The Federal Debt of the United States as a Percentage $x$

The federal debt of the United States as a percentage of the Gross Domestic Product (GDP) from 2001 to 2005 is shown in the table. In the table, $x$ represents the year, with $x = 0$ corresponding to 2002. $$\begin{array} { | c | c | } \hline \text { Year, } x & \% \text { of GDP } \\\hline - 1 & 57.4 \\\hline 0 & 59.7 \\\hline 1 & 62.6 \\\hline 2 & 63.7 \\\hline 3 & 64.3 \\\hline\end{array}$$ Find the least squares regression parabola $y = a x ^ { 2 } + b x + c$ for the data by solving the following system. $$\left\{ \begin{aligned}5 c + 5 b + 15 a & = 307.7 \\5 c + 15 b + 35 a & = 325.5 \\15 c + 35 b + 99 a & = 953.5\end{aligned} \right.$$ Use the model to predict the federal debt as percents of GDP in 2006. Round to the nearest tenth percents.

A) 56.5%
B) 61.9%
C) 64.2%
D) 52.7%
E) 59.6%