environment. The dataset consists of 599 observations, each corresponding to a different wheat line. Following the analysis done in [@GYp2010], we use 1279 predictors which indicate the presence or absence of molecular markers. The grain yield response is available in 4 distinct environments. We normalize the data so that the predictors are centered and scaled, and the response is centered. We then split the available observations into equally sized training and test sets. Finally, we apply cross validation to determine the model parameters.\
The test MSE is defined as $\sum_i(y_i-\hat{y}_i)^2/n$ for $i$ in the test set. We compare the error rates of the lasso, naive elastic net, elastic net and the component lasso. We fix the range of the number of components for the component lasso to be between 1 and 50. Table \[table:real\] contains the test MSE achieved by the different methods to predict grain yield in 4 environments.\

  **Method**          **Test MSE**   **Parameters**                                  **Variables Selected**
  ------------------- -------------- ----------------------------------------------- ------------------------
  **Environment 1**                                                                  
  Lasso               0.8547         $\lambda=5.1e^{-2}$                             45  
  Naive Elastic Net   0.9656         $\alpha=0.05$, $\lambda=2.43e^{-4}$             1195
  Elastic Net         0.9122         $\alpha=0.05$, $\lambda=9.58e^{-4}$             1151
  Component Lasso     0.7552         $\alpha=0.05$, $\lambda=1.8e^{-4}$, $noc=29$    548
  **Environment 2**                                                                  
  Lasso               0.8875         $\lambda=6.18e^{-3}$                            38  
  Naive Elastic Net   1.1104         $\alpha=0.05$, $\lambda=2.68e^{-4}$             1191
  Elastic 