Difference between glmnet() and cv.glmnet() in R?

glmnet() is a R package which can be used to fit Regression models,lasso model and others. Alpha argument determines what type of model is fit. When alpha=0, Ridge Model is fit and if alpha=1, a lasso model is fit.

cv.glmnet() performs cross-validation, by default 10-fold which can be adjusted using nfolds. A 10-fold CV will randomly divide your observations into 10 non-overlapping groups/folds of approx equal size. The first fold will be used for validation set and the model is fit on 9 folds. Bias Variance advantages is usually the motivation behind using such model validation methods. In the case of lasso and ridge models, CV helps choose the value of the tuning parameter lambda.

In your example, you can do plot(reg) OR reg$lambda.min to see the value of lambda which results in the smallest CV error. You can then derive the Test MSE for that value of lambda. By default, glmnet() will perform Ridge or Lasso regression for an automatically selected range of lambda which may not give the lowest test MSE. Hope this helps!

Hope this helps!

Between reg$lambda.min and reg$lambda.1se ; the lambda.min obviously will give you the lowest MSE, however, depending on how flexible you can be with the error, you may want to choose reg$lambda.1se, as this value would further shrink the number of predictors. You may also choose the mean of reg$lambda.min and reg$lambda.1se as your lambda value.