A Residual Analysis for the Removal of Biological Oxygen Demand through Rotating Biological Contactor

Regression is a statistical method that is generally used for forecasting and prediction. It helps us to estimate the relationship between a dependent variable and one or more independent variables. This is the most widely used technique that best approximates the individual data points. It has found numerous successful applications in Engineering, Science, business and other fields. Getting average removal % of Biological Oxygen Demand (BOD5) from greywater through Rotating Biological Contactor (RBC), following experiment was conducted in Sindh University hostels using different parameters such as Hydraulic Retention Time (HRT) i.e. 2 hours (0.42 liter per min), 2.5 hours (0.33 l/min) and 3 hours (0.28 l/min) and multiple number of discs i.e. 40, 42, 44, 46, 48, 50 and 52. Consequences reveal that linear estimate of HRTs and numbers of disc are considerable whereas linear and quadratic estimates of number of discs are highly significant, which evidence the significance of time and discs. However, as p-value is greater than 0.05, hence quadratic estimate of HRT is not significant. By using coefficients of the table the regression equation is Removal = - 79.995 + 6.88 time + 2.90 disc, where the sample standard deviation is 7.151, coefficient of correlation is 0.86 and coefficient of determination is 0.742. Distributions of errors are approximately normal as probability plot of the residuals is approximately linear. Residual analysis shows that against each predicted variable, residuals plot falls approximately in a horizontal band symmetric and centered about the horizontal axis and against predicted y-values. Moreover, Residual plot shows the constant standard deviations and linearity assumptions appear to be met.

Modelling extreme precipitation: an application to two selected rainfall stations in Malaysia

Statistical models of rainfall have been applied in the understanding of the rainfall past trends, identifying for any anomalies, and making projections of future climate change in Malaysia. Herein, we analyse the rainfall data of 7-year period using the gamma and beta regression models to fit Malaysian extreme precipitation events of two stations, each in the West Coast region and the East Coast region, with extreme precipitation calendar date (in the angular form) as the predictor of the models. While the significance test as the p-value is much less than 0.05, it shows that there is a significant relationship between the climatology response variables. The deviance residual plot will be used to check the goodness of fit for diagnostic checking. The results show the models are useful in highlighting the latest trends and projections of climate change in Malaysia.

Effects of Second-Order Velocity Slip and the Different Spherical Nanoparticles on Nanofluid Flow

The paper theoretically investigates the heat transfer of nanofluids with different nanoparticles inside a parallel-plate channel. Second-order slip condition is adopted due to the microscopic roughness in the microchannels. After proper transformation, nonlinear partial differential systems are converted to ordinary differential equations with unknown constants, and then solved by homotopy analysis method. The residual plot is drawn to verify the convergence of the solution. The semi-analytical expressions between NuB and NBT are acquired. The results show that both first-order slip parameter and second-order slip parameter have positive effects on NuB of the MHD flow. The effect of second-order velocity slip on NuB is obvious, and NuB in the alumina–water nanofluid is higher than that in the titania–water nanofluid. The positive correlation between slip parameters and Ndp is significant for the titania–water nanofluid.

Corrosion rate of Al-Si Alloy Reinforced with B4C Nanoparticle prepared by Powder Metallurgy Method using RSM

The current work aims to optimize the Al-Si alloy reinforced with B4C nanoparticles prepared through powder metallurgy technique. The sample was prepared with different weight percentage 0, 4 and 8; the size of the sample was 20 mm x 20mm and sintered in a furnace upto 500oC with argon gas and their by furnace cooled to room temperature. The samples were brushed to remove the slag present in it, and polished by emery paper. Then the samples were weighed in an electric balancing apparatus to measure the initial weight of the sample before dipping it into acid solution. The weight loss was measured to calibrate the corrosion rate of the samples for 9 days. Response surface methodology was designed for three factors at three levels with a response as corrosion rate. The Analysis of Variance (ANOVA) was used to identify the most influencing factor on corrosion rate. The normal probability plot, residual plot, and desirability plot demonstrates the influence of corrosion rate of the composites.

