For datasets of higher dimensions, how do I decide if a Linear model is sufficient to fit the data or if I have to use non linear models like regression trees to fit the data ?
NOTE:I did try both linear and non linear models to fit the data and observed that the mean squared error is substantively reduced by replacing linear regression model with a non-linear regression model (like M5 Regression Trees). But I do not understand how to visualize linear relationships in higher dimensions. So if I fit my 5 dimensional dataset using a linear model, what would be a threshold that would suggest that there is a necessity to adopt non linear models like Regression Trees ?
I am beginning to learn statistics only recently, so apologize if this question is too elementary in nature.