Measurements on Babies

Keywords: analysis of covariance, spurious correlation.

Description

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.

Download

Data File (tab delimited text)

Source

Professor Chris Lloyd, University of Hong Kong. See his original mailing to the ANZStat mailing list discussion.

Analysis

x2 is independent of x1 after adjustment for Age.
Dependence of x2 on Age is approximately linear.
There is some evidence of increasing variance, which can be handled by using gamma rather than normal regression.

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