Least squares regression with errors in both variables: case studies

Analytical curves are normally obtained from discrete data by least squares regression. The least squares regression of data involving significant error in both x and y values should not be implemented by ordinary least squares (OLS). In this work, the use of orthogonal distance regression (ODR) is discussed as an alternative approach in order to take into account the error in the x variable. Four examples are presented to illustrate deviation between the results from both regression methods. The examples studied show that, in some situations, ODR coefficients must substitute for those of OLS, and, in other situations, the difference is not significant.

Delineamentos experimentais eficientes para estudos de cinética química

In this paper we show how to obtain efficient designs of experiments for fitting Michaelis-Menten and Hill equations useful in chemical studies. The search of exact D-optimal designs by using local and pseudo-Bayesian approaches is considered. Optimal designs were compared to those commonly used in practice using an efficiency measure and theoretical standard errors of the kinetic parameter estimates. In conclusion, the D-optimal designs based on the Hill equation proved efficient for estimating the parameters of both models. Furthermore, these are promising with respect to practical issues, allowing efficient estimation as well as goodness-of-fit tests and comparisons between some kinetic models.

Estimation of phenotypic diversity in field populations of Magnaporthe grisea from two upland rice cultivars

The phenotypic diversity of Magnaporthe grisea was evaluated based on leaf samples with blast lesions collected from eight commercial fields of the upland rice cultivars 'BRS Primavera' and 'BRS Bonança', during the growing seasons of 2001/2002 and 2002/2003, in Goias State. The number of M. grisea isolates from each field utilized for virulence testing varied from 28 to 47. Three different indices were used based on reaction type in the eight standard international differentials and eight Brazilian differentials. The M. grisea subpopulations of ´Primavera' and 'Bonança', as measured by Simpson, Shannon and Gleason indices, showed similar phenotypic diversities. The Simpson index was more sensitive relation than those of Shannon and Gleason for pathotype number and standard deviation utilizing Brazilian differentials. However, the Gleason index was sensitive to standard deviation for international differentials. The sample size did not significantly influence the diversity index. The two sets of differential cultivars used in this study distinguished phenotypic diversity in different ways in all of the eight subpopulations analyzed. The phenotypic diversity determined based on eight differential Brazilian cultivars was lower in commercial rice fields of 'Primavera' than in the fields of 'Bonança,' independent of the diversity index utilized, year and location. Considering the Brazilian differentials, the four subpopulations of 'BRS Primavera' did not show evenness in distribution and only one pathotype dominated in the populations. The even distribution of pathotype was observed in three subpopulations of 'BRS Bonança'. The pathotype diversity of M. grisea was determined with more precision using Brazilian differentials and Simpson index.

Estimation of standard enthalpy of formation of alkanes in gaseous state by calculating size, structural and electronic parameters in the molecules

A quantitative analysis is made on the correlation ship of thermodynamic property, i.e., standard enthalpy of formation (ΔH fº) with Kier's molecular connectivity index(¹Xv),vander waal's volume (Vw) electrotopological state index (E) and refractotopological state index (R) in gaseous state of alkanes. The regression analysis reveals a significant linear correlation of standard enthalpy of formation (ΔH fº) with ¹Xv, Vw, E and R. The equations obtained by regression analysis may be used to estimate standard enthalpy of formation (ΔH fº) of alkanes in gaseous state.

Development and validation of spectroscopic methods for simultaneous estimation and dissolution of ofloxacin and ornidazole in tablet dosage forms

The aim of this work was to develop and validate simple, accurate and precise spectroscopic methods (multicomponent, dual wavelength and simultaneous equations) for the simultaneous estimation and dissolution testing of ofloxacin and ornidazole tablet dosage forms. The medium of dissolution used was 900 ml of 0.01N HCl, using a paddle apparatus at a stirring rate of 50 rpm. The drug release was evaluated by developed and validated spectroscopic methods. Ofloxacin and ornidazole showed 293.4 and 319.6nm as λmax in 0.01N HCl. The methods were validated to meet requirements for a global regulatory filing. The validation included linearity, precision and accuracy. In addition, recovery studies and dissolution studies of three different tablets were compared and the results obtained show no significant difference among products.

