with(LinearAlgebra):

with(plots):

#LS(L,x): Inputs a list of points, L, finds the Least Squares line (regression). For example, Try:
#LS([[1,1],[2,2],[3,3],[4,5]],x);
LS:=proc(L,x) local A,b,i:
A:=<<seq(1,i=1..nops(L))>|<seq(L[i][1],i=1..nops(L))>>:
b:=<seq(L[i][2],i=1..nops(L))>:
LeastSquares(A,b)[1]+LeastSquares(A,b)[2]*x:
end:

#LSc(L,x): Same as LS(L,x), but using multi-variable calculus instead of Linear Algebra. Try:
#LS([[1,1],[2,2],[3,3],[4,5]],x);
LSc:=proc(L,x) local b,m,f,v:

f:=add((L[i][2]-b-m*L[i][1])^2,i=1..nops(L)):
v:=solve({diff(f,b),diff(f,m)},{b,m}):
subs(v,b)+subs(v,m)*x:
end:

#PLS(L): Inputs a list of points, L. Oututs the scatter- plot and plots the Least Squares Line. Try:
#PLS([[1,1],[2,2],[3,3],[4,5]]);
PLS:=proc(L) local gu,x,mu,minx,maxx:
gu:=LS(L,x):

minx:=min(seq(L[i][1],i=1..nops(L))):
maxx:=max(seq(L[i][1],i=1..nops(L))):

mu:=plot(gu,x=minx..maxx,color=red):

mu:=mu,plot(L,style=point,color=black):

display(mu);

end: