Past exam of the mathematics course of the University of Cambridge / 2015 / iii / Paper 33 / 4 / d / Solution

At fraction $0.8$, the Lasso regularization path lies between the vertical lines marked steps 4 and 5. In that interval the first five predictors have nonzero slopes: $X_1,X_2,X_4,X_5$ are positive and $X_3$ is negative. The sixth predictor remains at zero until the later part of the path, beyond this fraction. Therefore the chosen Lasso model includesThe regression intercept is retained. In particular the negative $X_3$ trace has already left zero at fraction $0.8$; a small slope is not the same as a zero slope. The selected fraction came from ten-fold K-fold cross-validation, and is not a numerical value of the ridge penalty in the preceding parts.