I have a response variable(y) and 20 independent variables (Xs). I want to select several Xs in the linear regression, but I'm not sure how many variables should be selected. To select the best number of variables, I use the sum of the squared residuals (Res) in the 10-fold cross-validation given N selected variables (N=2~20). The process is repeated 1000 times given each N. My idea is that Res should firstly decrease as more variable could explain y better and then it should increase as too many variables should lead to over-fitting. To my surprise, Res decrease continually as N increase(see the Figure). I don't know how to explain it. Is it mean that all 20 variables contribute to y, or over-fitting happened?
P.S.: there are about 600 data points. The Res is calculated as the sum of the square of the difference between observed y and predicted y in each 10-fold cross-validation.