How can you find the nature of a graph?

Question

I have a physics project, and I have to develop an argument, but am not allowed to use phrases like "From the graph you can tell..."

How can the nature of the graph be determined manually, e.g. finding that it is expontential rather than quadratic?

Answer 1

Well if you guess that it is exponential, you could find a suitable change of variables so that the resulting pair of variables are supposed to be linearly related, and then you can draw a best-fit line and compute the correlation coefficient if appropriate. To test for a quadratic relation, you might want to use some polynomial interpolation technique. You may want to look at http://en.wikipedia.org/wiki/Linear_regression and http://en.wikipedia.org/wiki/Least_squares for details.