Bayesian Survival Approach to Analyzing the Risk of Recurrent Rail Defects

This paper develops a Bayesian framework to explore the impact of different factors and to predict the risk of recurrence of rail defects, based upon datasets collected from a US Class I railroad between 2011 and 2016. To this end, this study constructs a parametric Weibull baseline hazard function and a proportional hazard (PH) model under a Gaussian frailty approach. The analysis is performed using Markov chain Monte Carlo simulation methods and the fit of the model is checked using a Cox–Snell residual plot. The results of the model show that the recurrence of a defect is correlated with different factors such as the type of rail defect, the location of the defect, train speed limit, the number of geometry defects in the last three years, and the weight of the rail. First, unlike the ordinary PH model in which the occurrence times of rail defects at the same location are assumed to be independent, a PH model under frailty induces the correlation between times to the recurrence of rail defects for the same segment, which is essential in the case of recurrent events. Second, considering Gaussian frailties is useful for exploring the influence of unobserved covariates in the model. Third, integrating a Bayesian framework for the parameters of the Weibull baseline hazard function as well as other parameters provides greater flexibility to the model. Fourth, the findings are useful for responsive maintenance planning, capital planning, and even preventive maintenance planning.

Inflammatory markers at baseline (C1) and cycle 3 (C3) and their association with clinical outcomes in urothelial cancer patients (pts) treated with immunotherapy (IO).

390 Background: Neutrophil-to-lymphocyte ratio (NLR), monocyte-to-lymphocyte ratio (MLR), and platelet-to-lymphocyte ratio (PLR) have been explored as biomarkers for response to IO. We investigated the association between these biomarkers and clinical outcomes in urothelial cancer pts treated with IO. Methods: We conducted a retrospective review of 67 urothelial cancer pts treated with PD-1 or PD-L1 inhibitors at Winship Cancer Institute from 2015-2018. Overall survival (OS) and progression free survival (PFS) were measured from first dose of IO to date of death or hospice referral and clinical or radiographic progression, respectively. MLR, NLR, and PLR were collected at C1 and C3. The nonlinear relationship between log-transformed biomarkers and OS or PFS was examined by martingale residual plot and optimal cutoff (OC) values were determined. Multivariable analysis (MVA) used Cox proportional hazard model. Results: OC for C1 and C3 NLR, MLR, and PLR were 2.06 and 1.42, -0.331 and -0.153, and 5.7 and 5.6, respectively. Pts with C1 NLR and PLR above OC had worse OS and shorter PFS (all p<0.05) (Table). High C3 MLR portended shorter OS and PFS. NLR, MLR and PLR were highly correlated (Pearson correlation coefficients ≥ 0.67, p<0.0001). Conclusions: High NLR, MLR, and PLR at C1 and at C3 are associated with worse clinical outcomes in this cohort. These values warrant a larger study for validation. MVA† of MLR, NLR, and PLR at C1 and at C3 with OS and PFS. [Table: see text]

Pemodelan Farmakokinetika Berbasis Populasi dengan R: Model Dua Kompartemen Ekstravaskuler

A Tutorial of two-compartment extravascular population-based pharmacokinetics modeling was performed by differential equations and non-linear mixed effect model approach. First, three-level differential equations of two-compartment pharmacokinetics were generated. Then, covariate and non-covariate models were developed by nlmeODE and nlme packages installed in R. The best model was selected according to AIC, BIC, and LogLik value. A model without covariates model was selected as the best model. The selected model showed a goodness of fit with experimental dataset and residual plot of the model revealed that no violations of model assumtions. In conclusion, nlme and nlmeODE is capable to generate an adequate predictive model of two-compartment population-based pharmacokinetics for extravascular route

FRACTIONAL RESIDUAL PLOT FOR MODEL VALIDATION

A pairwise comparison is important to measure the goodness-of-fit of models. Error measurements are used for this purpose but it only limit to the value, thus a graph is used to help show the precision of the models. These two should show a tally result in order to defense the hypothesis correctly. In this study, a fractional residual plot is proposed to help showing the precision of forecasts. This plot improvises the scale of the graph by changing the scale into decimal ranging from -1 to 1. The closer the point to 0 will indicate that forecast is robust and value closer to -1 or 1 will indicate that the forecast is poor. Two error measurements which are mean absolute error (MAE) and mean absolute percentage error (MAPE) and residual plot are used to justify the results and make comparison with the proposed fractional residual plot. Three difference data are used for this purpose and the results have shown that the fractional residual plot could give as much information as the residual plot but in an easier and meaningful way. In conclusion, the error plot is important in visualize the accurateness of the forecast.