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simply means that the data can be reasonably approximated by a smooth line with three kinks in it.
If Bush's popularity took a sudden upswing, you'd need to add another kink, probably, making it a 5th degree polynomial, although you might find that a 3rd degree (two kinks) would do just about as well.
Curve fits are descriptive, not predictive. The lower the polynomial, the simpler the relationship, so a linear fit (no kinks) might even suggest that there is a simple predictive rule. For example a negative linear fit (a straight downward slope) might suggest a simple rule: the longer Bush stays president the more unpopular he becomes. However, the more kinks you have to include to fit the curve to the data, the more complex the relationship you have to posit.
What the fit really tells you is that there is a high degree of auto-correlation in the data - what Bush's rate was yesterday is a good determinant of what it will be today - in other words, on the whole the curve is smooth. It is also generally downward. Where it is not smooth is where a big event happens - 9/11, invasion of Iraq etc. However, the curve fit does not really capture this, as the upswings are much sharper than the slow declines, and you would need a very much higher order polynomial, or some other function altogether, to model this characteristic.
What the general shape of the plot (not the fit line) tells you is that a general rule (Bush gets more unpopular the longer he hangs around) is modified by a second rule which is that where big events occur, he gets a boost to his popularity. The fact that the polynomial fit has to have as many as 3 kinks to get a good fit tells you that these boosts are not uncommon.
So what I would conclude from TIA's plot is that Bush needs a big event to rescue him from his current decline, and that the probability of such an event in any given year is occurring is about one in two or one in three (and is there a trend for these events to become less common?) But we can't even say much about how far the current decline will continue, even if uninterrupted, because although the decline looks roughly linear after each boost, it probably has a floor somewhere above 0% (and a ceiling somewhere below 100%). Extreme percentages are inherently more rare than middling ones.
But drawing a wiggly line through a plot and assuming that the wiggle you chose was the right wiggle and that no future wiggles will occur in order to predict where the wiggly line will go next is not just politically ignorant - it's mathematically absurd.
Mind you, I still think Bush is toast.
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