Problem 2: The dataset Education - Post 12th Standard

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Problem 2:

The dataset Education - Post 12th Standard.csv contains information on various colleges. You are expected to do a Principal Component Analysis for this case study according to the instructions given. The data dictionary of the 'Education - Post 12th Standard.csv' can be found in the following file: Data Dictionary.xlsx.

• Perform Exploratory Data Analysis [both univariate and multivariate analysis to be performed]. What insight do you draw from the EDA?
• Is scaling necessary for PCA in this case? Give justification and perform scaling.
• Comment on the comparison between the covariance and the correlation matrices from this data.
• Check the dataset for outliers before and after scaling. What insight do you derive here?
• Perform PCA and export the data of the Principal Component scores into a data frame.
• Extract the eigenvalues and eigenvectors.[print both]
• Write down the explicit form of the first PC (in terms of the eigenvectors. Use values with two places of decimals only).
• Consider the cumulative values of the eigenvalues. How does it help you to decide on the optimum number of principal components? What do the eigenvectors indicate?
• Explain the business implication of using the Principal Component Analysis for this case study. How may PCs help in the further analysis? [Hint: Write Interpretations of the Principal Components Obtained]