How about:
@pgf Axis(
{ybar_stacked},
Plot(Coordinates([(1, 1), (2, 4), (3, 9), (4, 16)])),
Plot(Coordinates([(1, 6), (2, -8), (3, -4.5), (4, 8)])),
Plot(Coordinates([(1, -15), (2, -3), (3, 4.5), (4, -8)])),
Plot(Coordinates([(1, -1), (2, 3), (3, -3), (4, -4)])),
)
