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.

Logistic regression to estimate the welfare of broiler breeders in relation to environmental and behavioral variables

The increasing demand of consumer markets for the welfare of birds in poultry house has motivated many scientific researches to monitor and classify the welfare according to the production environment. Given the complexity between the birds and the environment of the aviary, the correct interpretation of the conduct becomes an important way to estimate the welfare of these birds. This study obtained multiple logistic regression models with capacity of estimating the welfare of broiler breeders in relation to the environment of the aviaries and behaviors expressed by the birds. In the experiment, were observed several behaviors expressed by breeders housed in a climatic chamber under controlled temperatures and three different ammonia concentrations from the air monitored daily. From the analysis of the data it was obtained two logistic regression models, of which the first model uses a value of ammonia concentration measured by unit and the second model uses a binary value to classify the ammonia concentration that is assigned by a person through his olfactory perception. The analysis showed that both models classified the broiler breeder's welfare successfully.

Adjust of regression models to estimate the rectal temperature of broilers for the first 14 days of life

The broiler rectal temperature (t rectal) is one of the most important physiological responses to classify the animal thermal comfort. Therefore, the aim of this study was to adjust regression models in order to predict the rectal temperature (t rectal) of broiler chickens under different thermal conditions based on age (A) and a meteorological variable (air temperature - t air) or a thermal comfort index (temperature and humidity index -THI or black globe humidity index - BGHI) or a physical quantity enthalpy (H). In addition, through the inversion of these models and the expected t rectal intervals for each age, the comfort limits of t air, THI, BGHI and H for the chicks in the heating phase were determined, aiding in the validation of the equations and the preliminary limits for H. The experimental data used to adjust the mathematical models were collected in two commercial poultry farms, with Cobb chicks, from 1 to 14 days of age. It was possible to predict the t rectal of conditions from the expected t rectal and determine the lower and superior comfort thresholds of broilers satisfactorily by applying the four models adjusted; as well as to invert the models for prediction of the environmental H for the chicks first 14 days of life.

The cardiopulmonary reflexes of spontaneously hypertensive rats are normalized after regression of left ventricular hypertrophy and hypertension

Cardiopulmonary reflexes are activated via changes in cardiac filling pressure (volume-sensitive reflex) and chemical stimulation (chemosensitive reflex). The sensitivity of the cardiopulmonary reflexes to these stimuli is impaired in the spontaneously hypertensive rat (SHR) and other models of hypertension and is thought to be associated with cardiac hypertrophy. The present study investigated whether the sensitivity of the cardiopulmonary reflexes in SHR is restored when cardiac hypertrophy and hypertension are reduced by enalapril treatment. Untreated SHR and WKY rats were fed a normal diet. Another groups of rats were treated with enalapril (10 mg kg-1 day-1, mixed in the diet; SHRE or WKYE) for one month. After treatment, the volume-sensitive reflex was evaluated in each group by determining the decrease in magnitude of the efferent renal sympathetic nerve activity (RSNA) produced by acute isotonic saline volume expansion. Chemoreflex sensitivity was evaluated by examining the bradycardia response elicited by phenyldiguanide administration. Cardiac hypertrophy was determined from the left ventricular/body weight (LV/BW) ratio. Volume expansion produced an attenuated renal sympathoinhibitory response in SHR as compared to WKY rats. As compared to the levels observed in normotensive WKY rats, however, enalapril treatment restored the volume expansion-induced decrease in RSNA in SHRE. SHR with established hypertension had a higher LV/BW ratio (45%) as compared to normotensive WKY rats. With enalapril treatment, the LV/BW ratio was reduced to 19% in SHRE. Finally, the reflex-induced bradycardia response produced by phenyldiguanide was significantly attenuated in SHR compared to WKY rats. Unlike the effects on the volume reflex, the sensitivity of the cardiac chemosensitive reflex to phenyldiguanide was not restored by enalapril treatment in SHRE. Taken together, these results indicate that the impairment of the volume-sensitive, but not the chemosensitive, reflex can be restored by treatment of SHR with enalapril. It is possible that by augmenting the gain of the volume-sensitive reflex control of RSNA, enalapril contributed to the reversal of cardiac hypertrophy and normalization of arterial blood pressure in SHR.

Multivariate study and regression analysis of gluten-free granola

This study developed a gluten-free granola and evaluated it during storage with the application of multivariate and regression analysis of the sensory and instrumental parameters. The physicochemical, sensory, and nutritional characteristics of a product containing quinoa, amaranth and linseed were evaluated. The crude protein and lipid contents ranged from 97.49 and 122.72 g kg-1 of food, respectively. The polyunsaturated/saturated, and n-6:n-3 fatty acid ratios ranged from 2.82 and 2.59:1, respectively. Granola had the best alpha-linolenic acid content, nutritional indices in the lipid fraction, and mineral content. There were good hygienic and sanitary conditions during storage; probably due to the low water activity of the formulation, which contributed to inhibit microbial growth. The sensory attributes ranged from 'like very much' to 'like slightly', and the regression models were highly fitted and correlated during the storage period. A reduction in the sensory attribute levels and in the product physical stabilisation was verified by principal component analysis. The use of the affective test acceptance and instrumental analysis combined with statistical methods allowed us to obtain promising results about the characteristics of gluten-free granola.

Equacionamento da qualidade inicial de sementes de milho e soja para aplicação no modelo de probit

Objetivou-se, neste trabalho, equacionar a qualidade inicial das sementes (Ki), utilizada no modelo de probit, para a previsão da longevidade de sementes de milho (Zea mays) e soja (Glycine max), em função do resultado dos testes iniciais de germinação e vigor. Onze lotes de sementes de diferentes cultivares de milho e de soja foram submetidos aos testes de germinação (TG), envelhecimento acelerado (TEA), frio sem solo (TF), para milho, e tetrazólio (TZ), para soja, e a testes de envelhecimento acelerado, com condições constantes do grau de umidade e da temperatura das sementes, para determinar o valor de Ki. Dados da literatura contendo resultados de testes de TEA e TF para milho e TEA e TZ para soja também foram usados nesta pesquisa. Conduziram-se análises de regressão linear simples e múltipla para equacionar: a) Ki em função de TG e TEA para milho e soja, b) TEAm (envelhecimento acelerado do milho) em função de TF; c) TEAs (envelhecimento acelerado da soja) em função de TZ. As equações obtidas foram: Ki = 0,4230 + 0,4464 TG + 0,4131 TEA TEA M = - 0,4408 + 1,214 TF TEA S = - 0,1872 + 0,9875 TZ. A equação de Ki apresentou coeficiente de determinação ajustado (r²) de 0.80 (d.p. 0.18 probit e parâmetros significantes em p < 0.01, p < 0.02 e p < 0.05, respectivamente). A equação de TEAm apresentou r² de 0.80 (d.p. 0.24 probit e parâmetros significantes em p < 0.002). A equação de TEAs apresentou r² de 0.84 (d.p. 0.18 probit e parâmetros significantes em p < 0.005). O valor de Ki pode ser equacionado em função do resultado dos testes iniciais de germinação e vigor para milho e soja (TEA ou TF para milho e TEA ou TZ para soja).