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I have a data set of values for a particular measured metric for employees for the year 2013, and a set of values for the same measured metric for the year 2014.

I am looking to assess the repeatability of this metric from year to year for these raw numbers, and then I hope to adjust these values using other measured metrics from the corresponding year in order to improve the repeatability, in order to be able to better predict this year's values for the metric from the data I already have available.

The first thing I have tried is plotting the 2013 values on the x-axis vs the 2014 values on the y-axis and calculating the R-squared coefficient for this plot, which comes out at about 0.4.

The second thing I have tried is plotting the 2013 values on the x-axis and the difference between the 2013 and 2014 values on the y-axis and calculating the R-squared coefficient for this plot, which comes out at much lower than the above method.

My questions are: (1) is there a reason that the R-squared value in the second method is so much lower than in the first method, and (2) is there a better way for me to measure this repeatability and better predict future years' values?

Thanks in advance!

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R-squared is the square of the coefficient of correlation, which in turn is the covariance divided by the product of the standard deviations.

As I understand it, your second computation uses $Cov(X, X-Y) = Var(X) - Cov(X,Y)$ and the first uses just $Cov(X, Y)$. Without following the computations through to the end, I hope this gives you a clue why the two R-squareds are different. (If you are looking at output for 'adjusted R-square', then the formula is a little more complicated, but above distinction is still important.)

You are careful to note which variable is on which axis. That is important for regression results (intercept and slope), but not for correlation; $Cor(X, Y) = Cor(Y, X)$.

Notes: (1) Implicit in what you say seems to be that these are the same employees in both years. For your purposes, it is probably best to use data only for employees measured in both years. (2) Without knowing a lot more about these measures (and others you might use along with them), I can't really comment on methods to 'improve repeatability.' I'm just suggesting you think about whether it might be a good or a bad thing if these measures steadily changed in one direction or another across the years.

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