The variance of the covariates influences the amount of shrinkage of the regression estimator induced by ridge regularization. Some deal with this through rescaling of the covariates to have a common unit variance. This is discussed at the end of Section Role of the variance of the covariates . Investigate this numerically using the data of the microRNA-mRNA illustration discussed in Section Illustration .

• Load the data by running the first R-script of Section Illustration .
• Fit the linear regression model by means of the ridge regression estimator with [math]\lambda=1[/math] using both the scaled and unscaled covariates. Compare the order of the coefficients between the both estimates as well as their corresponding linear predictors. Does the top 50 largest (in an absolute size) coefficients differ much between the two estimates?
• Repeat part b), now with the penalty parameter chosen by means of LOOCV.