Answer
$y=45x+25$
Projected index in 2011:$\quad 520.$
Work Step by Step
The regression line is
$\qquad y=mx+b$
where
$m=\displaystyle \frac{n(\sum xy)-(\sum x)(\sum y)}{n(\sum x^{2})-(\sum x)^{2}}\qquad b=\frac{\sum y-m(\sum x)}{n},$
$n=$ number of data points.
$\left[\begin{array}{lllll}
& x & y & xy & x^{2}\\
& & & & \\
\hline & 0 & 50 & 0 & 0\\
& 5 & 200 & 1000 & 25\\
& 10 & 500 & 5000 & 100\\
\hline & & & & \\
\sum & 15 & 750 & 6000 & 125\\
& & & &
\end{array}\right]$
$m=\displaystyle \frac{3(6000)-(15)(750)}{3(125)-(15)^{2}}=\frac{6750}{150}=45$
$b=\displaystyle \frac{750-3(15)}{3}=\frac{75}{3}=25$
$y=45x+25$
In the year 2011 ($11$ years after 2000) we have:
$y=45(11)+25=520$
