Assignment Task:

Analyzing Data and Comparing Performance

Questions:

1. A consumer advocacy group was interested in comparing the prices at two major hardware store companies, both of which give a price guarantee for having the lowest prices. Members of the advocacy group sampled the websites of the two hardware stores and recorded 116 identical items that were sold by both.

   a. Obtain summary statistics of prices at StoreA and StoreB, and comment on these.

   b. Produce histograms of prices at Store A and StoreB, and comment.

   c. Why does it make sense to log the values of prices at Store A and StoreB before proceeding with the analysis? Note: Use logged values of prices from now on.

   d. Which of the two forms of analysis makes the most sense: Comparing means from two independent samples or a paired data analysis? Justify your answer.

   e. Produce an appropriate plot of the response variable used for your chosen form of analysis and comment on it.

   f. Perform an appropriate analysis, check assumptions, and make necessary inference output.

   g. Write Methods and Assumption Checks (you do not need to give the model equation).

   h. Write an Executive Summary.

2. It was of interest to compare and quantify the performance of investment portfolios in two different financial sectors. Thirty-eight portfolios, each from a randomly selected finance company, were utilized. The companies were classified by which financial sector they were in, which we have called sectors A and B for this assignment. The portfolios ranged from one to twelve years in age. The variable of interest is the value that an initial investment $1000 would now be worth.

   a. Comment on both of the provided scatter plots of the data.

   b. Why does it make sense to fit a linear model to the logged values?

   c. Fit an appropriate linear model and check assumptions. Make necessary inference output.

   d. If you had invested $1000 in financial sector B ten years ago, what would it be worth today? Produce the relevant prediction output for this.

   e. Interpret the prediction interval above and include the interpretation of this in your Executive Summary.

   f. Write appropriate Methods and Assumption Checks.

   g. Write an Executive Summary. (Remember to address ALL of the questions of interest.)

   h. There may be a reason to question whether the values are independent observations. Briefly comment on this.