Part I: Similarity Measures $(5$ points$)$

What do you mean by similarity metric? List and explain any two. $(03$ points$)$

Find Euclidean distance between two points in $2-$D space $(x-Y$ plane$)$ where $1^{st}$ point

$p_1$ is denoted by $(2,4)$ and $2^{st}$ point $p_2$ is denoted by $(3,1)(1$ point$)$

Find Jaccard similarity between two sets:

Set $A$:$\{2,3,5,7,11,13\}$

Set $B$:$\{1,2,3,5,8,13\}(1$ point$)$

Part II: Classification trees $(7$ points$)$

Dataset description: A simulated data set containing sales of child car seats at $400$ different

stores. It has $400$ observations on the following $07$variables.

Variables with description:

$1.$ High: A factor variable to denote if a store is a high sales store or low$-$sales store. It is

equal to "Yes" if a store sells more than $10,000$ units else $"$No$".$

$2.$ CompPrice: Price charged by a competitor at each location $($in dollars$)$

$3.$ Income: Community income level $($in thousands of dollars$)$

$4.$ Advertising: Local advertising budget for the company at each location $($in thousands of

dollars$)$

$5.$ Price: The price company charges for car seats at each site $($in dollars$)$

$6.$ ShelveLoc: A factor with levels Bad, Good, and Medium indicating the quality of the

shelving location for the car seats at each site

$7.$ Age: Average age of the local population $($in years$)$

swer the following questions:

Out of the total observations in the node within the orange box, what is the proportion

of observations with the target variable label "Yes"? $(02$ points$)$

Calculate the total number of observations in the node inside the box. $(02$ points$)$

What is the entropy of the root node in this dataset? $(03$ points$)$