Multiple Linear Regression and Artificial Neural Networks to Predict Time and Efficiency of Soil Vapor Extraction

The prediction of the time and the efficiency of the remediation of contaminated soils using soil vapor extraction remain a difficult challenge to the scientific community and consultants. This work reports the development of multiple linear regression and artificial neural network models to predict the remediation time and efficiency of soil vapor extractions performed in soils contaminated separately with benzene, toluene, ethylbenzene, xylene, trichloroethylene, and perchloroethylene. The results demonstrated that the artificial neural network approach presents better performances when compared with multiple linear regression models. The artificial neural network model allowed an accurate prediction of remediation time and efficiency based on only soil and pollutants characteristics, and consequently allowing a simple and quick previous evaluation of the process viability.

Methods of Estimation in Multiple Linear Regression: Application to Clinical Data

Nesse artigo, tem-se o interesse em avaliar diferentes estratégias de estimação de parâmetros para um modelo de regressão linear múltipla. Para a estimação dos parâmetros do modelo foram utilizados dados de um ensaio clínico em que o interesse foi verificar se o ensaio mecânico da propriedade de força máxima (EM-FM) está associada com a massa femoral, com o diâmetro femoral e com o grupo experimental de ratas ovariectomizadas da raça Rattus norvegicus albinus, variedade Wistar. Para a estimação dos parâmetros do modelo serão comparadas três metodologias: a metodologia clássica, baseada no método dos mínimos quadrados; a metodologia Bayesiana, baseada no teorema de Bayes; e o método Bootstrap, baseado em processos de reamostragem.

A Combinatorial Approach to the Variable Selection in Multiple Linear Regression: Analysis of Selwood et al Data set -A Case Study.

A combinatorial protocol (CP) is introduced here to interface it with the multiple linear regression (MLR) for variable selection. The efficiency of CP-MLR is primarily based on the restriction of entry of correlated variables to the model development stage. It has been used for the analysis of Selwood et al data set [16], and the obtained models are compared with those reported from GFA [8] and MUSEUM [9] approaches. For this data set CP-MLR could identify three highly independent models (27, 28 and 31) with Q2 value in the range of 0.632-0.518. Also, these models are divergent and unique. Even though, the present study does not share any models with GFA [8], and MUSEUM [9] results, there are several descriptors common to all these studies, including the present one. Also a simulation is carried out on the same data set to explain the model formation in CP-MLR. The results demonstrate that the proposed method should be able to offer solutions to data sets with 50 to 60 descriptors in reasonable time frame. By carefully selecting the inter-parameter correlation cutoff values in CP-MLR one can identify divergent models and handle data sets larger than the present one without involving excessive computer time.

Data analysis methods in optometry Part 7: multiple linear regression

Multiple regression analysis is a complex statistical method with many potential uses. It has also become one of the most abused of all statistical procedures since anyone with a data base and suitable software can carry it out. An investigator should always have a clear hypothesis in mind before carrying out such a procedure and knowledge of the limitations of each aspect of the analysis. In addition, multiple regression is probably best used in an exploratory context, identifying variables that might profitably be examined by more detailed studies. Where there are many variables potentially influencing Y, they are likely to be intercorrelated and to account for relatively small amounts of the variance. Any analysis in which R squared is less than 50% should be suspect as probably not indicating the presence of significant variables. A further problem relates to sample size. It is often stated that the number of subjects or patients must be at least 5-10 times the number of variables included in the study.5 This advice should be taken only as a rough guide but it does indicate that the variables included should be selected with great care as inclusion of an obviously unimportant variable may have a significant impact on the sample size required.

Predicting class I major histocompatibility complex (MHC) binders using multivariate statistics:comparison of discriminant analysis and multiple linear regression

The accurate in silico identification of T-cell epitopes is a critical step in the development of peptide-based vaccines, reagents, and diagnostics. It has a direct impact on the success of subsequent experimental work. Epitopes arise as a consequence of complex proteolytic processing within the cell. Prior to being recognized by T cells, an epitope is presented on the cell surface as a complex with a major histocompatibility complex (MHC) protein. A prerequisite therefore for T-cell recognition is that an epitope is also a good MHC binder. Thus, T-cell epitope prediction overlaps strongly with the prediction of MHC binding. In the present study, we compare discriminant analysis and multiple linear regression as algorithmic engines for the definition of quantitative matrices for binding affinity prediction. We apply these methods to peptides which bind the well-studied human MHC allele HLA-A*0201. A matrix which results from combining results of the two methods proved powerfully predictive under cross-validation. The new matrix was also tested on an external set of 160 binders to HLA-A*0201; it was able to recognize 135 (84%) of them.

