Surface-fitting by partitioned multiple regression equations in oblique territories and its use in coordinate transformations

This study was to attempt the cutting-edge 3D remote sensing technique of static terrestrial laser scanning (TLS) for parametric 3D reconstruction of juvenile understory trees. The data for test was collected with a Leica HDS6100 TLS system in a single-scan way. The geometrical structures of juvenile understory trees are extracted by model fitting. Cones are used to model trunks and branches. Principal component analysis (PCA) is adopted to calculate their major axes. Coordinate transformation and orthogonal projection are used to estimate the parameters of the cones. Then, AutoCAD is utilized to simulate the morphological characteristics of the understory trees, and to add secondary branches and leaves in a random way. Comparison of the reference values and the estimated values gives the regression equation and shows that the proposed algorithm of extracting parameters is credible. The results have basically verified the applicability of TLS for field phenotyping of juvenile understory trees.

Achieving and maintaining optimal fluid status remains a major challenge in maintenance hemodialysis (MHD). The aim of this study was to establish a body composition–based multiple regression equation for use in the estimation of overhydration (OH) in the setting of MHD while using a body composition monitor (BCM) to guide patient dry weight management. We initially retrospectively analyzed factors associated with OH in 314 healthy Chinese individuals and obtained a multiple linear regression equation to determine OH level. Next, 49 stable MHD patients were enrolled to validate whether our multiple regression formula was applicable to such patients. Prior to hemodialysis, BCM measurements were performed; OHpre was defined as OH directly measured by BCM; while OHstd was defined as OH estimated by the multiple regression equation. In our multivariate linear regression analysis, PhA (β = − 1.266, 95% CI (− 1.532 ~ − 1.341), p < 0.001), LTM (β = 0.987, 95% CI (0.086 ~ 0.109), p < 0.001), and age (β = − 0.307, 95% CI (− 0.023 ~ − 0.015), p < 0.001) were independent predictors of OH in healthy Chinese individuals. The multiple linear regression equation that we developed for calculating OH was as follows: OHstd = 6.203 − 0.019 × age − 0.083 × gender − 0.006 × fat + 0.098 × LTM − 1.437 × PhA (F = 189.896, R2 = 0.755, p < 0.001). Linear correlation and Bland-Altman analyses were performed between OHpre and OHstd in MHD patients; correlation was found to be high (r = 0.786, p < 0.001). Bias between OHpre and OHstd was 0.45 L as assessed using 95% CI limits of agreement ranging from − 0.73 to 1.62 L. We found that our multiple regression equation formulated using data from healthy individuals provides applicable guidance for dry weight management in MHD patients.

This paper presents empirical research on coordinate transformation models that enable coordinate transformations between the historical astro-geodetic datums and datums related to the European Terrestrial Reference System (ETRS), through a case study of the Republic of Croatia. Thirteen models were investigated for the transformation from the historical Croatian State Coordinate System (HDKS) to the Croatian Terrestrial Reference System (HTRS96): Molodensky 3 and 5 parameter (standard and abridged) conformal transformation models, 7 parameter transformation models (Bursa-Wolf and Molodensky-Badekas model), Affine transformation models (8, 9, 12 parameter), Multiple Regression Equation approach, and several transformation models that include extending of the aforementioned 7 parameter and 8, 9, 12 parameter Affine transformation models with distortion modelling. Most of the models were investigated for the first time over the Croatian territory. Analysis of transformation models performance was conducted using an independent data set of reliable geodetic points. The study provides mutual comparison of the models and their comparison with the official Croatian transformation model called T7D. Furthermore, the most appropriate transformation model(s) were defined regarding the required accuracy and the available resources for the coordinate transformation models implementation. In addition, the paper provides a brief theoretical background and equations of each transformation model and summarises the bibliography on the research topic.

This study aimed to investigate the suitability of using ultrasonograph muscle thickness (MT) measurements to estimate the muscle volume (MV) of the quadriceps femoris as an alternative approach to magnetic resonance imaging (MRI). The subjects were 46 men aged from 20 to 70 years who were randomly allocated to either a validation or a cross-validation group. In the validation group, multiple and simple regression equations, which used a set of MT values determined at mid-thigh and thigh length (1) and the product of pi, (MT/2)2, and l [pi x (MT/2)2 x l], respectively, as independent variables, were derived to estimate the MV measured by MRI. Because the two equations were cross-validated, the data from the two groups were pooled to generate the final prediction equations: MV (cm3)=(MT x 311.732)+(l x 53.346) -2058.529 as the multiple regression equation and MV (cm3) = [pi x (MT/ 2)2 x l] x 1.1176+663.040 as the simple regression equation. In the multiple regression equation, MT explained 75% of the variation in the MV measured by MRI. The r2 and the standard error of the estimate (SEE) of the equations were 0.824 and 175.6 cm3 (10.6%), respectively, for the multiple regression equation and 0.829 and 173.7 cm3 (10.5%), respectively, for the simple regression equation. Thus, the present results indicate that ultrasonograph MT measurements at mid-thigh are useful for estimating the MV of knee extensors. However, the observed SEE values suggest that the prediction equation obtained in this study may be limited to population studies rather than individual assessments in longitudinal studies.

