Data Analysis with R, Second Edition - Second Edition

Second Anscombe relationship

The first relationship in Anscombe's Quartet (y1 ~ x1) is the only one that can appropriately be modeled with linear regression as is. In contrast, the second relationship (y2 ~ x2) depicts a relationship that violates the requirement of a linear relationship. It also subtly violates the assumption of normally distributed residuals with a mean of zero.

To see why, refer to Figure 9.11, which depicts its residual-fitted plot:

Figure 9.11: The top two panels show the first and second relationships of Anscombe's quartet, respectively. The bottom two panels depict each top panel's respective residual-fitted plot.