# polynomial trend

## polynomial trend

[¦päl·i¦nō·mē·əl ‚trend]
(statistics)
A trend line which is best approximated by a polynomial function; used in time series analysis.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
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A sequential testing procedure to distinguish between a piecewise polynomial trend superimposed by short-range dependence and that imposed by long-range dependence had been examined by Baek [15].
The wavelet-based method can detrend the records with polynomial trend because of the property of vanishing moments of wavelet, can avoid the spurious result caused by trend, and is suitable for water level records.
For example for the per capita income, the equation of the best fit polynomial trend lines is quadratic in nature with R2 value as 0.75, which makes the arrangement acceptable.
The regression equation of polynomial trend type (y = [a.sub.0] + [a.sub.1] x x + [a.sub.2] x [x.sub.2] + [epsilon]) and the respective coefficient of determination ([R.sup.2]) was derived (Figure 5).
BP neural network, GM (1, 1), exponential smoothing model, and polynomial trend extrapolation model are presented as follows since they are used widely and efficiently in the field of energy consumption forecasting.
Phase II also showed a similarity of pattern by trend line categorization in which polynomial trend lines showed the highest [r.sup.2] values for HR response.
The depth of each eclipse during outburst was measured by taking the difference in magnitude between the 4th order polynomial trend at mid-eclipse and the fitted minimum magnitude.
Polynomial trend lines have been used to graphically display trends in data and to analyze problems in relation to the last 50 years climate scenario and to predict future trends.
([double dagger]) LSD 0.05 is presented to compare rate means within entries only when polynomial trend analysis was significant at P < 0.05.
The data illustrate that: (1) regression approaches to ANOVA can be superior to classical ANOVA with respect to statistical power against Type II error; and (2) classical regression analysis can be used to test hypotheses typically but incorrectly associated only with ANOVA, such as polynomial trend and interaction hypotheses.
The results of the polynomial trend models and seasonal ratios in Table 4 are listed in the following calculations and shown in Figures 7 and 8:
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