I've got a bunch of data on pop singers' performance on the Hot 100 charts over time, and I'm trying to compare the early part of different artists' careers. For example, I might look compare Miley Cyrus' career to the commensurate period of Cher's career:
(The y axis is total "top 10 points" -- 10 points for a weekly #1, etc.)
I'm trying to identify the singer among the 2000-some in the database who had the most similar early career. Running a simple correlation on the first 7 years of everyone's career wasn't very fruitful:
My next idea was to fit a binomial to each person and compare. Here's Beyonce vs. The Beatles through six years, for example:
The trouble is, I have no idea how to compare a bunch of polynomials to figure out where they're similar.
Any ideas how to do that, or otherwise how to compare these datasets?