Problem

Calculating Distance with Categorical Predictors. This exercise with a tiny dataset illustrates the calculation of Euclidean distance, and the creation of binary dummies. The online education company Statistics.com segments its customers and prospects into three main categories: IT professionals (IT), statisticians (Stat), and other (Other). It also tracks, for each customer, the number of years since first contact (years). Consider the following customers; information about whether they have taken a course or not (the outcome to be predicted) is included:

Customer 1: Stat, 1 year, did not take course

Customer 2: Other, 1.1 year, took course

a. Consider now the following new prospect:

Prospect 1: IT, 1 year

Using the above information on the two customers and one prospect, create one dataset for all three with the categorical predictor variable transformed into 2 binaries, and a similar dataset with the categorical predictor variable transformed into 3 binaries.

b. For each derived dataset, calculate the Euclidean distance between the prospect and each of the other two customers. (Note: while it is typical to normalize data for kNN, this is not an iron-clad rule and you may proceed here without normalization.)

c. Using k-NN with k = 1, classify the prospect as taking or not taking a course using each of the two derived datasets. Does it make a difference whether you use 2 or 3 dummies?