An Article in the Journal of Statistics Education Reported the Price

An article in the Journal of Statistics Education reported the price of diamonds of different sizes in Singapore dollars (SGD).
The following table contains a data set that is consistent with this data, adjusted to US dollars in 2004: $\begin{array}{|c|c|}\hline \text { 2004 US \$ } & \text { Carat } \\\hline 494.82 & 0.12 \\\hline 768.03 & 0.17 \\\hline 1105.03 & 0.20 \\\hline 1508.88 & 0.25 \\\hline 1826.18 & 0.28 \\\hline 2096.89 & 0.33 \\\hline\end{array}$


$\begin{array}{|c|c|}\hline \text { 2004 US \$ } & \text { Carat } \\\hline 688.24 & 0.15 \\\hline 944.90 & 0.18 \\\hline 1071.75 & 0.21 \\\hline 1504.44 & 0.26 \\\hline 1908.28 & 0.29 \\\hline 2409.76 & 0.35 \\\hline\end{array}$


$\begin{array}{|c|c|}\hline \text { 2004 US \$ } & \text { Carat } \\\hline 748.10 & 0.16 \\\hline 1076.18 & 0.19 \\\hline 1289.20 & 0.23 \\\hline 1597.63 & 0.27 \\\hline 2038.09 & 0.32 \\\hline & \\\hline\end{array}$

-Explain the meaning of $R ^ { 2 }$
in the context of this problem.