LETTER

Collinearity: A Function of the Sample Size, Range, and Similarity of Observations

The authors' concerns are unfounded. There are numerous examples in the literature when both height and weight have been used to predict various dependent variables, e.g., body fat (1, 5, 7), blood pressure (6, 9), and the dependent variable of interest, peak O₂ (3, 8, 10, and unpublished observations of Nevill and Holder). In all these papers, the contributions of height and weight were both significant, and no collinearity was reported. For example, when blood pressure was used as the dependent variable (see Refs. 6, 9), the contributions from both height and weight provided highly significant exponents (P < 0.0001) but with opposite signs, i.e., predicting a stature-adjusted weight index (approximately the body mass index ratio) as a measure of "overweight."

There also exists overwhelming evidence that both height and weight are necessary when predicting peak O₂, i.e., taller subjects have significantly greater peak O₂, having already controlled for differences in body weight (3, 8, 10, and unpublished observations of Nevill and Holder). The sample sizes used in these studies were as follows; Baxter Jones et al. (3), n = 453 young elite athletes (231 men and 222 women); Welsman et al. (10), n = 156 school children (73 boys and 83 girls), and Nevill and Holder (unpublished observations), n = 1,732 adults, age 16 yr and over (852 men and 880 women). The strength of collinearity observed in Batterham et al. (2) (sample size n = 75) may be a function of the sample size and the range and similarity of observations (4), a problem more evident in Batterham et al. (2) than in the studies of Baxter-Jones et al. (3), Nevill (8), Welsman et al. (10), and Nevill and Holder (unpublished observations).

Nevill (8) suggested that the significant contribution of height in addition to body weight might be explained by a disproportionate increase in muscle mass with body size. However, based on the unpublished findings of Nevill and Holder, an alternative explanation now becomes apparent. The best model to predict maximal O₂ incorporated a significant contribution from forced vital capacity (FVC; also known to be predominately stature related) as well as body mass, whereas the height term became redundant, no longer making a significant contribution to the regression model. Clearly, on the basis of these findings, the apparent advantage of being taller would appear to be more accurately explained by the subjects' greater FVC. In effect, the significant contribution of the height term, found in the earlier studies (3, 8, 10), would appear to have been inadvertently providing an estimate of the subjects' FVC. This was an unexpected result, although not entirely surprising. Taking the analogy with the motor car engine, we would expect a greater performance (maximum speed and power output) from an engine with a greater cubic capacity, so perhaps we might also expect a greater maximum O₂ from a subject with a greater (forced) vital capacity.