Read the Investopedia primer Understanding Stock Splits, which is available as a pdf at the class web site (stock-split.pdf). The bidAsk.csv le on the course web site uses data taken from the paper Securities Market Efciency, also available on the coursewebsite. For each of 2,464 stocks listed on India's National Stock Exchange, this data records the market capitalization (price times shares outstanding) and the bid-ask spread (the difference betweenthepriceatwhichabuyerwantstobuyandthepriceatwhichasellerwantstosell) on a single day in January of2001.

(a)Make a scatter plot of bid-ask spread and marketcap.

(b)What is the correlation between bid-ask spread and marketcap?

(c)What is the correlation between bid-ask spread and market cap after making log trans- formations of both variables? Can you explain why the answer is different from the previous answer? Make a scatter plot of the transformedvariables.

(d)Findthebestlinearpredictorofthelog-spread,usinglog-marketcapasapredictor.Plot this line on the scatterplot. Does it appear to be a decentpredictor?

(e)Create two new data columns by segmenting log market capitalization and log bid- ask spread each into four disjoint bins, each with 25% of the total observations. Thisdiscretizes the continuousobservations.

(f)Thetwonewdiscretizeddatavectorseachhavelevels1through4.Computethedistri- butionofmarketcaplevel(1through4)giventhespreadlevel(1through4).Basedon these tables, are these two random variables independent? How did we already know this from answering earlierquestions?