Rob: I think your model is fun and interesting, so I spent some time with it.

Assuming I've correctly re-produced your results...

The question above is, roughly: what's the probability that the actual result is 0.7M km2 or more away from the predicted result? This occurred in: 1980, 1982, 1983, 1986, 1988, 1991, 2001, and 2006. That's 8 out of 39 years, or about a 20% chance.

Eyeballing the graph you published pretty much agrees that both 2001 and 2006 predictions are off by around 0.7M km2.

We can slightly simplify your approach by noting that you are predicting minimum extent as a linear combination of three variables: June snow area, June ice area, and June ice extent. The multi-variable linear regression package that I'm using (XL miner in google sheets) notes that the 'extent' parameter isn't very useful in this prediction. The software suggests there's a 6% probability that 'extent' should really be part of the equation.

Also, graphing the trend lines through the minimum and the predicted minimum, suggests that the prediction is diverging from actual (getting larger) as each year passes. Since both snow cover and minimum extent trend downward year by year, it might be interesting to add 'year' as a parameter to better explore how well snow cover helps explain minimum extent.

Overfitting a model based on year, snow area, and ice area to all data from 1979 through 2017, we get the second attached picture. And a forecast of 4.58 M km2 for the 2018 min extent. (With a 360 K km2 geometric mean error.) (Overfitting Dekker's model gives a forecast of 4.76 M km2 with a 435 K km2 geometric mean error.) (If I train the year-based model on just 1992 through 2015, the forecast is 4.64 M km2 with a 386 K km2 geometric mean error.)

My simple physical explanation for the year-based model would be: heat is accumulating worldwide year by year due to greenhouse gases; the snow and ice area (or lack thereof) takes into account how much insolation is absorbed in the northern hemisphere in June. Together, this suggests the amount of heat available for melting ice, subject to the vagaries of weather.