I need help in solving this : Implement Principal Component Analysis for Assignment Grades in R language

Assume we are given a class of students with grades on five courses and we want to order these students according to test performance. That is, we want to project the data onto one dimension, such that the difference between the data points become most apparent. We can use PCA. The eigenvector with the highest eigenvalue is the direction that has the highest variance, that is, the direction on which the students are most spread out. This works better than taking the average because we take into account correlations and differences in variances. (Rencher 1995)

1.Generate five different test result datasets for 100 students. Assume test results follow a Gaussian distribution.

2. Implement PCA and determine eigenvalues for each test result dataset.

3. Assuming all tests measure all students' performance equally, report the test, which differentiates the performances of the students best. Briefly explain your reasoning.

4. Report proportion of variance for the test you select and compare the proportion of variance values for using 2,3,4 tests (page 124 on course book).

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