Internet addiction has been found to be a widespread problem among university students. A small liberal arts college in Colorado conducted a survey of Internet addiction among its students using the Internet Addiction Test (IAT) developed by Dr. Kimberly Young. The IAT contains 20 questions that measure various aspects of Internet addiction. Individuals who score high on the IAT are more likely to have problematic Internet use. Also included in the data are the sex of the students (Sex, 1 for female and 0 for male) and whether or not they study at the graduate level (1 for Graduate and 0 for Undergraduate). A portion of the data set is shown in the accompanying table. 

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

b. How many principal components are computed? 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?

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Record IAT1 1 2 2 2 ⠀ # 350 1 IAT2 2 3 ⠀ 2 *** Graduate 1 0 ⠀ 0