Consider the following scenario where you use the same data
X (the same number of predictors
p, same number of observations
n) to predict a continuous outcome
y, in 2 different regression models (e.g. Linear Regression and Random Forests).
For both models you calculate
R-squared (assume simple correlation between y and y-hat, squared).
RMSE1 < RMSE2 R-squared1 < R-squared2
Could someone explain if this scenario is possible and how it occurs?
A simple simulation in
R could also do.