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Keywords: polynomial regression, multiple regression.
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)
| 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) |
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 |
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