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constructed by statistician Francis Anscombe [10] in 1973 to demonstrate the
importance of graphs in statistical analyses.
Figure 3.6
Anscombe's quartet
The four datasets in Anscombe's quartet have nearly identical statistical properties,
Table 3.3
Statistical Properties of Anscombe's Quartet
Statistical Property
Value
Mean of
9
Variance of
11
Mean of
7.50 (to 2 decimal points)
Variance of
4.12 or 4.13 (to 2 decimal points)
Correlations between and
0.816
Linear regression line
(to 2 decimal points)
Based on the nearly identical statistical properties across each dataset, one might
conclude that these four datasets are quite similar. However, the scatterplots in
Figure 3.7
tell a different story. Each dataset is plotted as a scatterplot, and the
fitted lines are the result of applying linear regression models. The estimated
regression line fits Dataset 1 reasonably well. Dataset 2 is definitely nonlinear.
Dataset 3 exhibits a linear trend, with one apparent outlier at . For Dataset
4, the regression line fits the dataset quite well. However, with only points at two
values, it is not possible to determine that the linearity assumption is proper.
