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

Chapter 13, Problem 9

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Consider the following four (x, y) data sets; the first threehave the same x values, so these values are listed only once(Frank Anscombe, Graphs in Statistical Analysis,Amer. Statistician, 1973: 1721):Data Set 13 1 2 3 4 4Variable 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 6.89For each of these four data sets, the values of the summarystatistics oxi, oxi2, oyi, oyi2, and oxiyi are virtuallyidentical, so all quantities computed from these five will beessentially identical for the four setsthe least squares linesy 5 3 1 .5xd, SSE, s2, r2, t intervals, t statistics, and soon. The summary statistics provide no way of distinguishingamong the four data sets. Based on a scatterplot anda residual plot for each set, comment on the appropriatenessor inappropriateness of fitting a straight-line model;include in your comments any specific suggestions for howa straight-line analysis might be modified or qualified.