Answer
$y=-0.2x+7.2$
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}{|c|c|c|c|c|c}
\hline & x & y & xy & xx & \\
\hline & 2 & 4 & 8 & 4 & \\
& 4 & 8 & 32 & 16 & \\
& 8 & 12 & 96 & 64 & \\
& 10 & 0 & 0 & 100 & \hline \\
\Sigma & {\bf 24} & {\bf 24} & {\bf 136} & {\bf 184} & \hline \\
points & 4 & & 544 & 736 & \hline \\
m= & -0.2 & & & & \\
b= & 7.2 & & & & \\
\end{array}
$m=\displaystyle \frac{n(\sum xy)-(\sum x)(\sum y)}{n(\sum x^{2})-(\sum x)^{2}}=\frac{544-(24)(24)}{736-(24)^{2}}=-0.2$
$b=\displaystyle \frac{\sum y-m(\sum x)}{n}=\frac{24-(-0.2)(24)}{24}=7.2$
$y=-0.2x+7.2$
