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.

Comparing the artificial neural network with parcial least squares for prediction of soil organic carbon and pH at different moisture content levels using visible and near-infrared spectroscopy

Visible and near infrared (vis-NIR) spectroscopy is widely used to detect soil properties. The objective of this study is to evaluate the combined effect of moisture content (MC) and the modeling algorithm on prediction of soil organic carbon (SOC) and pH. Partial least squares (PLS) and the Artificial neural network (ANN) for modeling of SOC and pH at different MC levels were compared in terms of efficiency in prediction of regression. A total of 270 soil samples were used. Before spectral measurement, dry soil samples were weighed to determine the amount of water to be added by weight to achieve the specified gravimetric MC levels of 5, 10, 15, 20, and 25 %. A fiber-optic vis-NIR spectrophotometer (350-2500 nm) was used to measure spectra of soil samples in the diffuse reflectance mode. Spectra preprocessing and PLS regression were carried using Unscrambler® software. Statistica® software was used for ANN modeling. The best prediction result for SOC was obtained using the ANN (RMSEP = 0.82 % and RPD = 4.23) for soil samples with 25 % MC. The best prediction results for pH were obtained with PLS for dry soil samples (RMSEP = 0.65 % and RPD = 1.68) and soil samples with 10 % MC (RMSEP = 0.61 % and RPD = 1.71). Whereas the ANN showed better performance for SOC prediction at all MC levels, PLS showed better predictive accuracy of pH at all MC levels except for 25 % MC. Therefore, based on the data set used in the current study, the ANN is recommended for the analyses of SOC at all MC levels, whereas PLS is recommended for the analysis of pH at MC levels below 20 %.

Classification of brain tumor extracts by high resolution ¹H MRS using partial least squares discriminant analysis

High resolution proton nuclear magnetic resonance spectroscopy (¹H MRS) can be used to detect biochemical changes in vitro caused by distinct pathologies. It can reveal distinct metabolic profiles of brain tumors although the accurate analysis and classification of different spectra remains a challenge. In this study, the pattern recognition method partial least squares discriminant analysis (PLS-DA) was used to classify 11.7 T ¹H MRS spectra of brain tissue extracts from patients with brain tumors into four classes (high-grade neuroglial, low-grade neuroglial, non-neuroglial, and metastasis) and a group of control brain tissue. PLS-DA revealed 9 metabolites as the most important in group differentiation: γ-aminobutyric acid, acetoacetate, alanine, creatine, glutamate/glutamine, glycine, myo-inositol, N-acetylaspartate, and choline compounds. Leave-one-out cross-validation showed that PLS-DA was efficient in group characterization. The metabolic patterns detected can be explained on the basis of previous multimodal studies of tumor metabolism and are consistent with neoplastic cell abnormalities possibly related to high turnover, resistance to apoptosis, osmotic stress and tumor tendency to use alternative energetic pathways such as glycolysis and ketogenesis.

Quantification of the least limiting water range in an oxisol using two methodological strategies

The least limiting water range (LLWR) has been used as an indicator of soil physical quality as it represents, in a single parameter, the soil physical properties directly linked to plant growth, with the exception of temperature. The usual procedure for obtaining the LLWR involves determination of the water retention curve (WRC) and the soil resistance to penetration curve (SRC) in soil samples with undisturbed structure in the laboratory. Determination of the WRC and SRC using field measurements (in situ ) is preferable, but requires appropriate instrumentation. The objective of this study was to determine the LLWR from the data collected for determination of WRC and SRC in situ using portable electronic instruments, and to compare those determinations with the ones made in the laboratory. Samples were taken from the 0.0-0.1 m layer of a Latossolo Vermelho distrófico (Oxisol). Two methods were used for quantification of the LLWR: the traditional, with measurements made in soil samples with undisturbed structure; and in situ , with measurements of water content (θ), soil water potential (Ψ), and soil resistance to penetration (SR) through the use of sensors. The in situ measurements of θ, Ψ and SR were taken over a period of four days of soil drying. At the same time, samples with undisturbed structure were collected for determination of bulk density (BD). Due to the limitations of measurement of Ψ by tensiometer, additional determinations of θ were made with a psychrometer (in the laboratory) at the Ψ of -1500 kPa. The results show that it is possible to determine the LLWR by the θ, Ψ and SR measurements using the suggested approach and instrumentation. The quality of fit of the SRC was similar in both strategies. In contrast, the θ and Ψ in situ measurements, associated with those measured with a psychrometer, produced a better WRC description. The estimates of the LLWR were similar in both methodological strategies. The quantification of LLWR in situ can be achieved in 10 % of the time required for the traditional method.

