For the case study and data provided concerning the customer churn data at QWE Inc., this assignment requires you to train a logistic regression classifier to predict the same. To guide you on your quest to find the best model, a few instructions and questions are provided which you are requested to follow and answer:

Build a logistic regression classifier and name it LC$1.$ This model should include all the variables in the dataset for predicting the output variable $($Churn$).$ What is the accuracy of this model after choosing an appropriate threshold? Mention your rationale for choosing the said threshold.

Build a new model LC$2,$ but this time the final model should only contain the variables that are significant to predicting the output variable. Report the accuracy and AUC metrics for this new model. What is your observation?

What can be done to improve the model AUC? Suggest and implement your solution and label your final model as LC$\_$Final. Comment on the final model's performance.