please help a sociologist struggling to get to grips with R and statistics in general..!

I've got a data set with 11 variables. I need to investigate the possible relationships between one of the variables (percentage of smokers in a population) and the rest of them- things like unemployment rate, education level, and so on. I'm working purely with linear regression.

I'm getting there with correlation, but having looked around at numerous examples on the web, I'm still unsure with regards to method. Apologies if it's completely obvious, but I can't seem to find an answer anywhere.

As I see it, it seems sensible to look for correlation between smoking and all the other variables firstly with scatterplots, and then by calculating the correlation coefficient if there is an identifiable linear relationship (Pearson's r or Spearman, depending on normality). If we then continue and do separate simple linear regressions between smoking rate and our identified variable, that all seems well and good.

But where does multiple regression fit in here? Does it make any sense, statistically speaking, to do simple linear regression first and then multiple linear regression also? Or would it be best to just jump straight from testing correlation to multiple regression?

Any help much appreciated!

  • 1
    $\begingroup$ Yes, you should do multiple regression. But since your dependent is a proportion, you should probably use beta-regression. I don't think you should try correlating the dependent against all explanatory variables independently. $\endgroup$ – Roland Apr 11 '14 at 10:16

Simple linear regression can be useful (or, as @Roland sensibly suggested, beta regression), but it is a separate task from multiple regression. Simple regression should not be used a screener for multiple regression.

The two ask different questions: In simple regression you ask about the relationship between the dependent variable (% of smokers) and a particular other variable. In multiple regression, you ask about relationships controlled for other variables; that is, e.g. "What is the relationship between smoking % and unemployment, holding XXX constant?".

I would also look at scatterplots of the DV with each IV.

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