For each task you should:

Summarize your data in verbal, tabular or graphic form. Perform EDA on the data.

Explain what the testing problem is about.

You should clearly state the null hypothesis and what its rejection means.

1. Returns on the Major U.S. Stock Exchanges (New York Stock Exchange (NYSE), American Stock Exchange (AMEX) and NASDAQ) for the period 12/31/1926 through 12/31/2018 are in the file exam2.indexReturns.csv in this Exam's data directory which is on Canvas in Canvas/Files/Data/_Exam 2 Data. NOTE: For your convenience and support, we also provide the long-form dataset that R requires, that filename is exam2.indexReturns.long.csv.

Universe refers to the major U.S. stock exchanges, (New York Stock Exchange (NYSE), American Stock Exchange (AMEX) and NASDAQ). Each of these indexes quote and trade thousands of securities. The return data is the annual percent return in an index (NYSE, AMEX, NASDAQ) for the year end date indicated.

There are four ways to calculate an index returns, these are the "type" factor. Each level corresponds to a different constituent stock weighting scheme in producing the index level, for which the annual returns (in percent) are found.  These levels are

vwretd Market capitalization-weighted return with dividend

vwretx Market capitalization-weighted return without dividend

ewretd Equal-weighted return with dividend

ewretx Equal-weighted return without dividend

The questions we seek to answer include:

• If there a difference in the universe considered?

• Is there a difference between types of market returns, i.e., EW and MW, with and without dividends?

• Are there interactions between the universe and the return type, and what is their meaning?

In addition, please answer the following questions:

a. Obtain the mean, median, and geometric mean (CAGR) annual returns for each universe and return type. Discuss these results.

b. Describe the data: time range, frequency, summary statistics, etc. Note that R's Anova and other functions require long-form data, which has been provided to you.

c. Check all major parametric Anova assumptions. You are familiar with normality and HOV diagnostics; independence can be checked with a runs test. Be sure and order your universe factors to NYSE, AMEX and NASDAQ, otherwise R assumes they are alphabetical, and we want to make comparisons relative to the NYSE.

d. Assuming you reject the omnibus hypothesis (be sure and state it), perform post-hoc testing to determine which regions of the market are significantly different.

e. Using R's {pwr} package or an online power program or GPower (freely available for Win or Mac OS-X; see tutorial provided in the Exam data directory), perform a power analysis for the problem. For this data, what power did we achieve? Determine the sample size required to detect a +- 4% difference in mean returns with a probability (power) of 80%.

dataexport-bg4mcqmu.zip