linear and nonlinear regressions
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Author(s):  
Talisson Sáteles Matos ◽  
Eduardo Morgan Uliana ◽  
Camila Aparecida da Silva Martins ◽  
Luis Miguel Castillo Rapalo

  This study aimed to regionalize maximum (Qmax), minimum (Q95), and long-term mean (Qltm) streamflows in the Juruena River Basin to further water-resource planning and management, especially regarding water-use grant rights, streamflow regulation, and hydraulic designs. To do that, a traditional method was used, which relates the interest streamflows with sub-basin physiographic parameters by linear and nonlinear regressions. In summary, the traditional method was efficient for regionalization of Q95, Qltm, and Qmax streamflows for the Juruena River Basin. Moreover, the explanatory variables able to provide the best results for regionalization of Q95 and Qltm stream flows are drainage area, total watercourse length, and sub-basin mean altitude. For Qmax regionalization, the best results were provided by explanatory variables like drainage area, perimeter, and total watercourse length.



Author(s):  
J. P. Assis ◽  
P. C. F. Linhares ◽  
R. P. Souza ◽  
M. F. S. Pereira ◽  
A. M. B. Almeida

<p>A mensuração da área foliar é requerida em vários estudos agronômicos, ecológicos e biológicos de uma maneira geral. O objetivo deste trabalho foi obter equações de regressões lineares e não lineares que estimem a área foliar real da espécie jitirana, em função das dimensões do comprimento ao longo da nervura principal (C) e largura máxima (L). Para isso 200 limbos foliares foram coletados em ecossistemas de ocorrência natural desta espécie vegetal, na região de Mossoró, no Estado do Rio Grande do Norte, limpas e acondicionadas em caixa de isopor e medidas imediatamente, inclusive sua área real através do Integrador de Área foliar. Considerando a parcimônia do modelo, o coeficiente de determinação e a significância do teste F da análise de variância a 3 % de probabilidade, as melhores equações para estimação da área foliar da jitirana em ordem de importância foram: modelo linear simples passando pela origem em função do produto do comprimento com a largura da folha; linear simples em função do comprimento; linear simples em função da largura; e o modelo de regressão linear múltipla, modelada em função do comprimento e largura simultaneamente. Onde <em>Merremia aegyptia</em> apresentou valores médios de comprimento das folhas, largura e área foliar real iguais a 13,5 cm, 28,8 cm e 202,38 cm<sup>2</sup>, respectivamente. 95% da área foliar de 200 limbos está relacionada com folhas de tamanho variando de 133,3 cm<sup>2</sup> a 299,0 cm<sup>2</sup>.</p><p><strong> </strong><strong>Estimation of leaf area “scarlet starglory” (<em>Merremia aegyptia </em>(l.) </strong><strong>Urban) through regression models</strong></p><p><strong>ABSTRACT - </strong>The measurement of leaf area is required in several agronomic studies, ecological and biological processes in general. The objective of this study was to obtain equations of linear and nonlinear regressions to estimate the real leaf area of Scarlet Starglory, depending on the dimensions of length along the main vein (C) and width (L). For this 200 leaves were collected in areas of naturally occurring ecosystems of this plant species in the region of  Mossoró, in Rio Grande do Norte state, Brazil, the plants were cleaned and wrapped, then they were measured immediately through Integrador of Area to foliate. Considering the parsimony of the model, the coefficient of determination, and the significance of the F test of analysis of variance of 3% probability, best equations that estimated the leaf area were in order of importance was: the model lineal simple going by the origin in function of the product of the length with the width of the leaf; lineal simple in function of the length; lineal simple in function of the width; and the model of multiple lineal regression, modeled in function of the length and width simultaneously. Where <em>Merremia aegyptia</em> apresentau medium values of length of the leaves, width and area to foliate real iguias to 13.5 cm, 28.8 cm and 202.38 cm<sup>2</sup>, respectively.</p>





Stroke ◽  
2014 ◽  
Vol 45 (suppl_1) ◽  
Author(s):  
Wendy Ziai ◽  
Saman Nekoovaght-Tak ◽  
Joshua F Betz ◽  
John Muschelli ◽  
Ryan N Fisico ◽  
...  

Introduction: The ABC/2 formula is the most common, rapid, and effective method to estimate intracerebral hemorrhage (ICH) volumes. However, ABC/2 overestimates clot volume with increasing error for larger hematomas. We used linear and nonlinear regressions to find if adjusting C, adjusting the denominator, or adjusting both would improve ICH volume estimation. Materials and methods: We assessed the diagnostic computed tomography (CT) scans of 373 patients enrolled in the MISTIE II (N=100) and CLEAR III (N=273) clinical trials using a standard central laboratory ABC/2 technique compared with planimetry volumetric calculations. Linear and nonlinear regressions were used to find optimal adjustments for C and the denominator, both individually and jointly. Results were stratified by study population to determine generality. Results: In MISTIE II (M2) patients, mean hematoma volume was 45.72 ± 27.1 (SD) cm 3 using ABC/2 vs. 39.48 ± 19.58 cm 3 using planimetry. In CLEAR III (C3) patients, mean hematoma volume was 11.11±8.30 (ABC/2) vs. 9.58±7.10 cm 3 (planimetry). The optimal denominator for the ABC approximation without adjusting C was 2.39 in M2 patients (95% CI 2.33, 2.46) and 2.37 in C3 patients (95% CI 2.31, 2.42). When these samples are combined, the optimal denominator was 2.39 (95% CI 2.35, 2.42). Without any correction to the denominator, the optimal adjustment for C was a decrease of 0.8352 in M2 patients (95% CI -0.976, -0.694) and a decrease of 0.5277 in C3 patients (95% CI -0.595, -0.46). In regression models adjusting C and the denominator, the optimal adjustment for C was an increase of 0.5707 in M2 patients (95% CI -0.215, 1.635), and an increase of 0.0485 in C3 patients (95% CI -0.383, 0.235). The optimal value of the denominator in these models was 2.64 in M2 patients (95% CI 2.29, 3.13) and 2.39 in C3 patients (95% CI 2.21, 2.62). Conclusion: Empirical evidence from a large international population of ICH patients suggests that ABC/2 consistently over-estimates ICH volumes. Shrinking the C-axis of the ellipse improves fit, but the optimal adjustment depends on ICH size. Using a denominator of 2.4 is a simple, objective way to improve rapid ICH assessment with the existing measurement paradigm, which is consistent in both large and small hematomas.





2010 ◽  
Vol 02 (04) ◽  
pp. 451-462 ◽  
Author(s):  
STAN LIPOVETSKY

Multiple regression's coefficients define change in the dependent variable due to a predictor's change while all other predictors are constant. Rearranging data to paired differences of observations and keeping only biggest changes yield a matrix of a single variable change, which is close to orthogonal design, so there is no impact of multicollinearity on the regression. A similar approach is used for meaningful coefficients of nonlinear regressions with coefficients of half-elasticity, elasticity, and odds' elasticity due the gradients in each predictor. In contrast to regular linear and nonlinear regressions, the suggested technique produces interpretable coefficients not prone to multicollinearity effects.





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