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1 Spanners: Okay, I just need to do a least squares fit to these planetary data, calculate the correlation coefficient, ...
2 Spanners: ... estimate the linear parameters, and use them to plot the projected distances of the remaining orbits.
3 Spanners: Goo goo, ga ga...
4 Paris: What happened?!
4 Iki Piki: He's regressed to his childhood.
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Linear regression is a statistical method for estimating the value of a dependent variable at a given value of some other variable, using data collected at other values. It's usually applied to physical systems. And the odd pun.
Looking at what Spanners is actually describing here, I don't think that analysis will realistically do what he wants. He'll end up with an empirical relationship between the planetary orbits and... some other variable he hasn't mentioned. Which is fine, but you can't then use that to predict remaining planetary orbit distances unless you have measurements of the other variable for those planets.
For example, if the other variable was mass (which is a ridiculous example, but let's run with it), then Spanners would have a set of measurements of mass and orbital distance for some planets, which he uses to calculate a relationship. Then given the masses of other planets, you could use that relationship to make predictions of where their orbits should lie (under the assumption that the relationship reflects a true physical, causal relationship between mass and orbital distance). So to make these predictions, you need the masses of the other planets... but if you had observations of the masses of those planets, then you pretty much necessarily also have to have their orbital distances, as that's probably the single most obvious thing about a planet. As soon as you detect the planet, you pretty much know where it is, after all.
This is true even of the many extrasolar planets we have now detected orbiting around nearby stars. One of the few parameters we actually know about such planets is the orbital distance, at least for all of the most common detection methods.
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