©2020, George J. Irwin. All rights reserved.
One of my favorite shows of the eighties was “Kate and Allie.” I even went to see a filming of one of the episodes. Somewhere in the archives, I have an extensive set of airings as well, copied from over the air to VHS tapes (look it up, kids).
There’s one episode in particular where Allie Lowell, played by Jane Curtin, has forgotten to put a turkey in the oven. Knowing that guests are coming for dinner, she reasons, “if it cooks for six hours at three hundred degrees, it can cook for three hours at six hundred degrees.” Hilarity ensues.
We here in Black Belt Land can take a cue from this misadventure which relates to regression analysis. As you probably know, regression is the attempt to determine whether one or more variables have an effect on another variable, for example, does the number of times someone says “Oh wow!” on a house hunting show influence the number of eye rolls I execute during said show. And yes, there is a correlation: the more “Oh wow”s the more eye rolls.
While this exercise is valuable, it has its limits. Simple regressions result in a straight line which represents the “best fit” of the data you have. The result is only good for the data points you have, and the line that’s created by your favorite analysis program.
It’s certainly OK to interpolate using the information you have: for example, if ten “Oh wow”s align with two eye-rolls, and twenty “Oh wow”s align with four eye-rolls, it’s reasonable to conclude with some certainly that fifteen “Oh wow”s align with three eye-rolls.
However, if the largest number of “Oh wow”s observed is thirty, aligning with eight eye-rolls, you cannot assume from the data that fifty “Oh wow"s will align with twelve eye-rolls. It might be that I go completely over the edge and give myself a severe headache with fifty eye-rolls. Or I may stop at a maximum of twelve eye-rolls because I’ve changed the channel, or thrown the television out the window in frustration and never reach fifty “Oh wow”s.
One of the more famous examples of the risk of extrapolation comes from Mark Twain, who wrote in Life on the Mississippi that if what was known about the observed shortening of the Mississippi River- 242 miles in 176 years— was to be extended in either direction in time, it would have started at over a million miles long and the Lower Mississippi will eventually shrink to under two miles in length. Neither is true, of course, but that’s what happens when a regression equation goes too far.
The same can be said for Allie Lowell’s predicament. But not to worry this time: I’ve never seen a standard kitchen oven that can be heated to six hundred degrees.