1. Read the following data into R and finish the following question: http://www.ams.sunysb.edu/~xing/statfinbook/_BookData/Chap03/m_logret_10stocks.txt (1) Compute the mean, variance-covariance, and correlation matrices of the data. (2) Run regression with intercept for AAPL on all other variables. Do you find any significance that AAPL return can be explained by other stock returns? (3) Based on your conclusion in (2), find regression models in which fewer explanation variables should be used than that in (2), i.e., select a subset of variables so that a better fit can be achieved. 2. For each pair of two stock returns in Problem 1, perform a t-test for the difference of the means of stock return. Do you find any stocks whose returns are (statistically) same (Your conclusion should be based on rigorous statistical hypothesis testing)? 3. Consider the data in Problem 1. Classify the 10 stocks into several groups based on their industry sector information. We also consider some range of stock returns, such as r<-0.1, -0.1<=r<0.1, and r>0.1. Design a chi-square test to see if the group and the return range effects are independent. (Hint: You may decide yourself the number of groups based on the industry section information. The industry section information can be found from Yahoo Finance or simply google it.) 4. Write a SAS DATA step to read the following data. The data is separated by the commas. The list of variables is ID, GENDER, SCORE, DOB (mmddyyyy), and AMOUNT. (Note that the variable AMOUNT is a four digit integer with a comma format. e.g:1,000=1000). Only input the observations on condition that the AMOUNT is greater than 1000. (hint: column input is not proper.) 001,M,99,10/11/1981,1,000 002,F,100,03/23/1982,9,999 003,M,89,04/11/1979,1,200 004,M,77,02/23/1985,5,300 5. The following character strings are the observations. Every string contains three types of information: STATE (NY or NJ), SCORE (the number between the letters) and GROUP (A, B or missing). Write a SAS DATA step to create a data set named QUES2 containing four variables: STATE, SCORE, GROUP and NEWSCORE, in which NEWSCORE=SCORE*100 if GROUP='A'; NEWSCORE is missing if GROUP is missing and NEWSCORE=SCORE if GROUP='B'. NY113A NY15B NY87A NY23 NJ10A NJ23B NY34A NJ9A NJ23B 6. 9 subjects were assigned to group A and 9 subjects were assigned to group B. The two groups using different training methods to improve the subjects' read speed. The results are as following: A: 500 B: 355 230 388 505 445 404 469 390 560 200 502 750 515 700 430 490 480 Read the data above to the SAS system. Perform t-test and nonparametric test to compare the two groups A and B. Check if it is proper to use t-test. And compare the results of t-test and nonparametric test