Question

a. Using the original values, compute the Euclidean distance between the first two observations. (Round intermediate calculations to at least 4 decimal places and your final answer to 2 decimal places.)

Euclidean distance between observations 1 and 2 ___________

b. Using the original values, compute the Manhattan distance between the first two observations. (Round your final answer to 2 decimal places.)

Manhattan distance between observations 1 and 2 ___________

c. Use z-scores to standardize the values, and then compute the Euclidean distance between the first two observations. (Round intermediate calculations to at least 4 decimal places and your final answer to 2 decimal places.)

The z-score standardized euclidean distance between observations 1 and 2 ___________

d. Use the min-max transformation to normalize the values, and then compute the Euclidean distance between the first two observations. (Round intermediate calculations to at least 4 decimal places and your final answer to 2 decimal places.)

The min-max standardized euclidean distance between observations 1 and 2 ___________

The accompanying data file contains 10 observations with two variables, x₁ and x₂.

x1	x2
3.05	3.12
9.28	4.02
7.09	4.1
8.52	2.76
2.27	2.48
5.57	3.21
4.51	1.29
6.9	3.89
4.33	2.75
6.04	3.98

Answer 1

(a) The fomula for the Euclidean distance between two points . Now the first two observations are (3.05,3.12) and (9.28,4.02) respectively.

Thus the Euclidean distance will be

(b)

The fomula for the Manhattan distance between two points . Now the first two observations are (3.05,3.12) and (9.28,4.02) respectively.

Thus the Manhattan distance will be

(c) The Z-score for a sample observation x is defined as

0.5128489	-0.4327802
6.7428489	0.4672198
4.5528489	0.5472198
5.9828489	-0.7927802
-0.2671511	-1.0727802
3.0328489	-0.3427802
1.9728489	-2.2627802
4.3628489	0.3372198
1.7928489	-0.8027802
3.5028489	0.4272198

Then the The z-score standardized euclidean distance between observations 1 and 2 is

(d)The min-max transformation for a sample observation x is given by

The min max normalized values are as follows

2.726177	2.6609253
8.956177	3.5609253
6.766177	3.6409253
8.196177	2.3009253
1.946177	2.0209253
5.246177	2.7509253
4.186177	0.8309253
6.576177	3.4309253
4.006177	2.2909253
5.716177	3.5209253

The min-max standardized euclidean distance between observations 1 and 2 is