Correlate 2 trendlines

Question

I am trying to correlate 2 trend lines.

Students take tests and they have an average grade. The number of students taking the tests gradually decreases and the average grade increases. This happens because only the students that are getting the higher score are sticking around for more. The thing is that eventually there won't be any students left or there would be just one left.

I want to find a relation between the average grade and the number of students taking the test. But i don't know how or if there is even a formula for that.

Example

Answer 1

First, write down the trendline formulas. I'll call them functions of y1 and y2 .

y1 = -224.9*ln(x)+871.11

y2 = 1.5092*ln(x)+0.7216

Solve for ln(x) in both equations:

ln(x) = (y1-871.11)/-224.9

ln(x) = (y2-0.7216)/1.5092

Set them equal to each other and use algebra to solve for y2 in terms of y1 (or vice versa):

(y1-871.11)/-224.9 = (y2-0.7216)/1.5092

y1-871.11 = (y2-0.7216)*-224.9/1.5092 = -149.02*y2+107.53

y1 = -149.02*y2+978.64

There is your formula to roughly correlate y1 and y2 .