Tuesday, December 7, 2010

Toasting Time is Not Easy

A couple of posts ago, I noted that the data collected by Dan Meyer indicated that a linear model is not the best fit for modeling the time spent toasting vs. the toaster setting.  I've been collecting some data of my own, and it does not look pretty.  The rough data is below.  Remember that the toaster settings were chosen (mostly) randomly.
Raw Toaster Data

From the graph below, it is easy to see there is a lot going on.
The Linear Regression for the Data
The problem with the data is the settings between 2 and 10, which looks linear with a different slope than the settings above 10.

The exponential model is listed below.  It is just a bit more accurate, but not noticeably.
The Exponential Regression for the Data

Finally, for your approval is the cubic regression.
The Cubic Regression for the Data

Well, it's back to the toaster.