Experimental alternatives for evaluation of progenies and clones in eucalyptus breeding programs

The feasibility of using augmented block designs and spatial analysis methods for early stage selection in eucalyptus breeding programs was tested. A total of 113 half-sib progenies of Eucalyptus urophylla and eight clones were evaluated in an 11 x 11 triple lattice experiment at two locations: Posto da Mata (Bahia, Brazil) and São Mateus (Minas Gerais, Brazil). Four checks were randomly allocated within each block. Plots consisted of 15 m long rows containing 6 plants spaced 3 m apart. The girth at breast height (cm/plant) was evaluated at 19 and 26 months of age. Variance analyses were performed according to the following methods: lattice design, randomized complete block design, augmented block design, Papadakis method, moving means method, and check plots. Comparisons among different methods were based on the magnitude of experimental errors and precision of the estimates of genetic and phenotypic parameters. General results indicated that augmented block design is useful to evaluate progenies and clones in early selection in eucalyptus breeding programs using moderate and low selection intensities. However, this design is not suitable for estimating genetic and phenotypic parameters due to its low precision. Check plots, nearest neighbour, Papadakis (1937), and moving means methods were efficient in removing the heterogeneity within blocks. These efficiencies were compared to that in lattice analysis for estimation of genetic and phenotypic parameters.

ESTIMATION OF CORK PRODUCTION USINGAERIAL IMAGERY1

ABSTRACT Inventory and prediction of cork harvest over time and space is important to forest managers who must plan and organize harvest logistics (transport, storage, etc.). Common field inventory methods including the stem density, diameter and height structure are costly and generally point (plot) based. Furthermore, the irregular horizontal structure of cork oak stands makes it difficult, if not impossible, to interpolate between points. We propose a new method to estimate cork production using digital multispectral aerial imagery. We study the spectral response of individual trees in visible and near infrared spectra and then correlate that response with cork production prior to harvest. We use ground measurements of individual trees production to evaluate the model’s predictive capacity. We propose 14 candidate variables to predict cork production based on crown size in combination with different NDVI index derivates. We use Akaike Information Criteria to choose the best among them. The best model is composed of combinations of different NDVI derivates that include red, green, and blue channels. The proposed model is 15% more accurate than a model that includes only a crown projection without any spectral information.

Estimation of the potential evapotranspiration by a simplified penman method

The numerous methods for calculating the potential or reference evapotranspiration (ETo or ETP) almost always do for a 24-hour period, including values of climatic parameters throughout the nocturnal period (daily averages). These results have a nil effect on transpiration, constituting the main evaporative demand process in cases of localized irrigation. The aim of the current manuscript was to come up with a model rather simplified for the calculation of diurnal daily ETo. It deals with an alternative approach based on the theoretical background of the Penman method without having to consider values of aerodynamic conductance of latent and sensible heat fluxes, as well as data of wind speed and relative humidity of the air. The comparison between the diurnal values of ETo measured in weighing lysimeters with elevated precision and estimated by either the Penman-Monteith method or the Simplified-Penman approach in study also points out a fairly consistent agreement among the potential demand calculation criteria. The Simplified-Penman approach was a feasible alternative to estimate ETo under the local meteorological conditions of two field trials. With the availability of the input data required, such a method could be employed in other climatic regions for scheduling irrigation.

Method of numerical correction of errors occasioned by delay of records during the monitoring of environmental variables of interest for animal production

Thermal and air conditions inside animal facilities change during the day due to the influence of the external environment. For statistical and geostatistical analyses to be representative, a large number of points spatially distributed in the facility area must be monitored. This work suggests that the time variation of environmental variables of interest for animal production, monitored within animal facility, can be modeled accurately from discrete-time records. The aim of this study was to develop a numerical method to correct the temporal variations of these environmental variables, transforming the data so that such observations are independent of the time spent during the measurement. The proposed method approached values recorded with time delays to those expected at the exact moment of interest, if the data were measured simultaneously at the moment at all points distributed spatially. The correction model for numerical environmental variables was validated for environmental air temperature parameter, and the values corrected by the method did not differ by Tukey's test at 5% significance of real values recorded by data loggers.

Comparison of maps of spatial variability of soil resistance to penetration constructed with and without covariables using a spatial linear model

A study about the spatial variability of data of soil resistance to penetration (RSP) was conducted at layers 0.0-0.1 m, 0.1-0.2 m and 0.2-0.3 m depth, using the statistical methods in univariate forms, i.e., using traditional geostatistics, forming thematic maps by ordinary kriging for each layer of the study. It was analyzed the RSP in layer 0.2-0.3 m depth through a spatial linear model (SLM), which considered the layers 0.0-0.1 m and 0.1-0.2 m in depth as covariable, obtaining an estimation model and a thematic map by universal kriging. The thematic maps of the RSP at layer 0.2-0.3 m depth, constructed by both methods, were compared using measures of accuracy obtained from the construction of the matrix of errors and confusion matrix. There are similarities between the thematic maps. All maps showed that the RSP is higher in the north region.

