Consider the following dataset (there is no outcome/output variable):

Record #	x1	x2
R1	3	5
R2	1	4
R3	2	2
R4	2	3
R5	4	1

To perform clustering we must compute the distance between every pair of points in the dataset. A natural way to present these distances is a matrix, whose elements we denote as d_ij, which is the distance between records Ri and Rj. For this analysis we use Euclidean distance. As a hint to keep you on track and save time, the entries in the first two columns are computed for you.

	R1 (3,5)	R2 (1,4)	R3 (2,2)	R4 (2,3)	R5 (4,1)
R1 (3,5)	0	2.236	d_13	d_14	d_15
R2 (1,4)	2.236	0	d_23	d_24	d_25
R3 (2,2)	3.162	2.236	d_33	d_34	d_35
R4 (2,3)	2.236	1.414	d_43	d_44	d_45
R5 (4,1)	4.123	4.243	d_53	d_54	d_55

To keep the calculations simple, for this analysis we will not normalize the data.

1. Choose the option below that is closest to the exact value of d_35 in the above matrix of Euclidean distances.

4

3

1

5

2

2.Choose the option below that is closest to the exact value of d_43 in the above matrix of Euclidean distances.

1

2

4

5

3

3. Choose the option below that is closest to the exact value of d_54 in the above matrix of Euclidean distances.

4

5

3

2

1