Optimization of wood flour acetylation by factorial design and partial least squares regression

Acetylation was performed to reduce the polarity of wood and increase its compatibility with polymer matrices for the production of composites. These reactions were performed first as a function of acetic acid and anhydride concentration in a mixture catalyzed by sulfuric acid. A concentration of 50%/50% (v/v) of acetic acid and anhydride was found to produced the highest conversion rate between the functional groups. After these reactions, the kinetics were investigated by varying times and temperatures using a 3² factorial design, and showed time was the most relevant parameter in determining the conversion of hydroxyl into carbonyl groups.

Alternative methodology for calculating the modulus of elasticity of wooden beams of structural dimensions

This study aims to present an alternative calculation methodology based on the Least Squares Method for determining the modulus of elasticity in bending wooden beams of structural dimensions. The equations developed require knowledge of three or five points measured in displacements along the piece, allowing greater reliability on the response variable, using the statistical bending test at three points and non-destructively, resulting from imposition of measures from small displacements L/300 and L/200, the largest being stipulated by the Brazilian norm NBR 7190:1997. The woods tested were Angico, Cumaru, Garapa and Jatoba. Besides obtaining the modulus of elasticity through the alternative methodology proposed, these were also obtained employing the Brazilian norm NBR 7190:1997, adapted to the condition of non-destructive testing (small displacements) and for pieces of structural dimensions. The results of the modulus of elasticity of the four species of wood according to both calculation approaches used proved to be equivalent, implying the good approximation provided by the methodology of calculation adapted from the Brazilian norm.

Application of the Hsu model to soybean grain hydration

A comparative analysis of the theoretical-experimental study, developed by Hsu on the hydration of Amsoy 71 soybean grain, was performed through several soaking experiments using CD 202 soybean at 10, 20, 30, 40, and 50 °C, measuring moisture content over time. The results showed that CD 202 soybean equilibrium moisture content, Xeq, does not depend on temperature and is 21% higher than that found by Hsu, suggesting that soybean cultivar exerts great influence on Xeq. The Hsu model was numerically solved and its parameters were adjusted by the least squares method, with maximum deviations of +/- 10% relative to the experimental values. The limiting step in the mass transfer process during hydration corresponds to water diffusion inside the grain, leading to radial moisture gradients that decrease over time and with an increase in temperature. Regardless of the soybean cultivar, diffusivity increases as temperature or moisture content increases. However, the values of this transport property for Amsoy 71 were superior to those of CD 202, very close at the beginning of hydration at 20 °C and almost three times higher at the end of hydration at 50 °C.

Sôbre uma propriedade da equação utilizada para interpolação da Lei de Mitscherlich

The author proves that equation, Σy n ΣZx | ΣxyZx ΣxZx ΣxZ2x | = 0, Σy ΣZx Σy2x | where Z = 10-cq and q is a numerical constant, used by Pimentel Gomes and Malavolta in several articles for the interpolation of Mitscherlih's equation y = A [ 1 - 10 - c (x + b) ] by the least squares method, always has a zero of order three for Z = 1. Therefore, equation A Zm + A1Zm -1 + ........... + Am = 0 obtained from that determinant can be divided by (Z-1)³. This property provides a good test for the correctness of the computations and facilitates the solution of the equation.

pH effect on the synthesis of magnetite nanoparticles by the chemical reduction-precipitation method

This work aimed at putting in evidence the influence of the pH on the chemical nature and properties of the synthesized magnetic nanocomposites. Saturation magnetization measurements evidenced a marked difference of the magnetic behavior of samples, depending on the final pH of the solution after reaction. Magnetite and maghemite in different proportions were the main magnetic iron oxides actually identified. Synthesis with final pH between 9.7-10.6 produced nearly pure magnetite with little or no other associated iron oxide. Under other synthetic conditions, goethite also appears in proportions that depended upon the pH of the synthesis medium.

Studies on the development of spectrophotometric method for the determination of haloperidol in pharmaceutical preparations

A spectrophotometric method based on the formation of ion-pair complex between haloperidol and eriochrome black T (EBT) at pH 1.85 has been described. The formed complex was extracted quantitatively into chloroform and measured at 510 nm. Infra red (IR) studies were performed to confirm the formation of ion-pair complex. Beer's law was obeyed in the concentration range of 2.0-9.0 µg mL-1 with molar absorptivity of 2.67 × 10(4) L mol-1 cm-1. The detection limit was found to be 0.18 µg mL-1. Statistical comparison of the results of the proposed method with those of the reference method shows excellent agreement and indicates no significant difference in accuracy and precision.

