The relationship between the volume of a liquid in a bottle as a function of the height of the liquid is used to illustrate polynomial regression and the fitting of spline models. A polynomial regression exercise is provided where students attempt to determine the shape of a bottle using only the height and volume data from the bottle, The height and volume data for bottles are easy-to obtain and provide an interesting data-collecting activity for introducing spline models in a regression course.
& Holcomb, J.
(2000). Spline Bottles. American Statistician, 54 (2), 129-135.