Dimension Reduction of the Explanatory Variables in Multiple Linear Regression

2002 Mathematics Subject Classification: 62J05, 62G35.

Applying Least Absolute Shrinkage Selection Operator and Akaike Information Criterion Analysis to Find the Best Multiple Linear Regression Models between Climate Indices and Components of Cow’s Milk

This study focuses on multiple linear regression models relating six climate indices (temperature humidity THI, environmental stress ESI, equivalent temperature index ETI, heat load HLI, modified HLI (HLI new), and respiratory rate predictor RRP) with three main components of cow’s milk (yield, fat, and protein) for cows in Iran. The least absolute shrinkage selection operator (LASSO) and the Akaike information criterion (AIC) techniques are applied to select the best model for milk predictands with the smallest number of climate predictors. Uncertainty estimation is employed by applying bootstrapping through resampling. Cross validation is used to avoid over-fitting. Climatic parameters are calculated from the NASA-MERRA global atmospheric reanalysis. Milk data for the months from April to September, 2002 to 2010 are used. The best linear regression models are found in spring between milk yield as the predictand and THI, ESI, ETI, HLI, and RRP as predictors with p-value < 0.001 and R2 (0.50, 0.49) respectively. In summer, milk yield with independent variables of THI, ETI, and ESI show the highest relation (p-value < 0.001) with R2 (0.69). For fat and protein the results are only marginal. This method is suggested for the impact studies of climate variability/change on agriculture and food science fields when short-time series or data with large uncertainty are available.

Multiple linear and principal component regressions for modelling ecotoxicity bioassay response

The ecotoxicological response of the living organisms in an aquatic system depends on the physical, chemical and bacteriological variables, as well as the interactions between them. An important challenge to scientists is to understand the interaction and behaviour of factors involved in a multidimensional process such as the ecotoxicological response.With this aim, multiple linear regression (MLR) and principal component regression were applied to the ecotoxicity bioassay response of Chlorella vulgaris and Vibrio fischeri in water collected at seven sites of Leça river during five monitoring campaigns (February, May, June, August and September of 2006). The river water characterization included the analysis of 22 physicochemical and 3 microbiological parameters. The model that best fitted the data was MLR, which shows: (i) a negative correlation with dissolved organic carbon, zinc and manganese, and a positive one with turbidity and arsenic, regarding C. vulgaris toxic response; (ii) a negative correlation with conductivity and turbidity and a positive one with phosphorus, hardness, iron, mercury, arsenic and faecal coliforms, concerning V. fischeri toxic response. This integrated assessment may allow the evaluation of the effect of future pollution abatement measures over the water quality of Leça River.

Comparison of Some Improved Estimators for Linear Regression Model under Different Conditions

Multiple linear regression model plays a key role in statistical inference and it has extensive applications in business, environmental, physical and social sciences. Multicollinearity has been a considerable problem in multiple regression analysis. When the regressor variables are multicollinear, it becomes difficult to make precise statistical inferences about the regression coefficients. There are some statistical methods that can be used, which are discussed in this thesis are ridge regression, Liu, two parameter biased and LASSO estimators. Firstly, an analytical comparison on the basis of risk was made among ridge, Liu and LASSO estimators under orthonormal regression model. I found that LASSO dominates least squares, ridge and Liu estimators over a significant portion of the parameter space for large dimension. Secondly, a simulation study was conducted to compare performance of ridge, Liu and two parameter biased estimator by their mean squared error criterion. I found that two parameter biased estimator performs better than its corresponding ridge regression estimator. Overall, Liu estimator performs better than both ridge and two parameter biased estimator.

Obstructive Sleep Apnea Is Common and Independently Associated With Atrial Fibrillation in Patients With Hypertrophic Cardiomyopathy