The Li+, Na+ and K+ ion exchange reaction process on the surface of mixed oxide SiO2/TiO2/Sb2O5 surface prepared by the sol-gel processing method

The porous mixed oxide SiO2/TiO2/Sb2O5 obtained by the sol-gel processing method presented a good ion exchange property and a high exchange capacity towards the Li+, Na+ and K+ ions. In the H+/M+ ion exchange process, the H+ / Na+ could be described as presenting an ideal character. The ion exchange equilibria of Li+ and K+ were quantitatively described with the help of the model of fixed tetradentate centers. The results of simulation evidence that for the H+ / Li+ exchange the usual situation takes place: the affinity of the material to the Li+ ions is decreased with increasing the degree of ion exchange. On the contrary, for K+ the effects of positive cooperativity, that facilitate the H+ / K+ exchange, were revealed.

Adsorption of hidrogen peroxide on the surface of silica - titania mixed oxide obtained by the sol-gel processing method

This work describes the sol-gel mixed oxide SiO2/TiO2 property, ST, as prepared, and submitted to heat treatment a 773 K, STC. SEM and EDS images show, within magnification used, a uniform distribution of the TiO2 particles in SiO2/TiO2 matrix. Both, ST and STC adsorb hydrogen peroxide on the surface and through EPR and UV-Vis diffuse reflectance spectra, it was possible to conclude that the species on the surface is the peroxide molecule attached to the Lewis acid site of titanium particle surface, alphaTi(H2O2)+. As the material is very porous, presumably the hydrogen peroxide molecule is confined in the matrix pores on the surface, a reason why the adsorbed species presents an exceptional long lived stability.

Escaping the flybottle: solipsism and method in Wittgenstein's Philosophical Remarks

The paper supports a dialectical interpretation of Wittgenstein's method focusing on the analysis of the conditions of experience presented in his Philosophical Remarks. By means of a close reading of some key passages dealing with solipsism I will try to lay bare their self-subverting character: the fact that they amount to miniature dialectical exercises offering specific directions to pass from particular pieces of disguised nonsense to corresponding pieces of patent nonsense. Yet, in order to follow those directions one needs to allow oneself to become simultaneously tempted by and suspicious of their all-too-evident "metaphysical tone" - a tone which, as we shall see, is particularly manifest in those claims purporting to state what can or cannot be the case, and, still more particularly, those purporting to state what can or cannot be done in language or thought, thus leading to the view that there are some (determinate) things which are ineffable or unthinkable. I conclude by suggesting that in writing those remarks Wittgenstein was still moved by an ethical project, which gets conspicuously displayed in these reiterations of his attempts to cure the readers (and himself) from some of the temptations expressed by solipsism.

Effects of pentoxifylline treatment before freezing on motility, viability and acrosome status of poor quality human spermatozoa cryopreserved by the liquid nitrogen vapor method

The objective of the present study was to investigate the effects of the direct addition of pentoxifylline (PF) to the ejaculates of men with poor sperm quality before freezing on post-thaw sperm motility, viability, acrosome integrity, and agonist-induced acrosome reaction. Semen specimens from 16 infertile men with impaired sperm count and motility (oligoasthenozoospermia) were divided into two equal aliquots: one received no treatment (control) while the other was incubated with 5 mM PF (treated). Both aliquots were cryopreserved by the liquid nitrogen vapor method. Motility was assessed according to WHO criteria. Acrosome integrity and spontaneous and calcium ionophore-induced acrosome reactions were assessed with fluorescein isothiocyanate-conjugated peanut agglutinin combined with a supra-vital dye (Hoechst-33258). Cryopreservation impaired sperm motility (percentage reduction: 87.4 (interquartile range, IQ: 70.3-92.9) vs 89.1 (IQ: 72.7-96.0%)), viability (25.9 (IQ: 22.2-29.7) vs 25.6 (IQ: 19.7-40.3%)) and acrosome integrity (18.9 (IQ: 5.4-38.9) vs 26.8 (IQ: 0.0-45.2%)) to the same extent in both treated and control aliquots. However, PF treatment before freezing improved the acrosome reaction to ionophore challenge test scores in cryopreserved spermatozoa (9.7 (IQ: 6.6-19.7) vs 4.8 (IQ: 0.5-6.8%); P = 0.002). These data show that pre-freeze treatment of poor quality human sperm with pentoxifylline did not improve post-thaw motility or viability nor did it prevent acrosomal loss during the freeze-thaw process. However, PF, as used, improved the ability of thawed spermatozoa to undergo the acrosome reaction in response to calcium ionophore. The present data indicate that treatment of poor quality human sperm with PF may enhance post-thaw sperm fertilizing ability.