Multiple regression and logistic regression equations were derived for the prediction of hail size based on data from 1992 through 1994. The multiple regression equation was formulated to predict hail diameter. The logistic regression equation was developed to predict the probability of hail size greater than or equal to 1.9 cm in diameter. Variables used for this study consisted of vertically integrated liquid (VIL) computed from the Weather Surveillance Radar-1988 Doppler (WSR-88D) radar and convective parameters derived from the skew-T/Hodograph analysis and research program. Data were obtained from the Baltimore, Maryland/Washington D.C., WSR-88D radar and Dulles, Virginia, upper-air soundings. Numerous parameters were tested; however, only VIL, 85-kPa temperature, freezing level, and mean storm-relative inflow in the lowest 2-km were retained for the multiple regression equation. These four parameters were used as a base to derive the logistic regression equation, and this derivation process...

According to revisions of survey law taking effect on January 1, 2003, the Korean geodetic datum has been changed from a local geodetic to a world geodetic system. Since the datum change demands a geographical data transformation, the National Geographic Information Institute has established step-by-step plans for the transformation of the land data constructed through the National GIS Project, and it is in progress. For maritime data, however, no detailed transformation plan has been established yet. Therefore, it is necessary to analyze the maritime geographic data obtained through the Maritime GIS project and set up the data transformation scheme to a world geodetic system. In this study, the datum transformation parameters especially for the maritime geographical data are determined. From database constructed through MGIS, a total of 492 coordinate pairs were used in parameter determination initially. At this stage, three popular seven parameter transformation models, Bursa-Wolf, Molodensky and Veis model, and the multi regression equation are applied, and the transformation parameters from the Molodensky model are selected for its accuracy and consistency with the land data transformation method. To eliminate the local bias caused by the nonequally distributed stations, a network optimization is applied and 42 stations are selected to determine the final transformation parameters. The distortion after applying the similarity transformation is modeled through a least squares collocation with Gaussian model, and high accuracy better than 15 cm in coordinate transformation is obtained.

The forecast of GDP has always been a popular research topic today, and its related influencing factors are also complicated. This paper selects three key factors in economic development: gold price, crude oil price, and stock market index, explores their relationship with U.S. GDP, and then uses these three factors as predictive variables to obtain a multiple linear regression equation related to GDP. The research methods of this paper are as follows: Firstly, monthly U.S. GDP, monthly crude oil price, monthly gold price, and monthly S&amp;P 500 index were collected. Secondly, correlation analysis was carried out on these data, including calculation of correlation coefficient and cross-correlation analysis. Correlation analysis showed that GDP had a significant positive correlation with other variables. Then, a multiple linear regression model was established with monthly U.S. GDP as the predicted variable, monthly crude oil price, monthly gold price, and monthly S&amp;P 500 index as the predictor variable. Finally, multiple regression equations are obtained through testing. This multiple regression equation can be used to predict GDP further.

ABSTRACTAim The aim of this study is to determine the patterns of nitrogen (N) concentrations in leaf litter of forest trees as functions of climatic factors, annual average temperature (Temp, °C) and annual precipitation (Precip, dm) and of forest type (coniferous vs. broadleaf, deciduous vs. evergreen, Pinus, etc.).Location The review was conducted using data from studies across the Eurasian continent.Methods Leaf litter N concentration was compiled from 204 sets of published data (81 sets from coniferous and 123 from broadleaf forests in Eurasia). We explored the relationships between leaf litter N concentration and Temp and Precip by means of regression analysis. Leaf litter data from N2‐fixing species were excluded from the analysis.Results Over the Eurasian continent, leaf litter N concentration increased with increasing Temp and Precip within functional groups such as conifers, broadleaf, deciduous, evergreen and the genus Pinus. There were highly significant linear relationships between ln(N) and Temp and Precip (P &lt; 0.001) for all available data combined, as well as for coniferous trees, broadleaf trees, deciduous trees, evergreen trees and Pinus separately. With both Temp and Precip as independent variables in multiple regression equations, the adjusted coefficient of determination () was evidently higher than in simple regressions with either Temp or Precip as independent variable. Standardized regression coefficients showed that Temp had a larger impact than Precip on litter N concentration for all groups except evergreens. The impact of temperature was particularly strong for Pinus.Conclusions The relationship between leaf litter N concentration and temperature and precipitation can be well described with simple or multiple linear regression equations for forests over Eurasia. In the context of global warming, these regression equations are useful for a better understanding and modelling of the effects of geographical and climatic factors on leaf litter N at a regional and continental scale.

