# Using a zero slope coefficient predictor variable in multiple regression

I ran multiple regression with three predictor variables, which according to the theory I am using, should all predict the dependent variable.

However, one of the variable's partial plot shows what looks like a zero slope. The standardised coefficient is -.032 for this variable.

Below is the partial plot. Does it make sense to include this in the regression model? I was initially not going to include it on the grounds that it violates the assumption of linearity, but then I realised that there is some form of linear relationship, albeit a zero/horizontal slope.

This is m first project I have had to use statistics for, and I have no teaching in it at all, so have had to self-study so excuse any naivety. I would really appreciate your help so if you read this and can help please please do so :)

First off, the assumption of linearity applies only to the parameters $\beta$, $x_i$ can be squared, loged or whatever you would like. You assume only that $y$ can be written as linear combination of $x_i$. Try using something more flexible, and see where that takes you.