http://drunks-and-lampposts.com/2012/01/12/marketing-mix-lab-multicolinearity-and-ridge-regression/

Multicollinearity and Ridge Regression.r

#TV now coincides with winter. Carry over is dec, theta is dim, beta is ad_p,
tv_grps<-rep(0,5*52)
tv_grps[40:45]<-c(390,250,100,80,120,60)
tv_grps[92:97]<-c(390,250,100,80,120,60)
tv_grps[144:149]<-c(390,250,100,80,120,60)
tv_grps[196:201]<-c(390,250,100,80,120,60)
tv_grps[248:253]<-c(390,250,100,80,120,60)

if (adstock_form==2){adstock<-adstock_calc_2(tv_grps, dec, dim)}
else {adstock<-adstock_calc_1(tv_grps, dec, dim)}
TV<-ad_p*adstock

# Accompanying radio campaigns
radio_spend<-rep(0,5*52)
radio_spend[40:44]<-c(100, 100, 80, 80)
radio_spend[92:95]<-c(100, 100, 80, 80)
radio_spend[144:147]<-c(100, 100, 80)
radio_spend[196:200]<-c(100, 100, 80, 80)
radio_spend[248:253]<-c(100, 100, 80, 80, 80)
radio<-radio_p*radio_spend

 > cor(test[,c(2,4:6)])
#                  temp radio_spend        week     adstock
#temp         1.0000000 -0.41545174 -0.15593463 -0.47491671
#radio_spend -0.4154517  1.00000000  0.09096521  0.90415219
#week        -0.1559346  0.09096521  1.00000000  0.08048096
#adstock     -0.4749167  0.90415219  0.08048096  1.00000000

 
coefs<-NA 
 
for (i in 1:10000){

   sim<-create_test_sets(base_p=1000,
                       trend_p=0.8,
                       season_p=4,
                       ad_p=30,
                       dim=100,
                       dec=0.3,
                       adstock_form=1,
                       radio_p=0.1,
                       error_std=5)
  lm_std<-lm(sales~week+temp+adstock+radio_spend, data=sim)
  coefs<-rbind(coefs,coef(lm_std))
  
}

col_means<-colMeans(coefs[-1,])
for_div<-matrix(rep(col_means,10000), nrow=10000, byrow=TRUE)
mean_div<-coefs[-1,]/for_div

m_coefs<-melt(mean_div)
ggplot(data=m_coefs, aes(x=value))+geom_density()+facet_wrap(~X2, scales="free_y") + scale_x_continuous('Scaled as % of Mean') 
 
 
library(MASS)
 
for (i in 1:1000){

   sim<-create_test_sets(base_p=1000,
                       trend_p=0.8,
                       season_p=4,
                       ad_p=30,
                       dim=100,
                       dec=0.3,
                       adstock_form=1,
                       radio_p=0.1,
                       error_std=5)
  lm_rg<-lm.ridge(sales~week+temp+adstock+radio_spend, data=sim, lambda = seq(0,20,0.5))
  if (i==1){coefs_rg<-coef(lm_rg)}
  else {coefs_rg<-rbind(coefs_rg,coef(lm_rg))}
  
}
 
colnames(coefs_rg)[1]<-"intercept"
 
m_coefs_rg<-melt(coefs_rg)
  
names(m_coefs_rg)<-c("lambda", "variable", "value")

ggplot(data=m_coefs_rg, aes(x=value, y=lambda))+geom_density2d()+facet_wrap(~variable, scales="free")