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I am trying to find out what is the effect of activities(like jumping, weight lifting etc.) on behavior (such as attitude towards participating in a marathon). (sample size of 60 observations for each variable)

I have 10 different activities coded as 1-participated, 0-did not participate. Based on these I also created a composite variable that measures exposure to the activities.

When I run a regression for the exposure it shows no effects which is fine. However now I want to dive deeper and find out whether one or more of the 10 activities might actually have an effect on future behavior.

But when I run multivaried regression with 10 activities the model is not significant and none of the coefficients is significant either. However when I run 10 simpler regressions I find that some of the activities have significant effect (both coefficient and R2). A similar thing happens when I take 3-4 activities with lowest p scores and run another multivaried regression with only those 3-4 variables, then some of them show significant effects.

So my question is, how should I approach this? Is it okay to just compare simple regressions in this case?

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so if anyone ever has a similar problem to this I will describe how I went about solving this. Long story short I used the backward elimination method on the regression model which essentially eliminates all non-significant variables until only the significant ones are left (For this I used a 90% interval to when predictors are significant). However the downside of this method is that it can remove important variable that are not significant, for that reason the results should be viewed by comparing the trimmed and original model. Also, if you have significant predictors in a model with a non-significant F test, it often means that the variables which have no effect on the model are diluting the F test. Also control variables should not be trimmed during the backward elimination as they generally are backed by literature and therefore should be always included in the model. Hope this helps somebody :)

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