Digits := 100:
pts := [
[0,1.6360859487373782262],
[0.26628213077765677808,1.9034275747385935862],
[0.39293391446564374103,1.956638259327336371],
[0.8171560921786148457,1.3508287506880372053],
[1,1.0256115640632861297],
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 ):
Lfwd := 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Efwd := [seq( [i[1], abs( i[2] - eval( f, x = i[1] ) )], i = Lfwd )]:
LL := plots[pointplot]( Efwd, style = point, symbol = cross, color = aquamarine, symbolsize = 3 ), LL:
MSEfwd := add( Efwd[i][2]^2, i = 1..N ):
Lbak := 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Ebak := [seq( [i[1], abs( i[2] - eval( f, x = i[1] ) )], i = Lbak )]:
LL :=  plots[pointplot]( Ebak, style = point, symbol = diagonalcross, color = red, symbolsize = 3 ), LL:
MSEbak := add( Ebak[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] );
sqrt( MSEopt/N ), sqrt( MSEfwd/N ), sqrt( MSEbak/N );