I am wondering if you can help with non-parametric linear regression.

[DJGS]

I have a set of tooth wear data (from a non-human species) in the form of ratios--- the ratios are the amount of dentine exposure divided by the areas of the chewing surface of the tooth.  These ratios are not normally distributed. 

I am interested in comparing males and females in terms of their wear ratios as a function of age. So, I  have plotted these ratios against the ages of the individuals, and males seem to have a steeper linear slope than do females-- that is, the males wear ratios appear to increase faster as a function of age than do the females' wear ratios. I would like to know the best way to statistically compare males and females in terms of their linear regression slopes but the data, as I say, are not normal. Googling a bit, it seemed that Theil regression might work, but I am not sure. What would you recommend and if you have a recommendation can you point me in the direction of some SAS code that would help? Many thanks! 

[PaigeMiller · Accepted solution]

The data does NOT have to be normally distributed for a linear regression to work. https://blogs.sas.com/content/iml/2018/08/27/on-the-assumptions-and-misconceptions-of-linear-regress...

The errors around the regression line have to be normally distributed (and independent and common variance).

 So go ahead and fit a linear regression and then check the residuals to see if they are approximately normal.

[DJGS]

WONDERFUL! Thank you.

[DJGS]

Thank you!!!!