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I am currently trying to show if a certain medical marker, say X, predicts a poor outcome, say time spent in hospital. Both values are continuous. I performed a simple linear regression to determine r2, df, F, and the sig.

I want to test whether other markers are better at predicting the time spent in hospital than our marker. I was thinking of doing a multiple regression analysis, but the markers are related -> hence my multicollinearity rule would be broken.

Can I perform a simple linear regression for each marker and time in hospital and then compare the r2, df, F, and sig. to determine which marker better predicts time in hospital? Would this be breaking any statistical rules?

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  • $\begingroup$ Sometime you have to work with what you've got and do the best you can. I personally would at least individually regress and inspect the variables for predictive power as an analytical start. Also it would be a good practice to first scatterplot each predictor variable against the outcome variable to determine if there is any obvious transform, such as log or exp, that might be useful in the regression. $\endgroup$ – James Phillips May 28 '19 at 10:50
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This is actually quite hard to do really well. The problem is usually called "model selection" so you might have some luck using resources for this. But it is IMHO very hard to distinguish which resources are actually good and there is a lot of advice out there that I personally think is heavily misguided. A good heuristic is to be careful around any sweeping claims about "good", "optimal", "wrong" methods if you can't evaluate the arguments for yourself. I would be especially wary of any method that claims it can do model selection fully automatically.

With that cleared, you can get some mileage from your proposed solution - the main advantage is that it is easy and (I presume) lets you use tools you are familiar with. I would use R^2 rather than siginificance as the difference between "significant" and "not significant" is not itself statistically significant.

@James Phillips is right that scatterplots are definitely a way to go - and listen to the wise words of XKCD: https://www.xkcd.com/1725/

Multiple regression can also be OK with reasonable amount of collinearity so maybe you could run that on top of the individual regressions and see if you arrive at similar conclusions.

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  • $\begingroup$ Upvoted for the excellent advice. $\endgroup$ – James Phillips May 28 '19 at 17:34

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