Anscombe (1973) created four data sets that had interesting properties. Let's use tools from this chapter to describe and understand these data sets. The data is in a Stata data file called AnscombesQuartet.dta. There are four possible independent variables \((\mathrm{X} 1-\mathrm{X} 4)\) and four possible dependent variables (Y1-Y4). Create a replication file that reads in the data and implements the analysis necessary to answer the following questions. Include comment lines that explain the code.

(a) Briefly note the mean and variance for each of the four \(\mathrm{X}\) variables. Briefly note the mean and variance for each of the four \(\mathrm{Y}\) variables. Based on these, would you characterize the four sets of variables as similar or different?

(b) Create four scatterplots: one with \(\mathrm{X} 1\) and \(\mathrm{Y} 1\), one with \(\mathrm{X} 2\) and

\(\mathrm{Y} 2\), one with \(\mathrm{X} 3\) and \(\mathrm{Y} 3\), and one with \(\mathrm{X} 4\) and \(\mathrm{Y} 4\).

(c) Briefly explain any differences and similarities across the four scatterplots.