Problem 3 (PCA. 15 points) 1. For each of the 30 stocks in the Dow Jones Industrial Average. download the closing prices for every trading day from January 1, 2010 to January 1, 2011. You can use http://finance.yahoo.com to find the data. To download the prices for symbol AA, for example, use the url http: / / ichart.fina nce.ya hoo.com / ta ble.csv?s=AA&a=00&b=1&c=2010&d=00&e=1&f=201 1&g=d&ignore=.csv This is the URL generated by Yahoo finance when we try to download their historical prices to a spreadsheet. See this page for the page in which the above link can be found. Please find a way to download the data efficiently. 2. Perform a PCA on the prices and create the biplot (call function princompO and use cor=FALSE). Do you see any structure in the biplot, perhaps in terms of the types of stocks? How about the screeplot - how many important components seem to be in the data? 3. Repeat part 2 with cor=TRUE. This is equivalent to scale each column of the data matrix. 4. Calculate the return for each stock, and repeat part 3 on the return data. In looking at the screeplot, what does this tell you about the 30 stocks in the DJIA? If each stock were fluctuating up and down randomly and independent of all the other stocks. what would you expect the screeplot to look like