# Explanation for unstable lasso regression coefficients?

I have run a lasso regression on a dataset of 100 observations and 80 variables (using 10-fold cross-validation to find the minimum lambda subsequently used in the final model). The lasso regression found approximately 40 of the variables to have non-zero coefficients.

I wanted to check my model and therefore divided those 100 observations into two sets (70/30 - the idea being that I would have a train and test set) and ran a lasso regression on the 70. All coefficients calculated were 0 (except for the intercept) - a dramatically different result than in the first model using all 100 variables.

Confused, I ran another lasso regression on just the 30 observations and found 3 variables to have non-zero coefficients.

I assume that my drastically different results stem from the fact that the data I have does not do a good job of explaining the dependent variable, but perhaps there is a better explanation?

In case this is helpful - I am interested in using lasso regression for prediction.

• Something sounds amiss. Did you randomly divide your data into the two groups of 70 and 30 observations? If so, I would expect the results to be somewhat similar to the results you got on the full 100 observations. Are you confident that there is not an error in the way you carried out the lasso or selected the lambda? – Jean V. Adams Aug 21 '13 at 12:32
• As soon as you have many fewer observations than coefficients your model is grossly undetermined: there is no reasonable expectation that the fits for the two groups would have much in common with each other or with the model on all observations. – whuber Aug 17 '17 at 19:23