Based on a linear regression/correlation analysis of monthly mean atmospheric sea level pressure (SLP) data from the National Centers for Environmental Prediction (NCEP) reanalysis (1948--2000), we find a significant anticorrelation between pressure in the northern North Atlantic and North Pacific only if the stratospheric circulation is in the strong polar vortex regime but not when the vortex is weak. Since some general circulation models (GCMs) (e.g., European Center/Hamburg (ECHAM4)) are biased toward the strong vortex regime (SVR), they tend to reproduce this anticorrelation already in the mean. The pattern of the Arctic Oscillation (AO) is shown to be consistent with the mean surface pressure differences between the two stratospheric regimes. The typical SW-NE tilt of the node line of the North Atlantic Oscillation (NAO) found with linear analyses (i.e., with such that do not take the regime character of the stratospheric circulation into account) in Northern Hemisphere winter is due to a superposition of correlation patterns based on physical processes working in the troposphere (a strictly meridional dipole and the pattern resulting from planetary wave refraction in the strong vortex regime) and those produced by the rapid transition from one stratospheric regime to the other with subsequent downward propagation of the signal. This result underlines the necessity of the application of nonlinear statistics or the restriction of linear statistics to variations in the stable (quasi-linear) environment of natural regimes.