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I've fitted a linear model using:

m2 <- lm(GPP ~ rainfall + summer.temp + parcel.size + soil.nutrients, data=gpp)

As seen from the partial relationship plots below, the linear model for parcel.size and summer.temp is not entirely appropriate and does not capture the pattern in the data very well.

enter image description here

enter image description here

I want to know how I can capture the these non-linear relationships (i.e. parcel.size and summer.temp) better (while still using a linear model [lm] if possible). I've tried polynomial regression for these explanatory variables as well as log transforming the response (GPP). Both methods does not work. Removing outliers / influential points from the data is not allowed. Any advice would be appreciated!

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  • $\begingroup$ I suggest visually inspecting scatterplots of the dependent variable versus each of the independent variables to determine if any obvious data transform such as log or exponent might help in the regression. $\endgroup$ – James Phillips Mar 23 at 16:27
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I am not sure if these relationships are non-linear.

Generalized additive models (GAM) are a flexible semi parametric tool which have similar assumptions of a lm.

Take a look on mgcv package. GAM are at least useful to explore your data.

Best

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