Consider the following four (x, y) data sets; the first three have the same x values, so

Question:

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

For each of these four data sets, the values of the summary statistics Î£xi, Î£xi2, Î£yi, Î£yi2, and Î£xiyi are virtually identical, so all quantities computed from these five will be essentially identical for the four sets-the least squares line (y = 3 + .5x), SSE, s2, r2, t intervals, t statistics, and so on. The summary statistics provide no way of distinguishing among the four data sets. Based on a scatterplot and a residual plot for each set, comment on the appropriateness or inappropriateness of fitting a straight-line model; include in your comments any specific suggestions for how a "straight-line analysis" might be modified or qualified.