Curves

Recently, we had to do a physics lab involving capacitors. We charged one up and as it was discharging, we measured the voltage across it every ten seconds for about twenty minutes. The directions said to wait until it went to zero, but if you know anything about exponential decay... Anyway, we were supposed to end up with a nice exponential decay function. The data came out almost perfectly, which is the Mew of physics labs, so I was pretty excited as I helped Moose (who was in my group) enter the data into the computer. Before we were done, I glanced over at Justine's graph, which was gorgeous. It had an RMSE value of 0.006002, which is awesome. If you don't know, (and even if you do,) the RMSE value is a number from -1 to 1 that measures how closely the data follows the model, with 0 being a perfect fit. To get a value that close to zero on a physics lab is virtually unheard of. I told her, "Justine, that is the prettiest graph I have ever seen in my entire life." Here, see for yourself (click both to enlarge):


She thanked me, and then Moose bet her five bucks that our graph would beat hers. She politely declined, and Moose offered simply to give her $5 if her graph turned out better. She didn't answer, and he took that for an OK. We finished entering the data and brought up ours:


An RMSE value of .008240. Ooo, that hurts. Well actually it's still awesome, but not quite awesome enough. Moose gave her the $5, which she gave back. He gave her $1, which she took. And that was that.

Thanks to Justine and Moose for the screen shots.