Investors usually consider a variety of information to make investment decisions. The accompanying table displays a sample of large publicly traded corporations and their financial information. Relevant information includes stock price (Price), dividend as a percentage of share price (Dividend), price to earnings ratio (PE), earnings per share (EPS), book value, lowest and highest share prices within the past 52 weeks (52 wk low and 52 wk high), market value of the company’s shares (Market cap), and earnings before interest, taxes, depreciation, and amortization (EBITDA in $billions).

a. Conduct principal component analysis on all the variables except the Name variable. Should you standardize the data? Explain. 

b. What percent of the total variability is accounted for by the first principal component? How many principal components must be retained in order to account for at least 80% of the total variance in the data? 

c. Which original variable is given the highest weight to compute the first principal component? Which original variable is given the highest weight to compute the second principal component? 

d. What is the principal component 1 score for the first record (3M)?

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Name 3M Abbott Lab B Zoetis Price 189.09 45.00 ⠀ 53.07 Dividend 2.48 2.34 ⠀ 0.79 ⠀ EBITDA 8.70 4.59 1.70