college.Rdata as follows Problem 3. The data file \" College.RData\" includes a

Question

college.Rdata as follows
Problem 3. The data file " College.RData" includes a number of variables for 777 different universities and colleges in the US. The variables are . Apps : Number of applications received . Accept : Number of applicants accepted Enroll : Number of new students enrolled ·Top Operc : New students from top 10% of high school class . Top25perc : New students from top 25% of high school class . F.Undergrad : Number of full-time undergraduates . P.Undergrad: Number of part-time undergraduates Outstate: Out-of-state tuition . Room.Board : Room and board costs . Books: Estimated book costs . Personal: Estimated personal spending . PhD : Percent of faculty with Ph.D.s . Terminal: Percent of faculty with terminal degree . S.F.Ratio: Student/faculty ratio perc.alumni : Percent of alumni who donate . Expend : Instructional expenditure per student . Grad.Rate: Graduation rate

Explanation / Answer

1.) Please find the first 3 principal components below with variance. I had removed Apps column before applying PCA.

Importance of components:

Comp.1 Comp.2 Comp.3
Standard deviation 2.2897727 1.9720572 1.0815315
Proportion of Variance 0.3276912 0.2430631 0.0731069
Cumulative Proportion 0.3276912 0.5707543 0.6438612

R-Code:

#### Preparing Data fro PCA

pca_data_college <- College[, -1]
ncol(pca_data_college)

###Applying PCA

fit <- princomp(pca_data_college, cor=TRUE)
summary(fit)
loadings(fit)

To get variance proportion, we will get it from summary(fit)

From loadings(fit), we will get full details of each and every component.

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