Problem$2$

Pharmaceutical Industry. An equities analyst is studying the pharmaceutical industry and would like your help in exploring and understanding the financial data collected by her firm. Her main objective is to understand the structure of the pharmaceutical industry using some basic financial measures.

Financial data gathered on $21$ firms in the pharmaceutical industry are available in the file Pharmaceuticals.csv$.$ For each firm, the following variables are recorded:

$1.$ Market capitalization $($in billions of dollars$)$

$2.$ Beta

$3.$ Price$/$earnings ratio

$4.$ Return on equity

$5.$ Return on assets

$6.$ Asset turnover

$7.$ Leverage

$8.$ Estimated revenue growth

$9.$ Net profit margin

$10.$ Median recommendation $($across major brokerages$)$

$11.$ Location of the firm$$s headquarters

$12.$ Stock exchange on which the firm is listed

Use Hierarchical cluster analysis to explore and analyze the given dataset as follows:

a$.$ Use only the numerical variables $(1$ to $9)$ to cluster the $21$ firms. Justify the various

Choices made in conducting the cluster analysis, such as weights for different variables,

The specific clustering algorithm$($s$)$ used, the number of clusters formed, and so on$.$

b$.$ Interpret the clusters concerning the numerical variables used in forming the

Clusters.

c$.$ Is there a pattern in the clusters concerning the numerical variables $(10$ to $12)?$

$($Those not used in forming the clusters$)$