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I am working on patients data (168614). I examined the correlation between blood test (HbA1c) and average weekly max temperature. I found a highly significant correlation but low Pearson (r) value (as in the photo): Correlation result

Now, is it true to report this result (finding) and apply further analysis such as regression? Or not!!

I would appreciate any help.

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If you've found small correlation between two variables, but the effect is highly significant, congratulations! This means you are working with a lot of patients and very powerful (i.e: likely to detect true effects) tests, as all reserach should be done!

I don't have too much knowledge about the exact hypothesis you are testing, but it seems that your target variable has a lot of "randomness", with the effect of your predictor being small, but consistent. If possible, you may want to work with a more complex model, using more independent predictors

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  • $\begingroup$ Thank you so much, David, for your useful comments and I really appreciate that for you. My hypothesis is high weather temperature can increase HbA1c (blood test of diabetes). $\endgroup$ – ph-abdallah Jun 17 '19 at 9:03
  • $\begingroup$ OK, so I guess the conclusion is that HbA1c levels are definitely higher at high temperatures. If you want to quantify by how much on average, you may want to fit a linear regression model and check the coefficients. However, there are many other factors that also play a role in HbA1c levels $\endgroup$ – David Jun 17 '19 at 9:13
  • $\begingroup$ Thank you very much David. I'll try to fit linear regression and I'll use more factors such as age and gender. $\endgroup$ – ph-abdallah Jun 17 '19 at 9:21
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You ask two questions:

Now, is it true to report this result (finding)

It is fine to report any result, significant or not, large or not, as long as you are honest about what you are reporting.

Apply further analysis such as regression? Or not!!

This sounds like you are doing bivariate screening for regression. This is a bad idea (although it is commonly done) regardless of the effect size and the significance.

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  • $\begingroup$ Thank you so much, Peter, for your useful comments. I would appreciate if you can recommend the best alternative for the bivariate screening for regression, please Peter. $\endgroup$ – ph-abdallah Jun 17 '19 at 8:59

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