In this study, the applicability of a multiple regression equation to predict breeding values based on the high-density SNP (single nucleotide polymorphism) markers that are found in the whole genome sequences of animals and plants was evaluated. The genotypes of a large number of SNPs distributed on chromosomes were treated as functional data and phenotypic values of a trait were treated as scalar target variables in the functional data multiple regression equations. The functional data analysis R package (“fda”, version 2.4.0) was used to create the functional data multiple linear regression equations. An outline of this procedure is presented in this paper. We evaluated the accuracy of the functional data multiple regression equations by predicting breeding values using simulated data sets of SNPs as predictors and phenotypic values of a trait as variables. We found that the regression equations predicted the breeding values with considerable accuracy even though the predictors were not selected, nor were prior distributions assumed.

This study aimed to provide multiple regression equations taking into account differences in running speed, leg length, and step characteristics to predict kinematics of maximal speed sprinting. Seventy-nine male sprinters performed a maximal effort 60-m sprint, during which they were videoed through the section from the 40- to 50-m mark. From the video images, leg kinematic variables were obtained and used as dependent variables for multiple linear regression equation with predictors of running speed, leg length, step frequency, and swing/support ratio. Multiple regression equations to predict leg kinematics of maximal speed sprinting were successfully obtained. For swing leg kinematics, a significant regression model was obtained to predict thigh angle at the contralateral foot strike, maximal knee flexion and thigh lift angular velocities, and maximal leg backward swing velocity (adjusted R2 = 0.194–0.378, medium to large effect). For support leg kinematics, a significant regression model was obtained to predict knee flexion and extension angular displacements, maximal knee extension velocity, maximal leg backward swing angular velocity, and the other 13 kinematic variables (adjusted R2 = 0.134–0.757, medium to large effect). Based on the results, at a given leg length, faster maximal speed sprinting will be accompanied with greater thigh angle at the contralateral foot strike, greater maximal leg backward swing velocity during the swing phase, and smaller knee extension range during the support phase. Longer-legged sprinters will accomplish the same running speed with a greater thigh angle at contralateral foot strike, greater knee flexion range, and smaller maximal leg backward swing velocity during the support phase. At a given running speed and leg length, higher step frequencies will be achieved with a greater thigh angle at contralateral foot strike and smaller knee flexion and extension ranges during the support phase. At a given running speed, leg length and step frequency, a greater swing/support ratio will be accompanied with a greater thigh angle at contralateral foot strike and smaller knee extension angular displacement and velocity during the support phase. The regression equations obtained in this study will be useful for sprinters when trying to improve their maximal speed sprinting motion.

In shallow geothermal systems, the main equivalent underground thermal properties are commonly calculated with a thermal response test (TRT). This is a borehole heat exchanger production test where the temperature of a heat transfer fluid is recorded over time at constant power heat injection/extraction. The equivalent thermal parameters (thermal conductivity, heat capacity) are simply deduced from temperature data regression analysis that theoretically is a logarithmic function in the time domain, or else a linear function in the log-time domain. By interpreting the recorded temperatures as a regionalized variable whose drift is the regression function, in both cases the formal problem is a linear estimation of the mean. If the autocorrelation function (variogram, covariance) of residuals is known, coefficient variance can be directly deduced. Coefficient estimates are independent of the drift form adopted, and the residuals are the same in the same points. The random function is different in the time domain, however, and in the log-time domain. In fact, residual variograms are different due to the transformation of the coordinate space. This paper uses a TRT case study to examine the consequences of coordinate space transformation for a random function, namely its variogram. The specific question addressed is the choice of coordinate space and variogram.

