ridge regression可以用来处理下面两类问题：一是数据点少于变量个数；二是变量间存在共线性。
当变量间存在共线性的时候，最小二乘回归得到的系数不稳定，方差很大。这是因为系数矩阵X与它的转置矩阵相乘得到的矩阵不能求得其逆矩阵，而ridge regression通过引入参数lambda，使得该问题得到解决。在R语言中，MASS包中的函数lm.ridge()可以很方便的完成。它的输入矩阵X始终为n x p 维，不管是否包含常数项。
Usage
lm.ridge(formula, data, subset, na.action, lambda = 0, model = FALSE,
x = FALSE, y = FALSE, contrasts = NULL, ...)
> install.packages("MASS")
> library('MASS')
> longley
> names(longley)[1] <- "y"
> lm.ridge(y ~ ., longley)
GNP Unemployed Armed.Forces Population Year Employed
2946.85636017 0.26352725 0.03648291 0.01116105 -1.73702984 -1.41879853 0.23128785
> plot(lm.ridge(y ~ ., longley, lambda = seq(0,0.1,0.001)))
> select(lm.ridge(y ~ ., longley, lambda = seq(0,0.1,0.0001)))
modified HKB estimator is 0.006836982
modified L-W estimator is 0.05267247
smallest value of GCV at 0.0057