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  • $\begingroup$ Thank you for your excellent explanation and detailing of the different methods. I have one follow up question -- I've came across some papers in my field that say this "in linear models adjusted for age and sex, blood pressure was associated with %bodyfat (r=0.45, P<0.01)". How did they obtain a Pearson's R from a linear model? Thanks for your insight. $\endgroup$ Commented Jun 28, 2019 at 17:54
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    $\begingroup$ By linear models adjusted for age and sex, they likely mean $\text{BP} = \beta_0 + \beta_1 \cdot \text{BF} + \beta_2 \cdot \text{age} + \beta_3 \cdot \text{sex} + \epsilon$. Authors often include the coefficient of determination ($R^2$) as a means for the reader to judge the variance in $\text{BP}$ explained by the model. Maybe this is what they meant? You can calculate it as 1 minus the residual sum of squares divided by the total sum of squares: en.wikipedia.org/wiki/Coefficient_of_determination $\endgroup$ Commented Jun 28, 2019 at 22:32
  • $\begingroup$ Understood, and that makes sense. What do you think of this response? $\endgroup$ Commented Jun 29, 2019 at 2:26
  • $\begingroup$ I think the responder's second suggestion makes sense. That is, "fix" the effects of the covariates/confounders using the mean and then calculate the Y values with values of my actual predictor of interest $\endgroup$ Commented Jun 29, 2019 at 2:32
  • $\begingroup$ Setting the covariates to a suitable value only makes sense if such a value exists. For age you could argue that most people are around a certain age (like the mean), but for sex, would it really make sense to take the mean of the dummy variable? $\endgroup$ Commented Jun 29, 2019 at 8:53