Background: Hypertrophic cardiomyopathy (HCM) is associated with arrhythmias and cardiovascular death. Left atrial enlargement and atrial fibrillation (AF) are considered markers for death due to heart failure in patients with HCM. Obstructive sleep apnea (OSA) is independently associated with heart remodeling and arrhythmias in other populations. We hypothesized that OSA is common and is associated with heart remodeling and AF in patients with HCM. Methods: We evaluated 80 consecutive stable patients with a confirmed diagnosis of HCM by sleep questionnaire, blood tests, echocardiography, and sleep study (overnight respiratory monitoring). Results: OSA (apnea-hypopnea index [AHI] > 15 events/h) was present in 32 patients (40%). Patients with OSA were significantly older (56 [41-64] vs 38.5 [30-53] years, P < .001) and presented higher BMI (28.2 +/- 3.5 vs 25.2 +/- 5.2 kg/m(2), P < .01) and increased left atrial diameter (45 [42-52.8] vs 41 [39-47] mm, P = .01) and aorta diameter (34 [30-37] vs 29 [28-32] mm, P < .001), compared with patients without OSA. Stepwise multiple linear regression showed that the AHI (P = .05) and BMI (P = .06) were associated with left atrial diameter. The AHI was the only variable associated with aorta diameter (P = .01). AF was present in 31% vs 6% of patients with and without OSA, respectively (P < .01). OSA (P = .03) and left atrial diameter (P = .03) were the only factors independently associated with AF. Conclusions: OSA is highly prevalent in patients with HCM and it is associated with left atrial and aortic enlargement. OSA is independently associated with AF, a risk factor for cardiovascular death in this population. CHEST 2010; 137(5):1078-1084

Performance of classic electrocardiographic criteria for left ventricular hypertrophy in an African population.

ECG criteria for left ventricular hypertrophy (LVH) have been almost exclusively elaborated and calibrated in white populations. Because several interethnic differences in ECG characteristics have been found, the applicability of these criteria to African individuals remains to be demonstrated. We therefore investigated the performance of classic ECG criteria for LVH detection in an African population. Digitized 12-lead ECG tracings were obtained from 334 African individuals randomly selected from the general population of the Republic of Seychelles (Indian Ocean). Left ventricular mass was calculated with M-mode echocardiography and indexed to body height. LVH was defined by taking the 95th percentile of body height-indexed LVM values in a reference subgroup. In the entire study sample, 16 men and 15 women (prevalence 9.3%) were finally declared to have LVH, of whom 9 were of the reference subgroup. Sensitivity, specificity, accuracy, and positive and negative predictive values for LVH were calculated for 9 classic ECG criteria, and receiver operating characteristic curves were computed. We also generated a new composite time-voltage criterion with stepwise multiple linear regression: weighted time-voltage criterion=(0.2366R(aVL)+0.0551R(V5)+0.0785S(V3)+ 0.2993T(V1))xQRS duration. The Sokolow-Lyon criterion reached the highest sensitivity (61%) and the R(aVL) voltage criterion reached the highest specificity (97%) when evaluated at their traditional partition value. However, at a fixed specificity of 95%, the sensitivity of these 10 criteria ranged from 16% to 32%. Best accuracy was obtained with the R(aVL) voltage criterion and the new composite time-voltage criterion (89% for both). Positive and negative predictive values varied considerably depending on the concomitant presence of 3 clinical risk factors for LVH (hypertension, age >/=50 years, overweight). Median positive and negative predictive values of the 10 ECG criteria were 15% and 95%, respectively, for subjects with none or 1 of these risk factors compared with 63% and 76% for subjects with all of them. In conclusion, the performance of classic ECG criteria for LVH detection was largely disparate and appeared to be lower in this population of East African origin than in white subjects. A newly generated composite time-voltage criterion might provide improved performance. The predictive value of ECG criteria for LVH was considerably enhanced with the integration of information on concomitant clinical risk factors for LVH.

Hypomagnesemia in critically ill cancer patients: a prospective study of predictive factors

Hypomagnesemia is the most common electrolyte disturbance seen upon admission to the intensive care unit (ICU). Reliable predictors of its occurrence are not described. The objective of this prospective study was to determine factors predictive of hypomagnesemia upon admission to the ICU. In a single tertiary cancer center, 226 patients with different diagnoses upon entering were studied. Hypomagnesemia was defined by serum levels <1.5 mg/dl. Demographic data, type of cancer, cause of admission, previous history of arrhythmia, cardiovascular disease, renal failure, drug administration (particularly diuretics, antiarrhythmics, chemotherapy and platinum compounds), previous nutrition intake and presence of hypovolemia were recorded for each patient. Blood was collected for determination of serum magnesium, potassium, sodium, calcium, phosphorus, blood urea nitrogen and creatinine levels. Upon admission, 103 (45.6%) patients had hypomagnesemia and 123 (54.4%) had normomagnesemia. A normal dietary habit prior to ICU admission was associated with normal Mg levels (P = 0.007) and higher average levels of serum Mg (P = 0.002). Postoperative patients (N = 182) had lower levels of serum Mg (0.60 ± 0.14 mmol/l compared with 0.66 ± 0.17 mmol/l, P = 0.006). A stepwise multiple linear regression disclosed that only normal dietary habits (OR = 0.45; CI = 0.26-0.79) and the fact of being a postoperative patient (OR = 2.42; CI = 1.17-4.98) were significantly correlated with serum Mg levels (overall model probability = 0.001). These findings should be used to identify patients at risk for such disturbance, even in other critically ill populations.

