75. Consider the following four (x, y) data sets; the rst three have the same x values, so these values are listed only once (Frank Anscombe, Graphs in Statistical Analysis, Amer. Statist., 1973: 17—21):

1–3 1 2 3 4 4 x y y y x y 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 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 12.0 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 four data sets, the values of the summary statistics xi, , yi, , and xiyi are virtually identical, so all quantities computed from these ve will be essentially identical for the four sets the least squares line (y  3  .5x), SSE, s2, r2, t intervals, t statistics, and g gy2i g gx2i g

so on. The summary statistics provide no way of distinguishing among the four data sets. Based on a scatter plot and a residual plot for each set, comment on the appropriateness or inappropriateness of tting a straight-line model; include in your comments any speci c suggestions for how a straight-line analysis might be modi ed or quali ed.