I think the
curve over the given range of data can be modeled with a cubic curve. I
looked at the fourth degree curve and found that the coefficient of the x^4
term was so small, it would not have a significant impact on the fit of the
curve. My problem with using the cubic curve to model the data is that it
cannot be used to predict BMIs after the age of 20 since the curve drops off
sharply after the age of 20 (and becomes zero and negative). A similar
problem would be found with a fourth degree except that it rises too sharply
after 20 and would also not be a good predictor. A sine curve would
suggest an oscillating BMI which would also not make sense. The other
problem I have encountered is that my students have not been able to find data
for BMIs for ages past 20 to help them find a model function that works past
20. I have suggested to students that they try to suggest what may happen
to the BMI after age 20 and then find a function that would model this. I
have also suggested that they could use one function to model
the situation over the given range of data and a second function to model
what the predicted BMI might be.

. Simple
analytical methods do not produce sufficient consistency for any obvious curve
(the initial numerical/algebraic analysis that students are supposed to do
prior to using higher order use of technology). It seems to me that the task
intends the students to actually make an "educated" guess on the curve,
then try it out and refine it - as opposed to having some fairly consistent
analysis that regression tools confirm. Furthermore, none of the curves
actually work beyond around age 32 (I even had a go at a sine curve - on the
basis that if the period was large enough it could be justified!!) As a task
that "ticks" all the boxes for the criteria it is good but as a task
that is supposed to give at least some consistency in the initial analysis it
has the potential to be frustrating for students unless they are warned that
what they have to show is a process toward a model but immediate
"solutions" in the first stage are not available. I would recommend
that students first do some research into BMI for this task - it is vital to
understand the constraints bearing in mind the BMI data is median data and
should therefore not be more than around 30 (the cutoff for overweight) The
Wikipedia article is good as an introduction to BMI and the following website
(which I only found last night) actually shows the various curves: http://www.scielo.br/scielo.php?pid=S0021-75572006000500007&script=sci_arttext&tlng=en
If you would like a copy of what I have
done (although, to my mind, it needs modification) let me know and I will
upload it to the resources

go to
google and enter : bmi females data

http://en.wikipedia.org/wiki/Body_mass_index

http://www.atypon-link.com/AAP/doi/pdf/10.1375/twin.6.5.409?cookieSet=1

http://www.halls.md/ideal-weight/further1.htm

http://www.who.int/bmi/index.jsp?introPage=intro_3.html

http://www.fao.org/docrep/t1970e/t1970e08.htm

http://www.fao.org/docrep/t1970e/t1970e08.htm#P982_107315

http://www.fao.org/docrep/t1970e/t1970e08.htm#P948_104508

http://girl-wonder.org/papers/bmi.html

http://www.cdc.gov/nchs/data/nhanes/growthcharts/set1clinical/cj41l024.pdf

http://www.halls.md/bmi/heritage.htm

http://www.phi-bedsherts.nhs.uk/documents/pub_health_risk/BMI%20SHA.pdf

http://www.netwizardry.com/research/bmi/bmi.htm