I have a continuous dependent which is the concentration in the blood and several independent variables. I applied the linear regression and it seems that there is the violation of assumption.The R square of the model is 0.06. We have enough sample size around 900 observations but I was wondering if it is reasonable to apply linear regression in this example? I also took log of the dependent variable but again it seems we have the violation of the assumption especially linearity. Am I right? The dependent variable is very skew. Do you recommend using quantile regression or running the regression on the dependent variable If you believe the model is linear? enter image description here

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Here is the plot of residuals vs fitted values after taking log.

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  • $\begingroup$ What is your purpose in fitting the regression? Tell us more about the problem you are actually trying to solve. $\endgroup$ – Matthew Drury Sep 25 '17 at 2:25
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    $\begingroup$ Taking the log worked. $\endgroup$ – whuber Sep 25 '17 at 15:36
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    $\begingroup$ "Works" here just means that the model is about as good as you can get. Nothing guarantees encouraging $R^2$ if there isn't much of a pattern in the data. $\endgroup$ – Nick Cox Sep 25 '17 at 18:54
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    $\begingroup$ The red line is an exploratory smooth of the residuals, intended only to guide the eye. It is unreliable at the horizontal endpoints. Relative to the (vertical) spread in the residuals, it is essentially flat, confirming the absence of any appreciable systematic variation in the residuals with the fitted values. $\endgroup$ – whuber Sep 25 '17 at 20:57
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    $\begingroup$ One might characterize the original plot as basically horizontal (although the curvature is more pronounced). However, the residual distribution is strongly skewed in the first plot--and that alone is enough to suggest that a transformation of the response could be useful. $\endgroup$ – whuber Sep 25 '17 at 21:03

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