Weighted linear regression assumptions

#1
Hi all, question on linear regression with weights - when testing residual assumptions (homoscedasticity and normality), do I need to weight the residuals with the same weight? I am using proc reg "spec" option to check for homoscedasticity and proc univariate "normal" option to check for residual normality.

And a SAS question - how come sometimes proc univariate gives Shapiro Wilk test, while other times it does not (but still gives KS, Anderson Darling, etc)?

Thanks for your help!
 
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hlsmith

Less is more. Stay pure. Stay poor.
#2
I don't think you need to use the weight latter on after collecting residuals from the model. I would ignore formal normality tests and just look at the qqplot in proc univariate. Formal tests can be sensitivity to large sample sizes and reject normality based on small departures when CLT has already pretty much kick in.
 
#3
I don't think you need to use the weight latter on after collecting residuals from the model. I would ignore formal normality tests and just look at the qqplot in proc univariate. Formal tests can be sensitivity to large sample sizes and reject normality based on small departures when CLT has already pretty much kick in.
Thank you for the response. There are about 200 or so models, so looking at qqplots is not the most efficient way, so I was looking for some formal tests. Each model has anywhere from 100 - 1000 obs.
 

hlsmith

Less is more. Stay pure. Stay poor.
#4
It couldn't take more than a minute to look at 200 qqplots. You could merge (concatenate) all of the residual data sets into a single dataframe and have a categorical indicator variable to reference which model they were from, then add a class statement to the proc univariate and boom done.

Simulate a random normal distribution for 200 and 1000 obs and run a normality test. Report back what the results looked like and how you would interpret them. Then look at their qqplots. Which one is funner and more informative - I'd guess the plots!