6. Bid-Ask spread versus Market Capitalization The bidAsk . csv le on the course website uses data from the paper Securities Market E'iciency. 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 between the price at which a buyer wants to buy and the price at which a seller wants to sell) on a single day in January of 2001. (a) Make a scatter plot of the bid-ask spread and market cap. (b) What is the correlation between bid-ask spread and market cap? (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 transformed variables. (d) Find the best linear predictor of the log spread, using the log-market cap as a predictor. Plot this line on the scatterplot. Does it appear to be a decent predictor? (e) Create two new data columns by segmenting log market capitalization and log bid-ask spread into four disjoint bins, each with 25% of the total observations. This discretizes the continuous observations. (f) The two new discretized data vectors each have levels 1 through 4. Compute the distri- bution of market cap level (1 through 4) given the spread level (1 through 4). Based on these tables, are these two random variables independent? How did we already know this from answering earlier questions