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).

Data Set 1– 31 2 3 4 4 Variable xyyyxy 10.0 8.04 9.14 7.46 8.0 6.58 8.0 6.95 8.14 6.77 8.0 5.76 13.0 7.58 8.74 12.74 8.0 7.71 9.0 8.81 8.77 7.11 8.0 8.84 Data Set 1– 31 2 3 4 4 Variable xyyyx 11.0 8.33 9.26 7.81 8.0 8.47 14.0 9.96 8.10 8.84 8.0 7.04 6.0 7.24 6.13 6.08 8.0 5.25 4.0 4.26 3.10 5.39 19.0 12.50 10.84 9.13 8.15 8.0 5.56 7.0 4.82 7.26 6.42 8.0 7.91 5.0 5.68 4.74 5.73 8.0 6.89 For each of these data sets, the values of the summary quantities x, y, g 1x 2 x2 2

, and g 1x 2 x2 1 y 2 y2 are identical, so all quantities computed from these will be identical for the four sets: the estimated regression line, SSResid, se, r 2

, 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.