# Compute measures of central tendency (mean and median), measures of variation (the quartiles, IQR, range, variance and standard deviation).

Question
TASK 1: Use week 1 methods of descriptive statistics to generate graphic and numeric measures of descriptive statistics for MO returns and for S&P returns. Compute measures of central tendency (mean and median), measures of variation (the quartiles, IQR, range, variance and standard deviation). Generate graphic displays including histograms and five-number summary, as well as a scatterplot (week 7) to visualize a potential linear relationship between the response (return on MO) and the market (return on S&P). Comment on the shape of the distribution for MO and for S&P.
TASK 2: Using week 4 and week 5 inference techniques generate confidence intervals for both MO and S&P variables and perform hypothesis testing at the 95% confidence level to determine if the returns are statistically different from 0 (zero) for the covered period. Use the Student’s t distribution as we do not know the true population standard deviation. Compute a 95% confidence interval for the difference in returns between the two equities. Assume MO – S&P for the confidence interval. Perform a hypothesis test for MO – S&P to determine the p-value (observed level of significance) and compare it to the desired level of significance (alpha) of 0.05 at the 95% confidence level. Compare the conclusions based on the confidence interval to that of the hypothesis test. (Hint: is 0 inside the confidence interval or not?)
TASK 3: Use week 7 linear regression methods to compute the correlation between MO and S&P and a linear regression model for the return of MO in terms of the return of the S&P 500. Using these model parameters compute model predicted response for each value of the predictor variable. Perform descriptive statistics on model predicted response and compare the mean of the model predicted response to the mean of the original response variable. Comment on the similarities and differences between observed response and model predicted response. Compute the error as the difference between observed value – model predicted value for each of the 83 observations. Generate graphic and numeric descriptive statistics for the error and comment on your observations. Be sure to include a histogram of the error and compare it to a normal distribution. Comment on your observations regarding error.
TASK 4: Write a report covering your analysis. Use software output as supporting evidence not as the report. Comment on the relationship between the two returns and whether or not an investor could use the market return to predict the return of MO.