Orthogonal Polynomial Regression Research Articles

A method of numerical solution for unsteady state problems: Inversion of Laplace transforms by recursive orthogonal polynomial regression

An improved method of numerical inversion of Laplace transforms is presented. The method employs a set of recursive orthogonal polynomials and eliminates the need for matrix inversion in the evaluation of regression coefficients. Thus the numerical instability inherent in the conventional numerical inversion technique by curve fitting is avoided. Application examples show that the method is efficient and the result accurate. The method is useful in the study of unsteady state behaviour of processes when the analytical solution is not available.

Demographic factors influencing psychiatric rating scales (Zung SDS and SAS).

Zung's Self-Rating Anxiety Scale (SAS) and Self-Rating Depression Scale (SDS) were completed by 489 healthy volunteers (314 men, 175 women) aged 15-84 years. The total scores were analysed in function of sex, age, occupational class, professional group, marital status, religion, foreigner status and nationality. Analysis by orthogonal polynomial regression showed no statistically significant differences between different age groups. In contrast to this, the study revealed highly significant SAS and SDS score differences between both sexes (Mann-Whitney U-test). In addition, there were statistically significant associations between the SAS scores and occupational class, professional group, religion, foreigner status and nationality; compared with significant associations between the SDS scores and marital status, foreigner status and nationality (Kruskal-Wallis test/Mann-Whitney U-test). The requirements for data analysis in clinical trials, for a differential diagnosis between transient variations of normal health and disorders, and for a differential diagnosis between anxiety and depression are discussed.

Measurement for Warm-Up Decrement: A Review

Research dealing with warm-up decrement shows there is diversity in measurement of this phenomenon. It would be advantageous to have a standardized method of measurement that is objective and does not require the determination of a peak trial. One such technique is orthogonal polynomial regression.

Orthogonal Polynomial Regression

Summary We discuss in basic terms the orthogonal polynomial regression approach for curve fitting when the independent variable occurs at unequal intervals and is observed with unequal frequency. The computations required for determining orthogonal polynomials are described with a simple example.

Orthogonal Polynomial Regression for Unequal Spacing and Frequencies

A simple procedure is described to determine the orthogonal polynomials when the levels of the predictor variable occur at unequal intervals and are observed with unequal frequency. A computer prog...

Relationships between fatty acid composition of lamb fat and dietary ingredients.

One hundred thirteen wether feeder lambs were individually fed to study the effects of ration and location of fat in the carcass upon fatty acid composition. The rations consisted of dehydrated alfalfa (17% protein) and corn. The proportions of alfalfa and corn varied from 0% to 100% in the 21 different rations by 5% increments. A urea-mineral supplement was added to rations containing 50% corn or more. The lambs were slaughtered after a feeding period of 105 days. Loin, dock and kidney fat samples were obtained from chilled (48 hr) carcasses. Fat samples were extracted, esterified and analyzed by gas-liquid chromatography. Data were statistically analyzed by analysis of variance and orthogonal polynomial regression. Depot fat contents of unsaturated acids (myristoleic, palmitoleic, oleic, linoleic, and linolenic) were affected by rations. Myristoleic, palmitoleic and linoleic significantly increased curvilinearly, oleic increased linearly and linoleic decreased linearly as level of corn increased. Linoleic acid contents were confounded by saturation of dietary linolenic, and oleic contents were confounded by saturation of dietary linoleic.

An analysis of the factors determining yields in crosses between semi-dwarf and taller wheat varieties

SUMMARYThe growth and development of two semi-dwarf winter wheat varieties, of two taller varieties, and of random selections from two crosses between semi-dwarf and taller varieties were compared over 2 years. Changes with time of crop dry weight/m2, leaf area index and ear size were expressed as orthogonal polynomial regression coefficients. Significant correlations were obtained between yield, the polynomial coefficients and growth measurements relating to number of tillers and flag leaf area duration, but many of these variables were significantly correlated with each other. Multiple regression equations were therefore calculated expressing yield in terms of the variables. These showed flag leaf area duration and rate of ear growth to be the most important characters determining crop yield. The greatest reduction in total yield variance was obtained by the simultaneous consideration of characters relating to photosynthetic capacity and ear development. The significance of this finding in relation to the relative importance of ‘apos;source’ and ‘sink’ in determining grain yield are discussed.

A Method of Recording Germination Curves

A method of recording germination curves by fitting the linear and the two non-linear parameters of a normal function to germination data is presented and applied to some data of Veronica arvensis L. The germination data could be adequately described by this method. This method has been compared with orthogonal polynomial regressions.

A Method of Measuring Seed Germination in Physiological Studies

Methods of comparing germination curves are described and these are discussed in relation to the problem under consideration. In a study of chemical factors which modify seed germination (here all inhibitory), the changes in the rate of germination appeared to be associated with the inhibitory factors. These curves could be adequately described by orthogonal polynomial regressions. It is noted that some coefficients devised to represent the course of germination were not adequate for these purposes. The reasons are discussed.

Varietal differences in growth parameters of wheat and their importance in determining yield

The growth and development of five winterwheat varieties and of random selections from hybrids between them were compared. Successive sampling demonstrated varietal differences in orthogonal polynomial regression coefficients fitted to data for tiller number, shoot weight and leaf area. The correlation coefficients between these parameters and yield were statistically significant, but when polynomial regression equations of yield on them were determined, only the terms relating to shoot weight and leaf area duration after anthesis were significant.The heritabilities of these parameters in each of 2 years were determined from measurements of genetic and environmental variance. The results obtained were compared each year with estimates of yield derived from parameters determined in the other year. The correlation between successive estimates of yield was found to be closer than that of of yield was found to be closer than that of yield with any of the growth parameters.Separate analyses of crosses involving each of the parental varieties showed seasonal and varietal differences in the usefulness of the growth parameters for predicting yield.The value of this approach to the choice of parents is discussed in view of these findings.