I am reposting this since there was some confusion on the data (I pasted the data source in the comments, but I that is too hard to work with). I have posted the data file here:

http://thetruthindata.com/stock.dat

Here is the question, I'd like help on all portions of the problem. I'm struggling to apply this in R, but also I need some help with the explanations as well. Thank you so much!

2. The weekly rates of return for five stocks for n = 103 weeks are recorded, the first few weeks are given below. The full data set can be found in the file stock . dat on RamCT. The columns correspond to JP Morgan, Citi, and Wells Fargo (all banks), and Shell and ExxonMobil (oil companies). Perform a principal components analysis using the correlation matrix. JPMorgan Citi WFargo Shell ExMobil 0.0130 -0.0078 -0.0032 -0.0448 0.0052 0.0085 0.0167 -0.0062 0.0120 0.0135 -0.0179 -0.0086 0.0100 0.0000 -0.0061 . . . Denote the random vector which corresponds to the stock returns as X = (X1, X2, . .., X5), and the vector of principal components as Y = (Y1, Y2, ..., Y5). (a) Provide an estimate of the variance of Y2. (b) The first observation (after standardization) is x1 = (0.58, -0.41, -0.32, -1.82, 0.04) T. Obtain the first principal component corresponding to this observation. (c) Choose an appropriate number of principal components to retain and justify your answer. (d) Provide as best you can an interpretation of the first two principal components. To do this, you will need to look at and interpret the first two loadings (eigenvectors). (e) Produce a plot of the first two principal components of the data. Label the points by the week of occurrence. Week 63 should be a bit of an outlier. Describe in terms of the returns on these stocks, what happened in week 63