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# Childhood Respiratory Disease

Keywords: polynomial regression, multiple regression.

## Description

FEV (forced expiratory volume) is an index of pulmonary function that measures the volume of air expelled after one second of constant effort. The data contains determinations of FEV on 654 children ages 6-22 who were seen in the Childhood Respiratory Desease Study in 1980 in East Boston, Massachusetts. The data are part of a larger study to follow the change in pulmonary function over time in children.

 ID - ID number Age - years FEV - litres Height - inches Sex - Male or Female Smoker - Non = nonsmoker, Current = current smoker

Data File (tab-delimited text)

## Source

 Tager, I. B., Weiss, S. T., Rosner, B., and Speizer, F. E. (1979). Effect of parental cigarette smoking on pulmonary function in children. American Journal of Epidemiology, 110, 15-26. Rosner, B. (1990). Fundamentals of Biostatistics, 3rd Edition. PWS-Kent, Boston, Massachusetts.

The data has also been described by:

 Kahn, M. (2003). Data Sleuth. STATS, 37, 24. Kahn, M. (2005). An exhalent problem for teaching statistics. Journal of Statistical Education, 13(2). Smyth, G. K. (1998). Polynomial approximation. In: Encyclopedia of Biostatistics, P. Armitage and T. Colton (eds.), Wiley, London, pp. 3425-3429. (Postscript)

## Analysis

Consider height as a function of age for the 318 girls in the study. Height might be described roughly by a straight line over a short range of ages, say ages 5 to 10, but over wider age ranges a more general function is needed. We fit sixth order orthogonal polynomials, and find that only the quadratic is significant. We might prefer to use the quartic approximation in practice though, because it is almost significant, and because the quadratic is not monotonic over the range of the data.

Table 1. Coefficients and standard errors for orthogonal polynomial
regression of Height on Age for the respiratory disease study.

 Coefficient Value Std. Error t-value P-value a0 60.2119 0.1426 422.1543 0.0000 a1 65.0285 2.5435 25.5669 0.0000 a2 -31.3549 2.5435 -12.3276 0.0000 a3 4.4838 2.5435 1.7629 0.0789 a4 4.9562 2.5435 1.9486 0.0522 a5 -2.1465 2.5435 -0.8439 0.3994 a6 2.4170 2.5435 0.9503 0.3427