Can Pearson's Correlation coefficient distinguish between y=x and y = x ?For a set of points (x,y), I obtained a Pearson's r of 0.9936004531.For the same set of points, I changed them to ( x , y ) (took the square root of every x value), and I obtained a Pearson's r of 0.9997411537, which is greater by 0.0061407006.These data were obtained from an Physics experiment I did, where theoretically, y ∝ x .How should I interpret this result?I am leaning towards the idea that because the difference in Pearson's r is so small, we cannot conclude whether y ∝ x or not, rather we can only vaguely conclude that as x increases, y increases in some fashion.Thank you very much for the help..Edit: There were only five data points, precise to 3 decimal places.The five points:(5,0.321)(10,0.395)(15,0.457)(20,0.510)(25,0.550)

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Can Pearson&#039;s Correlation coefficient distinguish between y=x and   y  =      x  ?For a set of points (x,y), I obtained a Pearson&#039;s r of 0.9936004531.For the same set of points, I changed them to   (      x    ,  y  ) (took the square root of every x value), and I obtained a Pearson&#039;s r of 0.9997411537, which is greater by 0.0061407006.These data were obtained from an Physics experiment I did, where theoretically,   y  ∝      x  .How should I interpret this result?I am leaning towards the idea that because the difference in Pearson&#039;s r is so small, we cannot conclude whether   y  ∝      x   or not, rather we can only vaguely conclude that as x increases, y increases in some fashion.Thank you very much for the help..Edit: There were only five data points, precise to 3 decimal places.The five points:(5,0.321)(10,0.395)(15,0.457)(20,0.510)(25,0.550)

stacan6t · Accepted Answer

Look at the Residual PlotsPearson correlation alone is never enough to test if some model fits. It&#039;s important to see that there be no noticeable trend in the residuals. In small regions especially, linear models can work quite well (if you&#039;ve taken calculus you know all nice functions are locally linear), so maybe it&#039;d be better to expand the domain in which your checking, or maybe your data doesn&#039;t provide strong evidence yet for the quadratic fit for some experimental reason.Importantly, though, if you look at the residuals for the linear fit, an easy tell that the linear model is not working well is if the residuals have a clear upward or downward trend, which will happen if the square law is really the case.

Can Pearson's Correlation coefficient distinguish between y=x and y = <msqrt> x </

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