Since 2014, the United Nations has conducted annual studies that measure the level of happiness among its member countries. Experts in social science and psychology are commissioned to collect relevant data and define measurements related to happiness. Happiness measurements are based on survey questions such as how people feel about their life (i.e., life ladder), levels of positive and negative emotion, freedom to make choices (Life choices), and aggregate indicators such as social support, life expectancy, and relative household income. These data are converted into numerical scores for each member country. The accompanying table shows a portion of the United Nation’s happiness data.

a. Conduct principal component analysis on all the variables except the Country 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. Display the weights used to compute the first principal component scores. 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 (Albania)?

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Country Life Ladder Albania 4.5111 Argentina 6.4272 E ⠀ Zimbabwe 3.7354 Social support 0.6384 0.8828 0.7684 ⠀ Household income 0.4165 0.3321 0.5967