Sunday, February 28, 2010

Regression Data and those "Found" pictures

When I teach regression or curve-matching, I like to use real-life stuff for most of the examples. Linear is easy but some of the others can be difficult to find right off the top of my head. Kids have a tougher time.

I think it's counter-productive to let them misfit curves to the real-world. I don't send them off to take random pictures and I won't accept a physically inappropriate curve fit to the image of a cloudbank, like this. Firstly, there isn't a curve there. Second, it's not a cubic. It isn't, won't and never will be.

Continued below the jump:

I know that the curve is domain-restricted and it's kinda close, but clouds don't operate that way and neither should we. A cubic? Importantly, regression needs a step before "monkey push button". We need the "think" stage and I believe that if the data doesn't physically follow the curve-type chosen, we shouldn't use it, at least not when TEACHING regression or polynomial curves.

I suppose, at the end of the year during June, when everyone wants outside and you're accomplishing nothing anyway, then this project can be a filler - slightly humorous and gee-whiz, "full of sound and fury, signifying nothing."

Here we have this bell tower which is so not curved. I realize that students are trying to fit a curve, but come on. There are a whole bunch of straight lines here. The red parabola isn't even close, really.

"What's the big deal? They're using math." No, actually they are playing mindless games with technology. There's both a circle and an ellipse there, ignored. I'd believe those arches are parabolic if you wanted to try and convince me. How about the moon?

This is akin to graphing the world record times for the mile-run and then using a linear regression. So the world record will be 32 seconds some time in 2015. Duh.

It isn't and that's not the way regression should be used -- or at least, the kids should be taught to recognize when the regression just isn't right. "I call Bullshit. If we extrapolate (or interpolate) to here, we get stupid answers."

That's how I use regression in the real world. We shouldn't give up a perfect WCYDWT situation in favor of lazy pictures.

I would much rather give the kids data that does, or should, fit a particular regression and let them discover the regression. I like using stop-motion for parabolics:

There is a physical law being followed here. Go find it.
Hang a lightmeter (now that I'm using digital cameras, I have no other real use for it!) on the board and move the projector back and forth. There is a physical law here. Go find it.
Here is temperature data for my teacup. There is a physical law here - GFI.

I would much rather have photographs of a hanging chain and a suspension bridge, try and fit the obvious parabola to both. Then we'll find that one fits but the other doesn't quite so well and we can talk about why.

Maybe it's just me: the cover of the TASCO catalog had a picture of the Gateway Arch and a smarmy looking guy holding a placard with a quadratic on it. AHHHHHHHH!


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