(Data that is neither linear nor quadratic.) We'll close this exercise set with two data sets that, for reasons presented later in the book, cannot be modeled correctly by lines or parabolas.
(a) This first data set came from a Summer 2003 publication of the Portage County Animal Protective League. They make the following statement: ``It doesn't take long for two cats to turn into 80 million. If two cats and their surviving offspring reproduced for ten years, you'd end up with 80,399,780 cats.'' We assume N(0)=2.
[table — see PDF]
Use Quadratic Regression to find a parabola which models this data and comment on its goodness of fit. (Spoiler Alert: Does anyone know what type of function we need here?)
(b) This next data set comes from the U.S. Naval Observatory giving the number of hours of daylight in Fairbanks, Alaska for 2009 on the 21st of each month. We'll let x=1 represent January 21, 2009, x=2 represent February 21, 2009, and so on.
[table — see PDF]
Use Quadratic Regression to find a parabola which models this data and comment on its goodness of fit. (Spoiler Alert: Does anyone know what type of function we need here?)