Hyperspectral field measurements to determine dry matter yield and nutritive value of legume-grass swards

Summary: Productivity, botanical composition and forage quality of legume-grass swards are important factors for successful arable farming in both organic and conventional farming systems. As these attributes can vary considerably within a field, a non-destructive method of detection while doing other tasks would facilitate a more targeted management of crops, forage and nutrients in the soil-plant-animal system. This study was undertaken to explore the potential of field spectral measurements for a non destructive prediction of dry matter (DM) yield, legume proportion in the sward, metabolizable energy (ME), ash content, crude protein (CP) and acid detergent fiber (ADF) of legume-grass mixtures. Two experiments were conducted in a greenhouse under controlled conditions which allowed collecting spectral measurements which were free from interferences such as wind, passing clouds and changing angles of solar irradiation. In a second step this initial investigation was evaluated in the field by a two year experiment with the same legume-grass swards. Several techniques for analysis of the hyperspectral data set were examined in this study: four vegetation indices (VIs): simple ratio (SR), normalized difference vegetation index (NDVI), enhanced vegetation index (EVI) and red edge position (REP), two-waveband reflectance ratios, modified partial least squares (MPLS) regression and stepwise multiple linear regression (SMLR). The results showed the potential of field spectroscopy and proved its usefulness for the prediction of DM yield, ash content and CP across a wide range of legume proportion and growth stage. In all investigations prediction accuracy of DM yield, ash content and CP could be improved by legume-specific calibrations which included mixtures and pure swards of perennial ryegrass and of the respective legume species. The comparison between the greenhouse and the field experiments showed that the interaction between spectral reflectance and weather conditions as well as incidence angle of light interfered with an accurate determination of DM yield. Further research is hence needed to improve the validity of spectral measurements in the field. Furthermore, the developed models should be tested on varying sites and vegetation periods to enhance the robustness and portability of the models to other environmental conditions.

Equacões preditivas para as pressões respiratórias estáticas máximas de adolescentes brasileiros

Introduction: The reference values and prediction equations for maximal respiratory pressures (MRP) differ significantly between the available studies. This large discrepancy can be attributed to the different methodologies proposed. Although the importance of MRP is widely recognized, there are no Brazilian studies that provide predictive equations and reference values for PRM adolescents. Objectives: The purpose of this study was to provide normal values and propose predictive equations for maximal static respiratory pressures of Brazilian adolescents. Methods: An observational cross-sectional study, which evaluated 182 adolescents of both sexes aged between 12 and 18 years, enrolled in schools of the state and private in the city of Natal / RN. The selection of schools and participants of the study was randomly through a lottery system. The spirometric evaluation was performed through the digital spirometer One Flow FVC prior to the assessment of respiratory muscle strength. The MICs were measured with MVD digital manometer 300. Statistical analysis was performed using the SPSS 17.0 software STATISTICS, assigning the significance level of 5%. The normality of data distribution was verified using the Kolmogorov-Smirnov (KS). The descriptive analysis was expressed as mean and standard deviation. We used one-way ANOVA test to verify the difference of the averages of MRPs between age and gender and comparing the averages of MRPs between levels of physical activity. The test t'Student unpaired compared the averages of MRPs being ages and sexes. The comparison of mean values obtained in this study PRM with the values predicted using the equations mentioned above was relizada by testing paired t'Student. To verify the correlation between the PRM and the independent variables (age, weight, height) was used Pearson correlation test. Levene's test evaluated the homogeneity of variance. To obtain predictive equations analysis was used stepwise multiple linear regression. Results: There was no significant difference in mean age between the PRM. The male adolescents, regardless of age, showed superiority in MRP values when compared to the opposite sex. Weight, height and sex correlated with the PRM. Regression analysis suggested in this study, pointed out that the weight and sex had an influence in MIP and MEP only in relation to sex influenced. The mean for each PRM adolescents classified as very active were superior to those observed in adolescents classified as irregularly active. Conclusion: This study provides reference values and two models of predictive equations for maximal inspiratory and expiratory pressures, and to establish the lower limits of normality that will serve as an indispensable condition for careful evaluation of respiratory muscle strength in Brazilian adolescents

Desenvolvimento de um Questionário Quantitativo de Freqüência Alimentar (QQFA) para gestantes usuárias de Unidades Básicas de Saúde de Ribeirão Preto, São Paulo, Brasil

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)