# Pearson Correlation of Device Values

I have a device which obtains velocity based values over a period of 1 minute (average). I also have another device with which I am comparing that device. Now the velocity values can be quite random, but both devices should be similar in terms of increase or decrease within each minute: essentially they should have the same flow.

I saw online that some research has utilized the Pearson correlation to compare these values, but what I'm wondering is why? I read that this correlation only works for linear based values, and from what I read up, the velocities themselves were quite random (although similar in terms of devices). Or at least I don't think they are linear.

If you think your two devices are measuring the same quantity despite fluctuations then equality is a reference case for you, so you should be considering whether $y = x$ is a good approximation for their measurements $y$ and $x$. That certainly qualifies as a linear relationship as it is merely a special case of $y = a + bx$ for which $a = 0$ and $b = 1$.
Conversely, correlation measures linearity of relationship, not agreement. The correlation between any $x$ and any $bx$ is identically $1$ for positive $b$, whether $b$ is 2 or 2 billion or anything else positive. Concordance correlation is a specialised measure of agreement, not linearity, which has its uses. So, you need to be careful as correlation only measures agreement in special circumstances.
• Indeed. In that case the correlation is not just positive but identically $1$ even though agreement is clearly imperfect. But watch out: what you are calling "nonlinear" is a plot of velocity versus time, which whatever its interest has nothing to do with the correlation between values paired for the same times. What is linear and what is nonlinear depends entirely on what graph you are looking at. – Nick Cox Nov 12 '14 at 12:18