Order Linear Regression Model Research Articles

Monothetic Analysis and Response Surface Methodology Optimization of Calcium Alginate Microcapsules Characteristics.

Owing to bio-polymer’s low-cost, environmental friendliness and mechanically stable nature, calcium alginate microcapsules have attracted much interest for their applications in numerous fields. Among the common production methods, the Electrospraying technique has shown a great potential due to smaller shape capsule production and ease of control of independent affecting parameters. Although one factor at a time (OFAT) can predict the trends of parameter effect on size and sphericity, it is inefficient in explaining the complex parameter interaction of the electrospray process. In the current study, the effects of the main parameters affecting on size and sphericity of the microcapsules using OFAT were optimized to attain calcium alginate microcapsules with an average diameter below 100 µm. Furthermore, we propose a statistical model employing the Surface Responses Methodology (RSM) and Central Composite Design (CDD) to generate a quadratic order linear regression model for the microcapsule diameter and sphericity coefficient. Experimentally, microcapsules with a size of 92.586 µm and sphericity coefficient of 0.771 were predicted and obtained from an alginate concentration of 2.013 w/v, with a flowrate of 0.560 mL/h, a needle size of 27 G and a 2.024 w/v calcium chloride concentration as optimum parameters. The optimization processes were successfully aligned towards formation of the spherical microcapsules with smaller average diameter of less than 100 µm, owing to the applied high voltage that reached up to 21 kV.

MODELING RELATION BETWEEN ATM LOCAL AND IMPLIED VOLATILITY FOR MICROSOFT STOCKS

In this work simple linear and polynomial regression to model the relation between at-the-money (ATM) implied and at-the-money local volatility of Microsoft stocks has been applied. Local volatility is extracted from the set of Vanilla option prices on Microsoft stocks by assuming that Microsoft stock price follows Dupire local volatility process. ATM Local volatility is then used in linear regression predictor while implied volatility is a resulting variable. The model is validated by predicting out-of-sample implied volatility with local volatility. The statistical significance and predictive ability of such model have been measured and autocorrelation tendencies have been studied. The conclusion that assumptions to use linear regression are held has been made. No autocorrelation tendencies were discovered in the time series. Finally, the conclusion that both the 1st and the 3rd order linear regression models demonstrate good predictive ability of local volatility over out-of-sample implied volatility has been made. None of the models proves statistical significance of local volatility as a predictor of the implied volatility but both can be actually used for practical purpose as they predict well out-of-the-sample implied volatilities. This is an important practical result as it means that complex non-linear relationship between implied and local volatilities formalized by Dupire can actually be reduced to simplier linear relationship that demonstrates reasonable discrepancies. Despite the 3rd order model fits the data better, but for the reasons of overfitting in general it’s safer to apply the 1st order model as it demonstrates more stable predictions over datasets with jumps.

Simplified performance correlation of an indirect evaporative cooling system: Development and validation

At present, there is an increasing interest in indirect evaporative coolers (IEC), which are an effective alternative to conventional cooling systems due to their high efficiency. In this study a new simplified first order linear regression model of an IEC system has been developed. The model is based on experimental data and results of the proposed correlation have been compared with ones of a phenomenological model and with further measurements collected in significant operating conditions (data center, desiccant evaporative cooling cycle and residential application). It is shown that deviations of wet bulb effectiveness are limited to 3.4% for the simplified model and 2.1% for the detailed one. Therefore, due to its good accuracy and low computational load, the simplified model could be suitable to be implemented in simulation tools.

Frequency estimation of a sinusoidal signal with time-varying amplitude and phase

Abstract This paper is devoted to frequency estimation of a non-stationary sinusoidal signal. The amplitude is supposed to be a known function within a constant factor, the phase should be known. Example of such problem statement is sensorless angular velocity estimation for permanent magnet synchronous motors. On the first step by reparametrization, a third order linear regression model is obtained. On the next step, an estimation algorithm is constructed based on a standard gradient approach. The frequency estimate can be computed from one of the model parameters using inverse trigonometric functions. To improve estimates quality for noisy measurements we propose a new identification method, which can be tuned to attenuate the noise influence. It is shown that the frequency estimation error converges to zero exponentially fast. The described algorithm does not require measuring or calculating derivatives of the input signal. The efficiency of the proposed approach is demonstrated through the set of numerical simulations.

