Perform principal component analysis on the accompanying data set.

Use the data with the Covariance method and choose Smallest number components explaining at least: $75\%$ of variance.

a$-1.$ How many principal components were created?

a$-2.$ What percent of total variance is accounted for by the calculated principal components?

Note: Round intermediate calculations to at least $4$ decimal places and your final answer to $4$ decimal places.

a$-3.$What are the weights for computing the first principal component scores?

Note: Round intermediate calculations to at least $4$ decimal places and your final answers to $4$ decimal places. Negative values should be indicated by a minus sign.

Use the data with the correlation matrix to perform PCA. Keep all the other options the same as in part a$.$

b$-1.$ How many principal components were created?

b$-2.$ What percent of total variance is accounted for by the calculated principal components?

Note: Round intermediate calculations to at least $4$ decimal places and your final answer to $4$ decimal places.

b$-3.$What are the weights for computing the first principal component scores?

Note: Round intermediate calculations to at least $4$ decimal places and your final answers to $4$ decimal places. Negative values should be indicated by a minus sign.