case study

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Part 1:

Case Analysis – Wentworth Medical Center

As part of a long-term study of individuals 65 years of age or older, sociologists and physicians at the Wentworth Medical Center in upstate New York investigated the relationship between geographic location and depression. A sample of 60 individuals, all in reasonably good health, was selected; 20 individuals were residents of Florida, 20 were residents of New York, and 20 were residents of North Carolina. Each of the individuals sampled was given a standardized test to measure depression. The data collected follow; higher test scores indicate higher levels of depression. These data are contained in the file Medical1.

A second part of the study considered the relationship between geographic location and depression for individuals 65 years of age or older who had a chronic health condition such as arthritis, hypertension, and/or heart ailment. A sample of 60 individuals with such conditions was identified. Again, 20 were residents of Florida, 20 were residents of New York, and 20 were residents of North Carolina. The levels of depression recorded for this study follow. These data are contained in the file named Medical2.

MANAGERIAL REPORT

  1. Use descriptive statistics to summarize the data from the two studies. What are your preliminary observations about the depression scores?
  2. Use analysis of variance on both data sets. State the hypotheses being tested in each case. What are your conclusions?
  3. Use inferences about individual treatment means where appropriate. What are your conclusions?

Part 2: (not the same assignment)

CASE STUDY – MEASURING STOCK MARKET RISK

One measure of the risk or volatility of an individual stock is the standard deviation of the total return (capital appreciation plus dividends) over several periods of time. Although the standard deviation is easy to compute, it does not take into account the extent to which the price of a given stock varies as a function of a standard market index, such as the S&P 500.

As a result, many financial analysts prefer to use another measure of risk referred to as beta. Betas for individual stocks are determined by simple linear regression. The dependent variable is the total return for the stock and the independent variable is the total return for the stock market. For this case problem we will use the S&P 500 index as the measure of the total return for the stock market, and an estimated regression equation will be developed using monthly data. The beta for the stock is the slope of the estimated regression equation (b1). The data contained in the file named Beta provides the total return (capital appreciation plus dividends) over 36 months for eight widely traded common stocks and the S&P 500.

The value of beta for the stock market will always be 1; thus, stocks that tend to rise and fall with the stock market will also have a beta close to 1. Betas greater than 1 indicate that the stock is more volatile than the market, and betas less than 1 indicate that the stock is less volatile than the market. For instance, if a stock has a beta of 1.4, it is 40% more volatile than the market, and if a stock has a beta of .4, it is 60% less volatile than the market.

Managerial Report

You have been assigned to analyze the risk characteristics of these stocks. Conduct analysis in RStudio. Prepare a report that includes but is not limited to the following items.

  • Compute descriptive statistics for each stock and the S&P 500. Comment on your results. Which stocks are the most volatile?
  • Compute the value of beta for each stock. Which of these stocks would you expect to perform best in an up market? Which would you expect to hold their value best in a down market?
  • Comment on how much of the return for the individual stocks is explained by the market.
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