Statistics for Environmental Engineers

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Anscombe (1973) published a famous and fascinating example of how R2 and other statistics that are routinely computed in regression analysis can fail to reveal the important features of the data. Table 39.i


FIGURE 39.1 An example of nonsense in regression. X is the first six digits of pi and Y is the first six Fibonocci numbers. R2 is high although there is no actual relation


between x and у.


TABLE 39.1


Anscombe’s Four Data Sets


A


B


C


D


x


y


x


y


x


y


x


y


10.0


8.04


10.0


9.14


10.0


7.46


8.0


6.58


8.0


6.95


8.0


8.14


8.0


6.77


8.0


5.76


13.0


7.58


13.0


8.74


13.0


i2.74


8.0


7.71


9.0


8.81


9.0


8.77


9.0


7.11


8.0


8.84


11.0


8.33


11.0


9.26


11.0


7.81


8.0


8.47


14.0


9.96


14.0


8.10


14.0


8.84


8.0


7.04


6.0


7.24


6.0


6.13


6.0


6.08


8.0


5.25


4.0


4.26


4.0


3.10


4.0


5.39


19.0


12.50


12.0


10.84


12.0


9.13


12.0


8.15


8.0

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