>a student collects a set of data for which an approximate model might be: > > y = 3log(x - 40) + 30 or even y = 3(x-40)^2 + 30 > >Am I right that there is no easy transformation which will "straighten" these >"curves"??? If so what should we do with the data when trying to model it?
Al, I think you are correct when the parameters are unknown. That is if the function form is y = a(x - h)^2 + k and a,h,k must be estimated from the data. This also occurs for exponential functions with a vertical shift y = a(b^x) + c.
I would suggest a two step process.
1) Visually fit the data and use the coordinates of points on the visual fit with algebra methods to get a first approximation to the parameters. For example, in the case of the quadratic, given three points you can find a parabola to fit the points.
2) Graph your fit, and calculate SSE = sum(yfit - ydata)^2. Adjust your parameters using trial-and-error to get smaller SSE.
This approach reviews some algebra and the concept of SSE.