onsider the population data provided for the 50 cities. Sort and prepare the data for a multivariate analysis. The purpose of this analysis is to ascertain whether the correlation among the seven population variables can be accounted for in terms of few latent variables or factors. Conduct a principal component analysis to determine how many important components are present in the data. To what extent are the important components able to explain the observed correlations between the variables? Rotate the components (if necessary) in order to make their interpretation more understandable in terms of a specific theory. Which tests have high loadings on each of the rotated components? Try to identify and name the rotated components. Also, ensure to do a summary, correlation matrix and obtain Eigen values, Eigen Vector, and correlation matrix between variables and factors. In addition, calculate: a. Squared cosines of variables using the factors b. Factor scores for the 50 cities c. Contribution of the observations (and Biplots) d. At least two component plots Note: You can use any other software from R, but include R script for the whole process. Remember, the R script is mandatory!!
