Hello, I am doing a multiple regression with one outcome measure and six predictors (say p1, p2, p3, p4, p5, and p6). The sample size is 140. When I perform a stepwise regression, I have 4 statistically significant predictors: p1,p2,p3, and p4 (p1 is the strongest and p4 the weakest). These are the results without any transformations of the raw data.
However, predictor p4 is not normally distributed, so I performed lg(10) of the predictor p4 and insert that predictor in the regression (instead of raw p4 data). This time, the results also indicate 4 statistically significant predictors but this time I have the following statistically significant predictors in the model: p4(lg10), p1, p5 and p3 (ranked by their size, p4(lg10) being the strongest and p3 the weakest).
So, the question is what should a possible write-up of these results be? Both of these models are theoretically sound but I wonder which one is „closer to the truth“.
Hello,
There is NO assumption about normality of the independent variables in multiple regression. So, you just have to check that the necessary assumptions are met on the final model (heteroscedasticity, linearity, multicollinearity, normality of residuals). In my opinion, you should present the first model mention.
Best regards
Thank you Stamatis for your reply. Although there are 6 predictors, I did not have any issues with regression assumptions you mentioned. It is just so surprising, that the model changes so drastically (in the sense of predictors) when I used lg(10) of p4. Both models are not "exceptionally good" in explaining variance of the dependent variable (the first model explains 24% and the second 28% of the variance).
I would urge you to discuss this with a local statistician. There are lots of pitfalls in your analysis (starting from the problems of stepwise selection and the interpretation of significanse and non-significance) and things to consider (e.g. is the error model appropriate? what is the purpose of the model?). If, for instance, prediction is a purpose, then significances of coefficients are not relevant (huh? how that?), and instead you should evaluate the predictive power on data that has not been used to find and fit the model. This is similar for forcasts, but this requires a different strategy in dividing the data into training- and test-sets. I don't think the models were constructed to learn something about the underlying processes, as this is entirely incompatible with stepwise selection.
Right now it seems that you just throw some algorithms onto the data, and it remains unclear what the results can tell you (and, more importantly, what they miss to tell you!).
Hi
Please refer to chapter 4, pages 89-125 of the book,
Landau S. and Everitt B. S. (2004) A Handbook of Statistical Analyses using SPSS, Chapman & Hall/CRC Press LLC.
Regards,
Zuhair
Hello,
Kindly spare some time to read through the following:
http://www.biostathandbook.com/multipleregression.html
The same is contained in McDonald, J.H. 2014. Handbook of Biological Statistics (3rd ed.). Sparky House Publishing, Baltimore, Maryland.
Kind regards.
Hello
You can see the attached documents, which contains good examples.
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