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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:

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(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:

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My next idea was to fit a binomial to each person and compare. Here's Beyonce vs. The Beatles through six years, for example:

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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?

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What you're talking about is Time Series Analysis. How to statistically compare two time series? should give you the approach you need.

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