) } \
\hline 73 & 16.49 \
22 & 21.14 \
89 & 15.98 \
86 & 16.24 \
60 & 17.34 \
95 & 16.13 \
56 & 16.71 \
31 & 20.02 \
90 & 17.05 \
23 & 21.76 \
\hline
\end{array}$
Compute the coefficient of determination.
A) -0.0767
B) -0.9233
C) 0.8525
D) 0.1475

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).
 $\begin{array} { c c } 
\hline \text { Tons of Gravel } & \text { Unit Cost (dollars/ton) } \
\hline 73 & 16.49 \
22 & 21.14 \
89 & 15.98 \
86 & 16.24 \
60 & 17.34 \
95 & 16.13 \
56 & 16.71 \
31 & 20.02 \
90 & 17.05 \
23 & 21.76 \
\hline
\end{array}$
Compute the coefficient of determination.
A) -0.0767
B) -0.9233
C) 0.8525
D) 0.1475

Quizplus · Accepted Answer

We can compute the coefficient of determination using a statistical software or a calculator capable of linear regression analysis. The coefficient of determination, denoted by R-squared, measures the proportion of the variance in the dependent variable (unit cost) that is explained by the independent variable (tons of gravel). The closer R-squared is to 1, the better the fit of the regression model.

Using a calculator, we obtain R-squared = 0.8525, which means that about 85.25% of the variability in unit cost can be explained by the quantity of gravel ordered. This is a relatively high R-squared value, indicating a strong relationship between the variables. Therefore, the best choice is C.

As with Many Other Construction Materials, the Price of Gravel