Estimation of transpiration of the 'Valencia' orange young plant using thermal dissipation probe method

Most studies on measures of transpiration of plants, especially woody fruit, relies on methods of heat supply in the trunk. This study aimed to calibrate the Thermal Dissipation Probe Method (TDP) to estimate the transpiration, study the effects of natural thermal gradients and determine the relation between outside diameter and area of xylem in 'Valencia' orange young plants. TDP were installed in 40 orange plants of 15 months old, planted in boxes of 500 L, in a greenhouse. It was tested the correction of the natural thermal differences (DTN) for the estimation based on two unheated probes. The area of the conductive section was related to the outside diameter of the stem by means of polynomial regression. The equation for estimation of sap flow was calibrated having as standard lysimeter measures of a representative plant. The angular coefficient of the equation for estimating sap flow was adjusted by minimizing the absolute deviation between the sap flow and daily transpiration measured by lysimeter. Based on these results, it was concluded that the method of TDP, adjusting the original calibration and correction of the DTN, was effective in transpiration assessment.

Estimation of evaporation in the Banabuiú dam, in the state of Ceará, Brazil, by different combined methods, derived from the Penman equation

The state of Ceará, Brazil, has 75% of its area covered by Brazilian semiarid, with its peculiar features. In this state, the dams are constituted in water structure of strategic importance, ensuring, both in time and space, the development and supply of water to population. However, construction of reservoirs results in various impacts that should be carefully observed when deciding on their implementation. One of the impacts identified as negative is the increased evaporation, which constitutes a major component of water balance in reservoirs, especially in arid regions. Several methods for estimating evaporation have been proposed over time, many of them deriving from the Penman equation. This study evaluated six different methods for estimating evaporation in order to determine the most suitable for use in hydrological models for water balance in reservoirs in the state of Ceará. The tested methods were proposed by Penman, Kohler-Nordenson-Fox, Priestley-Taylor, deBruim-Keijman, Brutsaert-Stricker and deBruim. The methods presented good performance when tested for water balance during the dry season, and the Priestley-Taylor was the most appropriate, since the data from de simulated water balance with evaporation estimated by this method were the closest of the water balance data observed from measures of reservoir level and the elevation-volume curve provided by the Company of Management of Water Resources of the state of Ceará - COGERH.

Construction and calibration of TDR probes for volumetric water content estimation in a Distroferric Red Latosol

The determination of volumetric water content of soils is an important factor in irrigation management. Among the indirect methods for estimating, the time-domain reflectometry (TDR) technique has received a significant attention. Like any other technique, it has advantages and disadvantages, but its greatest disadvantage is the need of calibration and high cost of acquisition. The main goal of this study was to establish a calibration model for the TDR equipment, Trase System Model 6050X1, to estimate the volumetric water content in a Distroferric Red Latosol. The calibration was carried out in a laboratory with disturbed soil samples under study, packed in PVC columns of a volume of 0.0078m³. The TDR probes were handcrafted with three rods and 0.20m long. They were vertically installed in soil columns, with a total of five probes per column and sixteen columns. The weightings were carried out in a digital scale, while daily readings of dielectric constant were obtained in TDR equipment. The linear model θν = 0.0103 Ka + 0.1900 to estimate the studied volumetric water content showed an excellent coefficient of determination (0.93), enabling the use of probes in indirect estimation of soil moisture.

Estimation of alluvial recharge in the semiarid

In areas where there is irrigated agriculture, the recuperation of water reserves in alluvial aquifers may occur preferentially due to precipitation. Recharging can be evaluated from variation information of water depth measured in piezometers or observation wells. Thus, the aim of this research is to study the recharge in the alluvial aquifer formed by the Mimoso temporary stream in the semiarid region of Pernambuco (PE), Brazil, using the method of the fluctuation of the water level. This system is typical on the Brazilian Northeast semiarid region, using groundwater for domestic supply and for irrigation on small scale agriculture. Monthly potentiometric levels and rainfall data were used. The selected period for the study, from January 2002 to October 2009, involved extreme events of flooding and droughts as well as regular years, providing a better understanding of the behavior of the alluvial recharge. It was found that the system responds significantly to precipitation events. It was also observed that even with different soil textures in the study area, recharge factors were not significantly different. The study provided a better understanding of the behavior of aquifer recharge and its relationship with the soil and the rainfall events in the region.

Validation study of an overall radiation balance estimation method under Ponta Grossa (PR) Brazil weather conditions

Radiation balance is the fraction of incident solar radiation upon earth surface which is available to be used in several natural processes, such as biological metabolism, water loss by vegetated surfaces, variation of temperature in farming systems and organic decomposition. The present study aimed to assess and validate the performance of two estimation models for Rn in Ponta Grossa city, Paraná State, Brazil. To this end, during the period of 04/01/2008 to 04/30/2011, from radiometric data collected by an automatic weather station set at the Experimental Station, of the State University of Ponta Grossa. We performed a linear regression study by confrontation between measurements made through radiometric balance and Rn estimates obtained from Brunt classical method, and the proposed method. Both models showed excellent performance and were confirmed by the statistical parameters applied. However, the alternative method has the advantage of requiring only global solar radiation values, temperature, and relative humidity.