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.

Data Dictionary:

1)      Names: Names of various university and colleges
2)      Apps: Number of applications received
3)      Accept: Number of applications accepted
4)      Enroll: Number of new students enrolled
5)      Top10perc: Percentage of new students from top 10% of Higher Secondary class
6)      Top25perc: Percentage of new students from top 25% of Higher Secondary class
7)      F.Undergrad: Number of full-time undergraduate students
8)      P.Undergrad: Number of part-time undergraduate students
9)      Outstate: Number of students for whom the particular college or university is Out-of-state tuition
10)   Room.Board: Cost of Room and board
11)   Books: Estimated book costs for a student
12)   Personal: Estimated personal spending for a student
13)   PhD: Percentage of faculties with Ph.D.’s
14)   Terminal: Percentage of faculties with terminal degree
15)   S.F.Ratio: Student/faculty ratio
16)   perc.alumni: Percentage of alumni who donate
17)   Expend: The Instructional expenditure per student
18)   Grad.Rate: Graduation rate

Names	Apps	Accept	Enroll	Top10perc	Top25perc	F.Undergrad	P.Undergrad	Outstate	Room.Board	Books	Personal	PhD	Terminal	S.F.Ratio	perc.alumni	Expend	Grad.Rate
Abilene Christian University	1660	1232	721	23	52	2885	537	7440	3300	450	2200	70	78	18.1	12	7041	60
Adelphi University	2186	1924	512	16	29	2683	1227	12280	6450	750	1500	29	30	12.2	16	10527	56
Adrian College	1428	1097	336	22	50	1036	99	11250	3750	400	1165	53	66	12.9	30	8735	54
Agnes Scott College	417	349	137	60	89	510	63	12960	5450	450	875	92	97	7.7	37	19016	59
Alaska Pacific University	193	146	55	16	44	249	869	7560	4120	800	1500	76	72	11.9	2	10922	15
Albertson College	587	479	158	38	62	678	41	13500	3335	500	675	67	73	9.4	11	9727	55
Albertus Magnus College	353	340	103	17	45	416	230	13290	5720	500	1500	90	93	11.5	26	8861	63
Albion College	1899	1720	489	37	68	1594	32	13868	4826	450	850	89	100	13.7	37	11487	73