Frequency estimation of a sinusoidal signal with time-varying amplitude

This paper is devoted to frequency estimation of a sinusoidal signal with a time-varying amplitude. The amplitude can take zero values, but should be known and bounded. The first order linear regression model is obtained. The estimation algorithm has been constructed basing on standard gradient approach. It is shown that the frequency estimation error converges to zero exponentially fast. The described algorithm does not require measuring or calculating derivatives of the input signal. The efficiency of the proposed approach is demonstrated through a set of numerical simulations.

Selection of Higher Order Regression Models in the Analysis of Multi-Factorial Transcription Data

IntroductionMany studies examine gene expression data that has been obtained under the influence of multiple factors, such as genetic background, environmental conditions, or exposure to diseases. The interplay of multiple factors may lead to effect modification and confounding. Higher order linear regression models can account for these effects. We present a new methodology for linear model selection and apply it to microarray data of bone marrow-derived macrophages. This experiment investigates the influence of three variable factors: the genetic background of the mice from which the macrophages were obtained, Yersinia enterocolitica infection (two strains, and a mock control), and treatment/non-treatment with interferon-γ.ResultsWe set up four different linear regression models in a hierarchical order. We introduce the eruption plot as a new practical tool for model selection complementary to global testing. It visually compares the size and significance of effect estimates between two nested models. Using this methodology we were able to select the most appropriate model by keeping only relevant factors showing additional explanatory power. Application to experimental data allowed us to qualify the interaction of factors as either neutral (no interaction), alleviating (co-occurring effects are weaker than expected from the single effects), or aggravating (stronger than expected). We find a biologically meaningful gene cluster of putative C2TA target genes that appear to be co-regulated with MHC class II genes.ConclusionsWe introduced the eruption plot as a tool for visual model comparison to identify relevant higher order interactions in the analysis of expression data obtained under the influence of multiple factors. We conclude that model selection in higher order linear regression models should generally be performed for the analysis of multi-factorial microarray data.

Quantitative prediction of integrase inhibitor resistance from genotype through consensus linear regression modeling.

BackgroundIntegrase inhibitors (INI) form a new drug class in the treatment of HIV-1 patients. We developed a linear regression modeling approach to make a quantitative raltegravir (RAL) resistance phenotype prediction, as Fold Change in IC50 against a wild type virus, from mutations in the integrase genotype.MethodsWe developed a clonal genotype-phenotype database with 991 clones from 153 clinical isolates of INI naïve and RAL treated patients, and 28 site-directed mutants.We did the development of the RAL linear regression model in two stages, employing a genetic algorithm (GA) to select integrase mutations by consensus. First, we ran multiple GAs to generate first order linear regression models (GA models) that were stochastically optimized to reach a goal R2 accuracy, and consisted of a fixed-length subset of integrase mutations to estimate INI resistance. Secondly, we derived a consensus linear regression model in a forward stepwise regression procedure, considering integrase mutations or mutation pairs by descending prevalence in the GA models.ResultsThe most frequently occurring mutations in the GA models were 92Q, 97A, 143R and 155H (all 100%), 143G (90%), 148H/R (89%), 148K (88%), 151I (81%), 121Y (75%), 143C (72%), and 74M (69%). The RAL second order model contained 30 single mutations and five mutation pairs (p < 0.01): 143C/R&97A, 155H&97A/151I and 74M&151I. The R2 performance of this model on the clonal training data was 0.97, and 0.78 on an unseen population genotype-phenotype dataset of 171 clinical isolates from RAL treated and INI naïve patients.ConclusionsWe describe a systematic approach to derive a model for predicting INI resistance from a limited amount of clonal samples. Our RAL second order model is made available as an Additional file for calculating a resistance phenotype as the sum of integrase mutations and mutation pairs.

