Chapter 13.1, Problem 9E

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):

Data Set	1-3	1	2	3	4	4
Variable	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 ∑x_i, ∑_x2, oyi, oyi 2, and oxiyi are virtually identical, so all quantities computed from these five will be essentially identical for the four sets—the least squares line sy 5 3 1 .5xd, 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.