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I thought the pearson-r is 0.1 is considered as a weak relationship but my instructor said sometimes it maybe strong relationship. I don't get it. And how it is related to ETA?

baba
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    Welcome to CV. Since you’re new here (and consider registering), you may want to take our [tour], which has information for new users. If you check [wikipedia](https://en.wikipedia.org/wiki/Pearson_correlation_coefficient) page, you will see that Pearson's $r$ is a measure of the **linear** correlation between two variables. If the relationship is strong but nonlinear, Pearson's $r$ might not capture that. Maybe this is what your instructor meant. Otherwise, the answers below provide nice explanations. – T.E.G. Aug 06 '17 at 00:21
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    What does "ETA" stand for? – whuber Aug 07 '17 at 22:57

3 Answers3

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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.

Tim
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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 be significantly different from 0. In the later case you might say that it is significant but to call it strong is a matter of judgement and depends on the subject matter.

Michael R. Chernick
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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.

Simone
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