Consider the following four (x, y) data sets: the first three have the same x values, so these values are listed only once (from "Graphs in Statistical Analysis," American Statistician [1973]: 17- 21). 

For each of these data sets, the values of the summary quantities

are identical, so all quantities computed from these will be identical for the four sets: the estimated regression line, SSResid, s_e, r², and so on. The summary quantities provide no way of distinguishing among the four data sets. Based on a scatterplot for each set, comment on the appropriateness or inappropriateness of fitting the simple linear regression model in each case.

x, y, (x-x)-, and (x-x)(y-y