Keywords: analysis of covariance, spurious correlation.
The data consist of measurements (x1, x2, Age in months) on 23 babies, collected in the Faculty of Medicine at the University of Hong Kong. It would be of great medical interest to find a relationship between x1 and x2. However, any correlation between them is likely spurious because both x1 and x2 tend to increase with age. See Chris Lloyd's original mailing to the ANZStat mailing list discussion.
Data File (tab delimited text)
Chris Lloyd, University of Hong Kong.
|x2 is independent of x1 given Age. In fact, as the ANOVA belows shows, the dependence on Age is nearly linear.|
Analysis of Variance Table Response: x2 Terms added sequentially (first to last) Df Sum of Sq Mean Sq F Value Pr(F) Age 1 25928.03 25928.03 15.68836 0.0010093 as.factor(Age) 1 6420.35 6420.35 3.88479 0.0652303 x1 1 2098.36 2098.36 1.26966 0.2754847 as.factor(Age):x1 2 515.02 257.51 0.15581 0.8569284 Residuals 17 28095.76 1652.69