Answer
$y=0.5x+0.8333$
Work Step by Step
Regression line $y=mx+b,$ where $m$ and $b$ are computed as follows:
$m=\displaystyle \frac{n(\sum xy)-(\sum x)(\sum y)}{n(\sum x^{2})-(\sum x)^{2}}\qquad b=\frac{\sum y-m(\sum x)}{n}$
$n=$ number of data points.
The quantities $m$ and $b$ are called the regression coefficients.
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Build a table
\begin{array}{|cc|c|c|c|cc|}
\hline & x & y & xy & xx \\
\hline & 0 & 1 & 0 & 0 \\
& 1 & 1 & 1 & 1 \\
& 2 & 2 & 4 & 4 \\\hline
\Sigma & {\bf 3} & {\bf 4} & {\bf 5} & {\bf 5} \\
& & & & \\
points & 3 & & 15 & 15 \\
\end{array}
$m=\displaystyle \frac{n(\sum xy)-(\sum x)(\sum y)}{n(\sum x^{2})-(\sum x)^{2}}=\frac{15-(3)(4)}{15-(3)^{2}}=\frac{3}{6}=\frac{1}{2}=0.5$
$b=\displaystyle \frac{\sum y-m(\sum x)}{n}=\frac{4-0.5(3)}{3}=\frac{2.5}{3}0.8333$
$y=0.5x+0.8333$
