Linear or non-linear regression model


I have 20 independent variables and 1 dependent. I've used the stepwise method to determined what predictors are more significant compared to other predictors and I ended up with 10 statistically significant predictors.

However, I am not sure how check if a nonlinear multiple regression would suite my analysis better. Should I plot (inspect) the dependencies between each independent variable and my dependent variable to see the shape and form of that dependency and then, based on the plot, I could determine whether the relation between them looks like linear or nonlinear. Is there any other method?

Also, is there any other method to determine what are the most important predictors in the model?

I am using Matlab to do the analysis (just an additional information).



TS Contributor
I would check the residuals first. Is the sum of squares errors significantly smaller for one of the models? Do you see any pattern when plotting the residuals against the fit or against one of the variables? The model behaving better would win.