Understanding Simple Linear Regression

Consider this small and simple dataset:

points $=$ pd$.$DataFrame $($

$\left[\begin{array}{cc}1& 1\\ 2& 1\\ 3& 3\\ 6& 5\\ 7& 7\\ 7& 6\end{array}\right],$

columns$=["x","y"]$

base $=$ alt. Chart$($points$).$ mark$\_$point$().$ encode$($

$x=\text{'}{?}^x\text{'},$

$y={?}^{\text{'}}{y}^{\text{'}}$

base

Now consider these three potential lines we could fit for the same dataset:

lines $=$ pd$.$DataFrame $($

$[$

$,$ 'Line A$\text{'}],$

$[7,5\mathrm{.}9868,$ 'Line A$\text{'}],$

$,$ 'Line B$\text{'}],$

$,$ 'Line B$\text{'}],$

$,$ 'Line $\{$:$C^{\text{'}}],$

$,$ 'Line $\{$:$C^{\text{'}}]$

$],$

columns$=["x,y,$ 'Name'$]$

base $+$ alt.Chart$($lines$).$mark$\_$line$().$encode$($

$y={?}^{\text{'}}{y}^{\text{'}},$

color $=$ 'Name $\text{'}$