In the polar ice post above, the term "linear regression" appears.

A linear regression is a rigorous, statistical trend line drawn through a set of scattered data points to try and detect if there is a tendency for those points to rise or fall, and by how much. It's a linear regression because the line is straight, although there is no reason why some other curve can't be used to model the general trend of data. There are logarithmic, exponential, power and geometric regressions, too, even trigonometric ones, although for the most part, a line gives a decent fit for most data sets. And of course, if you fiddle long enough, you're bound to find some kind of regression that will give you a plausible fit to any data you like, even random points.

The human eye is pretty good at drawing a line through a data, but there are mathematical procedures that do this too, to try and minimize bias. BTW, you cannot eliminate bias entirely, you can only make it less likely, or harder to spot. The old saw about 'figures don't lie but liars can figure' is proven true every day. I'm sure you're also familiar with 'there are lies, damn lies, and statistics'. By picking data, making assumptions, and selecting the right procedure and the right data, you can make the stats work for you, instead of the truth. This even happens subconsciouly, with the statistician sincerely not aware he is doing it.

The mathematical procdeure called a linear regression takes scattered data points and generates the equation of a line that tries to show the general trend of that data. The value of the resulting line is sometimes greater, sometimes less, than the value of the nearest point, but the idea is that these "residuals" tend to average out and approach zero. To put it in mathematical terms, "the root mean square of the sum of the residuals is minimized." BTW, this number, the RMS, is a clue as to how realistic your regression is, how accurately it has modeled the data. The smaller it is, the better.

So why bother? Why not just eyeball a line? It will probably be close enough for most analyses. Because we simply cannot trust ourselves to tell the truth, even if we are totally honest and sincere, we can always subconsciously inject bias into an analysis. All we can do is use impersonal procedures that rely less on the human mind's uncanny ability to impose order on chaos, even if there is no order there to begin with. And hopefully, those "impersonal procedures" will be more convincing to our critics than our own private passions.

Beware of science. It is our best tool, but it is not foolproof.