The accompanying file contains 1,000 observations with the binary target variable y along with the predictor variables x₁, x₂, and x₃. 

a. Perform KNN analysis on the data set. What is the optimal value of k? 

b. What is the misclassification rate for the optimal k? 

c. Report the accuracy, specificity, sensitivity, and precision rates and the AUC value for the test data set (for Analytic Solver) or validation data set (for R). 

d. Comment on the performance of the KNN classification model.