It is a "line of best fit" through a set of data points. It is calculated so that the average of all the distances from each of the points to the point on the line directly above or below it is minimized. Your HP48 has a program that does this.

This line does not connect the points 1979 - 2000, it models ALL the points from '79 to '09, it is derived with data from ALL the points contributing to it. The regression has to be reconstructed every time you add a data point, or every time you repeat the graph for a different month. Even without doing the math, you can see by visual inspection that the line is a very good fit, a characteristic of time- correlated data.

In fact, this is a linear regression, that is, the data is being represented by a straight line. The data might even be better modeled with a conic section, or a logarithmic or exponential or power function, although when you only have thirty data points and a lot of noise, as you do with climate numbers, that might be overkill. Curves are better fits when the rate of change itself is increasing or decreasing, but 30 years is too small a sample for data with this much scatter to reveal higher order trends.

Still, this data and that regression look right on to me, and highly correlated to boot, which suggests a causal relationship which is a function of time. This is consistent with global warming, although I concede it could conceivably be caused by something else altogether, like an increasing load of volcanic soot on the ice.

Now if you look at the Feb chart, just ignore the line and consider the relations you bring up. The regression has nothing to do with these statements, which are true by inspection.

February 2009 was the fourth lowest
yes, its higher than '07, '06 and '05

February 2007 was the third lowest.
yes, it's higher than '06 and '05

February 2006 was the second lowest.
yes, it's higher than '05

February 2005 was the lowest.
Absolutely.

"We'll just quietly leave 2008 out of it."
Why leave it out? It is higher than '09 and higher than '04 through '07. It bucks the trend somewhat, but not by that much. It's still lower than any sample prior to '04.

Will February 2010 be the fifth lowest? 2011 the sixth?
We don't know, they haven't happened yet.

If we have similar charts to this for every month of the year, or even most of them, it is very compelling evidence the icecap is melting, although again, I concede that is not necessarily proof that AGW is at fault. I suspect that the summer months show more dramatic negative slopes of the regression than Feb and Mar, because you would expect the winter ice cover to be less sensitive to thermal variation than the summer.

But trust me, this math looks legit to me.