Given the four boxes shown in the associated figure, answer the following questions. In the diagram, numbers indicate the lengths and widths, and you can consider each box to be a vector of two real numbers, length and width. For example, the top left box would be (2,1), while the bottom right box would be (3,3). Restrict your choices of similarity/distance measure to Euclidean distance and correlation. Briefly explain your choice.

(i) Which proximity measure would you use to group the boxes based on their shapes (not size)?

Choice (Euclidean/Correlation):

Explanation:

(ii) Which proximity measure would you use to group the boxes based on their size?

Choice (Euclidean/Correlation):

Explanation:

2 1 1 3 6 3