## Saturday, August 6, 2011

### "No linear relationship" does not mean "no relationship"

There's a dangerous type of argument that I've noticed recently: pundits will argue that a certain relationship is non-linear and use this to justify any claim they want to make about that relationship.

The example of the hour is the Laffer curve. The basic concept is so simple we expect every high school algebra student to grasp it: you have a function with a global maxima somewhere between zero and one; if you're to the left of that maxima you want to move to the right; if you're to the right you want to the left. Let me draw a picture I could explain it to reasonably attentive elementary schoolers. (Dynamic laffer effects are a different story that I'll leave to Noah Smith.)

We can argue where the peak is (or where it was in 1960 or 1980), but once you've accepted the basic concept, you have to accept the move-toward-the-peak implication. Despite this, you will routinely see supposedly knowledgeable people on television, in print and online using the Laffer Curve to justify the blanket statement that cutting taxes raises revenue.

We see something analogous with health and fitness journalism. The relationship between calories and weight loss is not linear. Neither is the relationship between aerobic exercise and weight loss. In both cases, it's a strong relationship and you generally won't get in trouble assuming that it's strictly monotonic (within reasonable ranges, of course).

Unless you're an athlete in training or a model getting ready for a swimsuit shoot, you can probably assume that eating less and exercising more will cause you to lose weight, but we still get endless experts citing phenomena like metabolism responding to diet and then concluding that there's no point in going to the gym and passing up that pound o' fries.

p.s. Joseph has a great example of how calorie consumption tends to dominate factors like diet make-up. If he'll answer his damned phone I'll see if we can get a post out of him.