The United Nations conducts annual studies that measure the level of happiness among its member countries. 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.

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a$-1.$ Conduct principal component analysis on all the variables except the Country variable. Should you standardize the data?

multiple choice

Yes

No

a$-2.$ What percent of the total variability is accounted for by the first principal component?

Note: Round your final answer to $2$ decimal places.

b$.$ How many principal components must be retained in order to account for at least $80\%$ of the total variance in the data?

c$-1.$ Display the weights used to compute the first principal component scores.

Note: Round your final answers to $4$ decimal places.

c$-2.$ Which original variable is given the highest weight to compute the second principal component?

d$.$ What is the first principal component score for the first record $($Albania$)?$

Note: Round your final answer to $4$ decimal places.