I want compare the out of sample prediction from an linear regression model (OLS) and a regression tree. I read that OLS outperforms regression tree if the relationship between the dependent variable and independent variables is strongly linear.
How I can check the linear relationship between dependent and independent variables?
A better approach is to think hard about the model specification and to seldom assume linearity, as it is unusual for variables to be linearly related to each other. With very small sample sizes we must sometimes force a linearity assumption because we can't do much else without penalized maximum likelihood estimation.
Making scatterplots isn't always a good idea as if you are using classical frequentist methods, using observed relationships will distort p-values and confidence intervals and also cause overfitting of the model.
My Regression Modeling Strategies book and course notes and accompanying R package rms go into great detail about this, and shows how to use regression splines to relax linearity assumptions.
Single regression trees are not competitive with regression and they do not properly handle continuous variables.
Your question is not very clear. But still you can check the linearity between the independent and dependent variables by plotting them as scatter plots. Scatter plots will give you a very good idea about the linearity of the variables. You will have to plot multiple scatter plots for each independent variables keeping the dependent variable constant.
