Digits := 100:
pts := [
[0,1],
[0.25,1.2840254166877413944],
[0.5,1.6487212707001281942],
[0.75,2.1170000166126747843],
[1,2.7182818284590450908],
NULL]:
f := CurveFitting:-PolynomialInterpolation( pts, x ):
Lopt := 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N := nops( Lopt ):
Eopt := [seq( [i[1], abs( i[2] - eval( f, x = i[1] ) )], i = Lopt )]:
LL := plots[pointplot]( Eopt, style = point, symbol = box, color = black, symbolsize = 3 ):
MSEopt := add( Eopt[i][2]^2, i = 1..N ):
Lbad := 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N := nops( Lbad ):
Ebad := [seq( [i[1], abs( i[2] - eval( f, x = i[1] ) )], i = Lbad )]:
LL := plots[pointplot]( Ebad, style = point, symbol = box, color = black, symbolsize = 3 ):
MSEbad := add( Ebad[i][2]^2, i = 1..N ):
plots[display]( plot( f, x = 0..1, colour = blue ), plots[pointplot]( pts, symbol = circle ) );

plots[display]( LL );
plots[display]( LL );
plots[display]( LL, view = [DEFAULT, 0..1e-15] );
plots[display]( LL, view = [DEFAULT, 0..1e-15] );