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copied!<p>One option would be to do a <a href="http://en.wikipedia.org/wiki/Linear_regression">linear regression</a> on the data set to get a best-fit line. If the data is linear, you'll get a very good fit and the <a href="http://en.wikipedia.org/wiki/Mean_squared_error">mean squared error</a> should be low. Otherwise, you'll get an okay fit and a reasonable error.</p> <p>Alternatively, you could consider transforming the data set by converting each point (x<sub>0</sub>, x<sub>1</sub>, ..., x<sub>n</sub>, y) to (x<sub>0</sub>, x<sub>1</sub>, ..., x<sub>n</sub>, e<sup>y</sup>). If the data was linear, now it will be exponential, and if the data was logarithmic, now it will be linear. Running a linear regression and getting the mean-squared error now will have a low error for the logarithmic data and a staggeringly huge error for the linear data, since the exponential function blows up extremely quickly.</p> <p>To actually implement the regression, one option would be to use a <a href="http://en.wikipedia.org/wiki/Ordinary_least_squares">least-squares regression</a>. This would have the added benefit of giving you a correlation coefficient in addition to the model, which could also be used to distinguish between the two data sets.</p> <p>Because you've asked for how to do this in Java, a quick Google search turned up <strong><a href="http://introcs.cs.princeton.edu/java/97data/LinearRegression.java.html">this Java code</a></strong> to do a linear regression. However, you might have a better fit in a language like Matlab that is specifically optimized to do these sorts of queries. For example, in Matlab, you can do this regression in one line of code by writing</p> <pre><code>linearFunction = inputs / outputs </code></pre> <p>Hope this helps!</p>

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