[julia-users] Precision problem in matrix inversion (for ridge regression)?

[Francisco C Pereira]

Hi, 

I deeply apologize in advance if this is a repeated question...  the 
question is relatively simple. How can this happen? I was estimating a 
basic ridge regression model but ran into strange results:

lambda=0
beta_hat=inv(Z'Z+lambda*eye(size(Z,2)))*(Z'*ys_dataset)
beta_hat2=inv(Z'*Z)*(Z'*ys_dataset)
beta_hat-beta_hat2

Output (it should be a vector with zeroes):
21-element Array{Float64,1}:

  -245.183      
  -436.175      
  2633.22       
    73.0047     
 -3345.18       
  1712.78       
  -354.545      
   187.102      
    49.8899     
   -49.4564     
    -2.91745    
    -0.253636   
    -0.186349   
     0.457511   
    -0.031112   
     0.0789713  
    -0.00130604 
    -0.00448352 
    -0.00324767 
     0.000248121
     0.000152718




Just for reference, here are the other variables:


xs_dataset=[-0.8,-0.6,-0.4,-0.2,0.0,0.2,0.4,0.6,0.8,1.0,1.2,1.4,1.6,1.8,2.0,2.2,2.4,2.6,2.8,3.0,3.2]

ys_dataset=[-194.74997124179467,-218.7737153673673,-262.705773686837,-151.42110150479215,-147.91115080458417,-208.4047152970189,-128.36970674967745,-114.53430386917461,-158.27662488829077,-142.21198729962245,-82.80260143610138,-27.621822591723756,-25.154050675997198,-6.99434298775955,-0.06912672996766567,-5.349114073043877,32.43503138931636,-37.228578783587075,-37.22806830522013,-113.28447052959032,-71.0209779039439]

Z=Array{Float32}([z^i for z in xs_dataset, i in 0:20])



I've been arguing that Julia is the best in the world, I need help to keep 
preaching! ;-)


Thanks!

   Francisco