Question Five: [10 marks]

Students in a statistical experiment have been classified into two groups based on the similarity of their letter grades in two subjects: Math and English as follows:

Group A	Math	English	Group B	Math	English
student Id			student Id
s01	A	C	s03	A	B
s02	C	A	s04	C	B

a. Find the Euclidean distance between a new student with id s20 and scores B in Math and C in English, and each of the 4 students above. Letter grades translate to points as follows: A =4; B = 3; C = 2. [2 marks]

b. To which student(s) is s20 most similar [1 mark]

c. In which group would a K nearest neighbors (KNN) classification algorithm with K = 3 and which uses simple majority voting classify s20? And why? [2 marks]

d. In which group would a K nearest neighbors (KNN) classification algorithm with K = 3 and which uses weighted voting classify s20? And why? [2 marks]

e. Suppose we applied the KNN algorithm to each member of a larger training set of stu-dents in the two groups (s01-s18) and we obtained the results shown below. Based on these results, which value of k would you choose? And why?: [3 marks]

		Correctly classified?
student Id	Group	k=3	k=5	k=7
s01	A	Y	Y	Y
s02	A	Y	Y	Y
s03	A	Y	Y	Y
s04	A	Y	Y	Y
s05	A	N	N	N
s06	A	N	N	N
s07	A	Y	Y	Y
s08	A	Y	Y	Y
s09	A	Y	Y	Y
s10	A	Y	Y	Y
s11	B	N	Y	N
s12	B	Y	Y	Y
s13	B	Y	Y	Y
s14	B	N	Y	Y
s15	B	Y	Y	Y
s16	B	Y	Y	Y
s17	B	Y	Y	Y
s18	B	Y	N	N