Objective: The aim of this study was to obtain morphometric measurements of adult human hip bones, examine the relationship among these measurement parameters, and develop regression equations to estimate the acetabular dimensions for acetabular reconstruction Material and Method: Seventy-eight (39 right and 39 left) dry hip bones of unknown age and gender located in the laboratory of Çukurova University Faculty of Medicine, Department of Anatomy, were included in the study. Eleven hip bones with fractures, deterioration, deformities, and defects that would affect the measurements were excluded from the study. In our study, 14 morphometric measurements of hip bones were obtained. IBM SPSS program was used for statistical analysis. Results: Single and multiple regression equations were developed from the hip bone morphometric measurements for the estimation of the morphometric measurements of the acetabulum. The standard error of estimate (SEE) values ranged from ±1.818 mm to ±3.546 mm in single regression equations, and between ±1.633 mm and ±2.107 mm in multiple regression equations. A lower SEE value was obtained in multiple regression equations than in single regression equations. Conclusion: The regression equations developed in this study will allow us to obtain personalized measurements, which will aid clinicians in the correct and safe placement of the implant in hip replacement surgeries as well as in the prevention of complications with the use of appropriate prostheses.

For the purpose of forecasting the prevalence of Japanese encephalitis in Japan, we tried to get the correlation of factors among average atmospheric temperatures of prefectures of June and July in 1965-1967 (T6, 7 in short), the date when HI reaction of swine became positive in degree of 50 per cent (D. pos. swine in short), the latitude and longitude in respective prefecture. And we estimated the mode date of this epidemic time curve of the prevalence from the regression equation of one variable and multiple regression equation from the above factors using an electronic computer. And the following results were obtained.1) To estimate mode date (y1, y2, y3, y4) of the epidemic time curve of the prevalence, we can use the next equation:The regression equation to estimate y from T6, 7 (x1) is as follows, y1=-3.36x1+145.2 σ0=11.1……………(1)The regression equation from D. pos. swine (x2) is as follows.y2=0.63x2+43.7 σ0=9.0……………(2)The multiple regression equation from T6, 7 and D. pos. swine is as follows.y3=-1.15x1+0.56x2+73.29 σ0=8.84……………(3)The multiple regression equation from T6, 7 D. pos. swine, latitude and longitude is as follows.y4=-0.73x1+0.43x2+2.15x3-0.03x4-2.30 σ0=8.8……………(4)

With the development of society, carbon emissions are increasing. The key organisms to maintain the stability of the carbon cycle are fungi that can be easily seen and ignored. In this paper, we selected several fungi to establish the model of decomposition and reproduction so that we can understand the role they played. First of all, we studied several physiological indexes of fungi, and established the degradation model through multiple regression analysis, and multiple linear regression equation for the relationship between decomposition rate, growth rate, unit volume density of mycelium, temperature and humidity tolerance. Next, we established the competitive growth model based on logistic model, simulated the competitive growth process of strains with different growth rates, humidity tolerance, and the total decomposition rate. In order to be closer to the real situation, we set up the competitive growth model among four species. By arranging fungal communities randomly to simulate different biodiversity, we analyzed the effects on the decomposition rate in the case of that the environmental temperature and humidity changed by 10% respectively. After that, we established a growth prediction model based on ARIMA. By querying the climate data of five typical climates, we established the competitive growth model with 4 combinations, and we obtained a short-term model, a medium-term trend and a long-tern forecast to describe growth, reproduction and decomposition rate. In order to refine the strains of the pressure of competition and the influence of the distance between the strains of competition, we have established improved competition evolution model based on the cellular automata theory of population. The model helped us comprehend the competition between species on a micro level. All these analyses showed us the significance of biodiversity and the great role decomposers play in Earth.

Multiple regression equations were developed to describe the relationship between percentage hard red spring wheat (Triticum aestivum L.) loss and the density and shoot dry weight of multi-species weed communities dominated by green foxtail [Setaria viridis (L.) Beauv.]. Data were collected over a 10-yr period from fields sown by farmers near Regina, Saskatchewan. Weed densities averaged 470 plants m−2, with green foxtail constituting 85% of the total number of plants and 57% by dry weight. Other important species included in the equations were stinkweed (Thlaspi arvense L.), common lamb’s-quarters (Chenopodium album L.), wild buckwheat (Polygonum convolvulus L.), and wild mustard (Sinapis arvensis L.). Including crop density as a variable made a significant improvement in the efficiency of the equations. Precipitation and growing degree-days (base 5 °C) were related to the residuals from the analysis relating wheat loss to weed abundance. These environmental variables were significantly related to crop loss, but only for the residuals of the equation where weed densities were used as independent variables. Hyperbolic and sigmoidal equations were less efficient at describing the data than were multiple linear regression equations. Key words: Green foxtail, spring wheat, competition, multi-species, multiple regression, crop loss