Fitting an Elephant

Because adding constants "helps" data fit a theory, there is an old joke: "Five constants?? You can fit an elephant with five constants!" In a 1975 article James Wei tested this and found that there is a least squares Fourier sine series that will fit these coordinates

that requires a minimum of 30 terms in the Fourier expansion. This Demonstration shows that you can get fairly close with 15 (five more if you want your elephant to have an eye).
The larger question addresses how far you should go to "back into" a theory from data. The plot of the data shows that it has little correlation. Indeed, Pearson's correlation coefficient for this data is very small. Yet with adequate computing power a set of equations can be found. The message becomes: if you want this elephant to have feathers, Mathematica can include them in the fit. Have you have found a theory in your data? No. Is your client impressed? Perhaps, if your client is a cartoon company.



  • [Snapshot]
  • [Snapshot]
  • [Snapshot]


More information is available in chapter eight of Private Real Estate Investment and at mathestate.com.
J. Wei, "Least Square Fitting of an Elephant," CHEMTECH, 5(2), 1975 pp. 128–129.
    • Share:

Embed Interactive Demonstration New!

Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details »

Files require Wolfram CDF Player or Mathematica.

Mathematica »
The #1 tool for creating Demonstrations
and anything technical.
Wolfram|Alpha »
Explore anything with the first
computational knowledge engine.
MathWorld »
The web's most extensive
mathematics resource.
Course Assistant Apps »
An app for every course—
right in the palm of your hand.
Wolfram Blog »
Read our views on math,
science, and technology.
Computable Document Format »
The format that makes Demonstrations
(and any information) easy to share and
interact with.
STEM Initiative »
Programs & resources for
educators, schools & students.
Computerbasedmath.org »
Join the initiative for modernizing
math education.
Step-by-Step Solutions »
Walk through homework problems one step at a time, with hints to help along the way.
Wolfram Problem Generator »
Unlimited random practice problems and answers with built-in step-by-step solutions. Practice online or make a printable study sheet.
Wolfram Language »
Knowledge-based programming for everyone.
Powered by Wolfram Mathematica © 2018 Wolfram Demonstrations Project & Contributors  |  Terms of Use  |  Privacy Policy  |  RSS Give us your feedback
Note: To run this Demonstration you need Mathematica 7+ or the free Mathematica Player 7EX
Download or upgrade to Mathematica Player 7EX
I already have Mathematica Player or Mathematica 7+