Overfitting with linear regression

We’ll reproduce the example given on page 11 of Statistical Learning with Sparsity: the Lasso and Generalizations by Hastie, Tibshirani, and Wainwright. (Code by Seth Flaxman).

data = read.csv("crime.txt",sep="\t")
names(data) = c("overall","violent","funding","hs","not-hs","college","college4")
library(glmnet)

## Loading required package: Matrix

## 
## Attaching package: 'Matrix'

## The following objects are masked from 'package:base':
## 
##     crossprod, tcrossprod

## Loading required package: foreach

## Loaded glmnet 2.0-3

library(plotmo) 

## Loading required package: plotrix

## Loading required package: TeachingDemos

data$overall = log10(data$overall)
par(mfrow=c(1,2))
fit.lasso = glmnet(data.matrix(data[,3:7]),data$overall)
plot.glmnet(fit.lasso,xvar="lambda")
fit.l2 = glmnet(data.matrix(data[,3:7]),data$overall,alpha=0)
plot.glmnet(fit.l2,xvar="lambda")

fit.lasso = cv.glmnet(data.matrix(data[,3:7]),data$overall)
plot(fit.lasso)
fit.l2 = cv.glmnet(data.matrix(data[,3:7]),data$overall,alpha=0)
plot(fit.l2)