I have a load of data that consists of websites and the "power" of their backlinks. The lowest power is 1. The highest is 949876. The average is 6056.
I want to be able to assign a site a ranking from 1-100 that denotes how powerful they are. I thought I could do this using a nice graph like this one (It's supposed to be a smooth curve 😉
http://i.stack.imgur.com/0fIRa.png
So, on the $x$-axis I have values from $0$ to $100$. I know the following points:
$$x = 1, y = 1$$ $$x = 50, y = 6056$$ $$x = 100, y = 949876$$
How can I find $y$ for another value of $x$? .. or am I approaching this in totally the wrong way?
Thanks!
Best Answer
Without more information, you can tell nothing about other values of x unless you know more about the graph.
If we assume that the equation is in the form $ax^2+bx+c=y$ which is likely the easiest form, replace x and y for each known value and solve for the values of a,b, and c. This would be the form I would fit data like this as an engineer unless I had more information knowing that this was a very inaccurate estimate.
these would be:
$$a+b+c=1$$ $$a*50^2+50b+c=6056$$ $$a*100^2+100b+c=949876$$
The values would be: $$a=218783/1155$$ $$b=-3671736/385$$ $$c=2159516/231$$
There are, however, and infinite number of other equations that would fit these 3 points. For instance: $$kx^3+jx^2+lx+m = y$$ would have those values on it for any value of k and some corresponding values of j,l, and m.
If you could give some context, I can help you out further but I need more information. For simple questions like these if I can't remember how to do it, I retreat to Wolfram Alpha first. (Later I would use Matlab or Scilab for most of my calculations.)
Addendum: if you have alot of them and you are not used to using other programs, place them in excel, and do curve fitting.
http://www.csupomona.edu/~seskandari/documents/Curve_Fitting_William_Lee.pdf