0.23 (0.01)
  Rescaled Lasso                              58.44 (1.54)     0.31 (0.01)     0.25 (0.01)
  Lasso-OLS Hybrid                            57.25 (1.64)     0.28 (0.01)     0.24 (0.01)
  Naive Elastic Net                           38.74 (0.93)     0.41 (0)        0.14 (0.01)
  Elastic Net                                 31.75 (0.69)     0.46 (0)        0 (0.02)
  Ridge                                       32.86 (0.74)     0.50 (0)        0 (0)
  Component Lasso                             31.16 (0.73)     0.46 (0)        0 (0.02)
  **Example 4**                                                                
  Lasso                                       46.62 (3.29)     0.60 (0.01)     0.37 (0.01)
  Rescaled Lasso                              28.67 (3.09)     0.29 (0.02)     0.31 (0)
  Lasso-OLS Hybrid                            15.75 (2.02)     0 (0.01)        0.32 (0.02)
  Naive Elastic Net                           44.90 (3.01)     0.47 (0.01)     0.20 (0.01)
  Elastic Net                                 23.79 (2.66)     0.25 (0.03)     0 (0.01)
  Ridge                                       61.74 (3.99)     0.62 (0)        0 (0)
  Component Lasso                             10.74\* (2.34)   0.06 (0.01)     0.04 (0.01)

  : *Median MSE, false positive and false negative rates for the four simulated examples using 7 regression methods. Numbers in parentheses are the standard errors.* []{data-label="table:allsims"}

For every data set, the connected-component split which gave the lowest validation MSE is chosen to compute the test error. Tables 2-6 show the distribution of the number of components that minimize the error in all examples. The number of components (NOC) by itself is not an appropriate measure to verify how the predictors are being grouped. [For example, consider the case where some of the connected 