We wish to visualize the relation between the lines $l,l^{\text{'}}$ in Problem $2.$ Fill Blanks

$(1)$ and $(2)$ below and draw the graph.

def min$\_$sq$($x$,$y$)$: # function for finding the intercept and coefficient of

the least$-$squares

x$\_$bar,y$\_$bar$=$np$.$mean $($x$),$np$.$mean$($y$)$

beta$\_$l$=$np$.$dot $($x$-$x$\_$bar,y$-$y$\_$bar$)/$np$.$linalg.norm $($x$-$x$\_$bar$)**2$

beta$\_0=$y$\_$bar$-$beta$\_\_1*$x$\_$bar

return $[$b$]$eta$\_1,$beta$\_\_0]$

N$\}=10$

a$=$np$.$random.normal$($loc$=2,$scale$=1)$ # mean, variance, size

b$=$randn$(1)$ # coefficient

x$=$randn $($N$)$

y$=$a$*$x$+$b$+$randn$($N$)$

al$,$bl$=$min$\_$sq$($x$,$y$)$ # estimating

xxx$=$x$-$# blangk$(1)$ #

yY$=$y$-$# blank$(2)$ #

a$2,$b$2=$min$\_$sq$($xxx$,$yy$)$ # estimating after centering

$(1\mathrm{.}7865393047324676,1\mathrm{.}067565008452225$e$-16)$

x$\_$seq$=$np$.$arange $(-5,5,0\mathrm{.}1)$

y$\_$pre$=$x$\_$seq$*$a$1+$b$1$

yY$\_$pre$=$x$\_$seq$*$a$2+$b$2$

plt$.$scatter$($x$,$y$,$c$=$"black"$)$

plt$.$axhline $($y$=0,$c$=$"black", $1$inewidth$=0\mathrm{.}5)$

plt$.$axvline $($ x$=0,$c$=$"black", linewidth$=0\mathrm{.}5)$

plt$.$plot$($x$\_$seq,y$\_$pre,c$=$"blue", label$=$"before$\_$centering"$)$

plt$.$plot $($x$\_$seq, yy$\_$pre, c$=$"orange", label$=$"after$\_$centering"$)$

plt$.$legend$(1$oc$=$"upper,left"$)$