If the Pearson r is .1, is there a weak relationship between the two variables? I thought Pearson's correlation $r$ equal to 0.1 is considered a weak relationship but my instructor said sometimes it may indicate a strong relationship. I don't get it. And how it is related to ETA?
 A: Let me again post the same quote from the web:

  
*
  
*I once asked a chemist who was calibrating a laboratory instrument to
  a standard what value of the correlation coefficient she was looking
  for. “0.9 is too low. You need at least 0.98 or 0.99.” She got the
  number from a government guidance document.
  
*I once asked an engineer
  who was conducting a regression analysis of a treatment process what
  value of the correlation coefficient he was looking for. “Anything
  between 0.6 and 0.8 is acceptable.” His college professor told him
  this.
  
*I once asked a biologist who was conducting an ANOVA of the size
  of field mice living in contaminated versus pristine soils what value
  of the correlation coefficient he was looking for. He didn’t know, but
  his cutoff was 0.2 based on the smallest size difference his model
  could detect with the number of samples he had.
  

It is true that correlation is a value between $-1$ and $+1$, where $0$ is "no correlation", $-1$ is perfect, negative correlation and $+1$ is perfect, positive correlation. However besides that, there is no such a thing as objectively "strong", or "week" correlation. It depends on the kind of data you are dealing with what magnitudes of correlation can you expect.
A: It depends on the sample size. If the sample size is small the estimate may not be significantly different from 0.  On the other hand, if the sample size is large it may be statistically different from 0. In the latter case you might say that it is significant but to call it strong is a matter of judgement and depends on the subject matter.
A: To add on the other answers, you might well also have a nonlinear dependency between the two  variables that the Pearson's $r$ does not capture. Then you might have a look at the Maximal Information Coefficient MIC: here. 
Anyway, the best thing you can probably do with two variables is to have a look at their scatter plot. So you can judge if you either have a weak or strong relationship yourself.
