Problem 2: The dataset Education - Post 12th Standard.csv is a...

Problem 2:

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

2.1) Perform Exploratory Data Analysis [both univariate and multivariate analysis to be performed]. The inferences drawn from this should be properly documented.

2.2) Scale the variables and write the inference for using the type of scaling function for this case study. 

2.3) Comment on the comparison between covariance and the correlation matrix.

2.4) Check the dataset for outliers before and after scaling. Draw your inferences from this exercise.

2.5) Build the covariance matrix, eigenvalues, and eigenvector.

2.6) Write the explicit form of the first PC (in terms of Eigen Vectors).

2.7) Discuss 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?

Perform PCA and export the data of the Principal Component scores into a data frame.

2.8) Mention the business implication of using the Principal Component Analysis for this case study. [Hint: Write Interpretations of the Principal Components Obtained]