Concentration additivity of coefficients for maxillofacial elastomer pigmented to skin colors

Objective The purpose of this study is to determine a regression model which performs accurately for predicting Kubelka–Munk (K–M) absorption ( K) and scattering ( S) coefficients of pigment mixtures in maxillofacial elastomer (MFE). Methods Specimens at varying thicknesses of 19 shades of skin-colored MFE were made incorporating tan, red, yellow and black pigments. Using a non-contact 45°/0° spectral reflectance system, reflectance values were obtained and fit by non-linear regression to corrected K–M theory to determine observed K and S values. Predicted values were calculated using: first order linear regression model (M 1), second order square-factor model (M 2S), second order interaction-factor model (M 2I) and complete second order model (M 2C). Errors between observed and predicted values for each model at each wavelength studied are evaluated. Differences in color and the Translucency Parameter (TP) at a thickness of 1.5 mm based on CIE2000 color difference formula between observed and predicted values were also analyzed using repeated-measures ANOVA ( α = 0.05). Results M 2C shows less absolute differences in color and TP (1.5 mm) than those for the M 1 and M 2S models ( P < 0.05). Significance Within limitations of this study, the complete second order regression model performs accurately in concentration additivity of pigmented maxillofacial elastomer mixture. This regression model is recommended as a viable alternative in the application of colorant formulation based on corrected K–M model for improving appearance match of pigmented maxillofacial prosthesis to human skin.

Bayesian Heuristic for Multiperiod Control

In multiperiod control problems, one needs to sequentially choose the value of a set of multiple input variables, xn, to keep the value of a single output variable, yn, close to a target, T. At any stage n, the selection of xn poses a difficult dilemma. On the one hand, xn has to be such that (yn(xn) - T)2 is small in expectation. On the other hand, xn has to be such that it maximizes the amount of information in yn(xn) about the model relating yn and xn, to help keep the value of future y's as close to T as possible. The main approach to this problem is through certainty equivalence designs, which select xn such that yn(xn) is estimated to be equal to T. Instead, myopic designs select the xn that would be optimal if yn(xn) was the last observation to be made. We propose designs that improve on certainty equivalence and on myopic designs by searching for the best design in a family that contains both. In that way, the proposed design reaches a good compromise between the certainty equivalence choice, known to have good asymptotic properties, and the myopic choice, which is close to optimal for problems with small horizons. The characteristics and performance of the new designs are explored for regression models in general and for the first order linear regression model in particular. We observe that certainty equivalence designs induce too much learning about the model, just opposite of what is sometimes implied by the engineering literature on adaptive control when certainty equivalence designs are treated as if they were myopic designs. Our approach can be exported to many other sequential and nonsequential design problems where the optimal rule is too difficult to compute.

Validation of a monoclonal antibody‐based indirect enzyme immunoassay method for picloram detection in soil and plants

Picloram (4‐amino‐3,5,6‐trichloro‐2‐pyridinecarboxylic acid) residues in authentic soil and plant samples were determined by indirect enzyme immunoassay (EIA) and by gas chromatography (GC). Results obtained by EIA methods correlated well with the GC results with coefficients of determination ranging from 0.778 to 0.891. Picloram levels determined by EIA in soil extracts obtained by a potassium hydroxide extraction method (EIA‐1) underestimated picloram levels determined by GC. Conversely, EIA determinations of soil extracts obtained by a more rigorous acetonitrile extraction method (EIA‐2) yielded picloram levels that overestimated levels determined by GC. First order linear regression models using EIA determinations as the independent variable resulted in dependent variable coefficients of 0.325 and 1.42 for EIA‐1 and EIA‐2 respectively. Picloram levels determined in plant extracts were approximately equivalent by EIA and GC methods. Using a point on the standard curve representing 5 ng ml−1 picloram as...