Lambda = 1e-04   Average squared error on test cases = 0.0006847857 
Lambda = 0.001   Average squared error on test cases = 0.00066484 
Lambda = 0.003   Average squared error on test cases = 0.0006370087 
Lambda = 0.01   Average squared error on test cases = 0.0006047621 
Lambda = 0.02   Average squared error on test cases = 0.0006036512 
Lambda = 0.03   Average squared error on test cases = 0.000615405 
Lambda = 0.05   Average squared error on test cases = 0.000651791 
Lambda = 0.1   Average squared error on test cases = 0.0007755724 
Lambda = 0.2   Average squared error on test cases = 0.001093676 

Best lambda value is 0.02