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With my data (Y and X variables) I have $R^2$ = 0.3736.

I used the data from an article that did the same type of experiment, and made a graph and found their $R^2$ = 0.3706.

I know that the values are very low, but that is all I think I can do with the data. Because both graphs have very similar $R^2$ values, does that mean that there is some sort of connection or similarity between both sets of data?

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    $\begingroup$ Similarity of $R^2$ doesn't of itself imply any kind of connection, no. $\endgroup$ – Glen_b Dec 29 '13 at 18:46
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The coefficient of determination (R²) is a statistic that measures how much of the model's outcome variation can be explained. For example:

$Y = \beta_0 + \beta_1X + \epsilon$

The R² will mean how much X can explain the the variation on Y, given a specific dataset.

You can't use the R² statistic to infer if data from two different graphs/datasets are connected.

However, if you found another study which used the same methodology as yours you could compare the results (R²) as an additional evidence to support if Y has (or hasn't) a relationship with X.

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