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I am stuck on something and think I may have made a big error.

My DV is ticket sales and I have 5 potential IVs: ticket price, income, review score, travel distance, and performance costs. I am trying to build a regression model that best fits the data.

First I performed a correlational analysis to see which IVs are correlated to the DV. This showed that all IVs are correlated to the DV apart from travel distance. So I ran a multiple regression analysis using the enter technique and excluded the predictor travel distance. This then showed that 3/4 predictors contributed to the model, whilst 1 (review score) did not. So I simplified the model by removing the non significant predictor review score.

However, my problem is now that I was messing around with re-running regressions and I entered the predictor that was Not correlated to the DV into the regression (travel distance)- this now shows that it is a significant predictor in the model! And then I went ahead and added in review score, which was not a significant contributor to my previous model. Now it is.

So can we add variables into the multiple regression analysis that were previously shown to not be significantly correlated to the outcome variable? How do you choose what to enter? I thought it was correlation results.. theory would suggest that travel distance should affect tickets bought, but the travel distance is within 20 miles for all participants so not that huge.

Not sure whether to re-do my analysis and results and include all IVs. If I do so, they all seem to be significant in the regression model. How would I make my regression model 'better' in this case?

Thanks

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    $\begingroup$ It does happen sometimes that variable is not correlating on univariate analysis but comes out to be significant on multivariate analysis. It should be taken as significant. $\endgroup$
    – rnso
    Apr 9, 2015 at 13:15
  • $\begingroup$ Thank you. So should you include all variables that you think (based on theory) will be predictors of the outcome variable/DV, even if Pearson correlations show they are not significantly correlated? $\endgroup$
    – Lora
    Apr 9, 2015 at 13:19
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    $\begingroup$ I think you should attempt that and see how the model works out. Final decision would depend on many other details of the study. $\endgroup$
    – rnso
    Apr 9, 2015 at 14:04
  • $\begingroup$ I know a lot of folks here don't like it, but have you tried a stepwise regression procedure? That might help you determine which variables are entered and which are excluded. In addition, you can document your subjective method for inclusion/exclusion criteria. $\endgroup$ Apr 9, 2015 at 14:30
  • $\begingroup$ You should be expecting different results from the univariate analysis & the multiple regression (otherwise what would be the point of the latter?) See here for an explanation. We have a tag for questions on model selection you might find useful; note that univariate screening is not a good method - see Babyak (2004) for an introductory account of the issues with it. $\endgroup$ Apr 9, 2015 at 20:31

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