Principal Component Analysis –
Colleges – Higher Education
This case study is based on a dataset which provides information on Colleges & Universities across the USA, student enrollments, enrollment pattern, expenses, faculty etc. Use data preparation approach and Principal Component Analysis (PCA) to answer the following problem statements.
The objective is to analyze the data, identify unnecessary components, perform PCA.
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Please submit your answers in a report format.
Problem Statements
1.Perform Exploratory Data Analysis [both univariate and correlation table to be performed]. What insight do you draw from the EDA?
2.Is scaling necessary for PCA in this case? Give justification and perform scaling.
3.Check the dataset for outliers before and after scaling. What insight do you derive here?
4.Perform PCA and export the data of the Principal Component scores into a data frame.
5.Write down the explicit form of the first PC (in terms of the eigenvectors. Use values with two places of decimals only).
6.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?
Data Definition:
Names Names of various university and colleges
Apps Number of applications received
Accept Number of applications accepted
Enroll Number of new students enrolled
Top10perc Percentage of new students from top 10% of Higher Secondary class
Top25perc Percentage of new students from top 25% of Higher Secondary class
F.Undergrad Number of full-time undergraduate students
P.Undergrad Number of part-time undergraduate students
Outstate Number of students for whom the particular college or university is Out-of-state tuition
Room.Board Cost of Room and board
Books Estimated book costs for a student
Personal Estimated personal spending for a student
PhD Percentage of faculties with Ph.D.’s
Terminal Percentage of faculties with terminal degree
S.F.Ratio Student/faculty ratio
perc.alumni Percentage of alumni who donate
Expend The Instructional expenditure per student
Grad.Rate Graduation rate
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