Find the regression coefficients $b_{yx}$ and $b_{xy}$ for the following data:
$n = 6$, $\;$ $\Sigma x = 30$, $\;$ $\Sigma y = 42$, $\;$ $\Sigma xy = 199$, $\;$ $\Sigma x^2 = 184$, $\;$ $\Sigma y^2 = 318$
$\begin{aligned}
b_{yx} & = \dfrac{\Sigma xy - \dfrac{\Sigma x \Sigma y}{n}}{\Sigma x^2 - \dfrac{\left(\Sigma x\right)^2}{n}} \\\\
& = \dfrac{199 - \dfrac{30 \times 42}{6}}{184 - \dfrac{\left(30\right)^2}{6}} \\\\
& = \dfrac{199 - 210}{184 - 150} = \dfrac{-11}{34} = - 0.3235
\end{aligned}$
$\begin{aligned}
b_{xy} & = \dfrac{\Sigma xy - \dfrac{\Sigma x \Sigma y}{n}}{\Sigma y^2 - \dfrac{\left(\Sigma y\right)^2}{n}} \\\\
& = \dfrac{199 - \dfrac{30 \times 42}{6}}{318 - \dfrac{\left(42\right)^2}{6}} \\\\
& = \dfrac{199 - 210}{318 - 294} = \dfrac{-11}{24} = - 0.4583
\end{aligned}$