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We are tasked to build a linear model to predict the current of the river based on river width, river depth, distance to the ocean and bank height in order to understand the variation in stream velocity (current). It also says to verify if there are any interaction effects.

As a beginner, what I was just thinking of doing is to make an additive/main effect model to see which of the four variables are significant: (current ~ width+depth+oceandistance+bankheight)

And then eventually do an interaction effect model to see if there are any significant interactions. (current ~ width*depth*oceandistance*bankheight)

I haven't tried anything but I'm not sure if this is the best way to do it. I've heard about stepwise reduction as well but I'm not quite sure how and when to use it.

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  • $\begingroup$ Please consider marking one of the answers as the accepted answer. $\endgroup$ Nov 10, 2020 at 18:34

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Stepwise is a bit unnecessary. Your predictor space is small enough (p=4) that you could do best subsets regression. Also, when exploring interaction effects check out lower order interaction terms. High order interactions like the one you listed arent often explored, unless there is a very very strong expert recommendation. For the purposes of your report I would assume first (maybe second) order interactions would suffice.

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  • $\begingroup$ I tried doing the subsets regression and it ended up that the 4-variable model has the highest adjusted R2 but the 2-variable model has the lowest BIC. $\endgroup$
    – Alexa
    Oct 5, 2020 at 10:22
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There is likely to be nonlinearity involved here.

I would approach this by trying to find some theoretical material that builds a mathematical model with the variables, and go from there.

You could also consider a GAM model.

In general stepwise procedures are not a good idea, especially where you have nonlinear and/or interaction terms.

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