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enter image description here

The picture below is the dependent variable on the Y and one of the IVs on the X axis. The Dependent variable is range bound between .5 and 12 while the IVs range from 0-over a million depending on the IV. When log base 10 transformed the Q-Q plot is very slightly right skewed compared to the non-transformed data that is very heavily right skewed. The dataset is around 250,000 data points and I am looking to ensure linearity requirement is met in order to perform linear regression.

Thanks,

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  • $\begingroup$ For one thing, you might want to consider how to tackle the apparent heteroschedasticity. $\endgroup$
    – Galen
    Commented Jun 17, 2021 at 1:30
  • $\begingroup$ Just looking at the plot, it doesn't appear linear or log-linear. It is difficult to get a sense of the density of points. Changing the transparency would help some, but also including histograms or a contour plot of the joint density might help show if there is an apparent function between these two variables. $\endgroup$
    – Galen
    Commented Jun 17, 2021 at 1:36
  • $\begingroup$ Your question is phrased with a commitment to linear regression, but I'm unsure that linear regression should be used for this data. What is the question you're trying to answer about the data generating process? $\endgroup$
    – Galen
    Commented Jun 17, 2021 at 1:38
  • $\begingroup$ Galen....I appreciate the comments and agree that I have entered into this analysis assuming linear regression is best. That might be an incorrect assumption. The question I would like to answer "Does company count influence CMS-HCC? " More broadly do specific IVs impact the DV while controlling for a few variables? $\endgroup$
    – Clambs
    Commented Jun 17, 2021 at 2:22
  • $\begingroup$ Would a box-cox transformation be appropriate for the heteroschedasticity issue? $\endgroup$
    – Clambs
    Commented Jun 17, 2021 at 2:23

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I noticed your comment ""Does company count influence CMS-HCC? " More broadly do specific IVs impact the DV while controlling for a few variables?".

Assuming you want to use linear regression, the normality assumption should hold for the residuals under the regression model. That is after controlling for relevant variables.

To get help in R, and further explanation, see here http://r-statistics.co/Assumptions-of-Linear-Regression.html

I hope this might help you to get further with your problem.

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