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Results for “Linear Regression”

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PubMed1984

Comparison of single time point and linear regression estimates of cell production in rat intestinal crypts after perturbation by hydroxyurea.

The present investigation compared the values obtained for the intestinal crypt cell production rate per hour ( CCPR ) at several sites in the intestine of rats using two variations in the application of metaphase arrest technique. The CCPR was determined both from the slope of a metaphase accumulation line obtained by linear regression analysis of measurements at several time points and by the single time point accumulation method. The comparison was performed for both the steady state in untreated controls and under perturbed conditions at 6, 12 and 24 h following intraperitoneal administration of 1000 mg/kg bodyweight of hydroxyurea to rats. In the steady state, the metaphase accumulation values were linear up to 3 h after vincristine sulfate in the proximal intestine (stomach to proximal ileum) and linear for up to 3 1/2 h in the distal ileum and the colon. Consequently the 3 h time point was selected for evaluation of CCPR values using the single time point method. The two methods gave equivalent results in the steady state, although in situations where there was good linearity of metaphase accumulation, the values obtained by the regression method were usually more precise. In the perturbed intestine poorer linearity of metaphase accumulation was observed and the duration of linearity was reduced sometimes to 2-2 1/2 h. Overall, under these circumstances, estimation of average CCPR was more precise by the single time point accumulation method. More importantly, significant differences were sometimes evident between the results of these two methods when applied to the same data.

Animals↗

PubMed2001

BJ: an S-Plus program to fit linear regression models to censored data using the Buckley-James method.

Most researchers are familiar with ordinary multiple regression models, most commonly fitted using the method of least squares. The method of Buckley and James (J. Buckley, I. James, Linear regression with censored data, Biometrika 66 (1979) 429-436.) is an extension of least squares for fitting multiple regression models when the response variable is right-censored as in the analysis of survival time data. The Buckley-James method has been shown to have good statistical properties under usual regularity conditions (T.L. Lai, Z. Ying, Large sample theory of a modified Buckley-James estimator for regression analysis with censored data, Ann. Stat. 19 (1991) 1370-1402.). Nevertheless, even after 20 years of its existence, it is almost never used in practice. We believe that this is mainly due to lack of software and we describe here an S-Plus program that through its inclusion in a public domain function library fully exploits the power of the S-Plus programming environment. This environment provides multiple facilities for model specification, diagnostics, statistical inference, and graphical depiction of the model fit.

Data Interpretation, Statistical↗

PubMed1990

Use of a Lotus 1-2-3 spreadsheet to plot the confidence and the prediction intervals in linear regression analysis.

Computer-derived spreadsheet programs such as Lotus 1-2-3 are being used by many investigators for individualized statistical calculations. Spreadsheet templates have been described for the performance of simple statistical tests by non-statisticians with relatively limited computer experience. This paper describes a template for use with Lotus 1-2-3 for automatic graphic display of confidence and prediction intervals of simple linear regression analysis. The graph can be printed using the Lotus printgraph program. The program also allows comparison of the slope and the intercept of two regression lines.

Computer Graphics↗

PubMed1992

Respiratory mechanics studied by multiple linear regression in unsedated ventilated patients.

Respiratory mechanics during artificial ventilation are commonly studied with methods which require a specific respiratory pattern. An alternative is to analyse the relationship between tracheal pressure (P) and flow (V') by multiple linear regression (MLR) using a suitable model. The value of this approach was evaluated in 12 unsedated patients, mechanically-ventilated for acute respiratory failure, and most with a history of chronic obstructive or restrictive respiratory disease. After correction for the non-linear resistance of the endotracheal tube, the data were analysed with the linear first order model: P = P0 + E.V + R.V' where E and R are total respiratory elastance and resistance, and P0 is the static recoil pressure at end-expiration. After exclusion of the cycles which clearly exhibited muscular activity, a good fit was observed in 25 out of 36 records (relative root-mean-square error less than 10%); the values of E and R were reproducible within cycles, and consistent with the patient's condition and the ventilatory mode. The intrinsic positive end-expiratory pressure (PEEPi), as derived from P0 and the applied PEEP, averaged 1.1 +/- 1.0 hPa. Using more sophisticated models, allowing for mechanical non-homogeneity or non-linearity of R or E, rarely improved the fit and often provided unrealistic data. In several subjects the discrepancy between the data and the first order model was consistent with expiratory flow limitation, which may severely impair the analysis. We conclude that, except in the case of expiratory flow limitation, the method is useful for routine clinical use and better implemented with the simple linear model.

Aged↗

PubMed1977

Kinetic parameter estimation by numerical algorithms and multiple linear regression: theoretical.

A new method is presented for the determination of kinetic parameters based on a functional relationship among experimental data derived from the postulated model. The data, even though containing errors, are manifestations of this relationship, which should be satisfied by parameters fitted to the system. The procedure involves the use of numerical integration and/or differentiation of the data, followed by multiple linear regression. It does not require initial estimates or repetitive iteration for linear systems and can be applied to nonlinear models. The accuracy of estimated parameter depends on the goodness of the particular numerical approximation method used.

Computers↗

PubMed2002

Prediction of tumoricidal activity and accumulation of photosensitizers in photodynamic therapy using multiple linear regression and artificial neural networks.

The biological activities of a congeneric series of pyropheophorbides used as sensitizers in photodynamic therapy have been predicted on the basis of their molecular structures, using multiple linear regression and artificial neural network (ANN) computations. Theoretical descriptors (a total of 81) were calculated by the 3DNET program based on the three-dimensional structure (3D) of the geometry-optimized molecules. These input descriptors were tested as independent variables and used for model building. Systematic descriptor selections yielded models with one, two or three descriptors with good cross-validation results. The predictive abilities of the best fitting models were checked by shuffling and cross-validation procedures. ANN was suitable for building models for both linear and nonlinear relationships. Lipophilicity was sufficient to predict the accumulation of the sensitizers in the target tissue. Weighted holistic invariant molecular descriptors weighted by atomic mass, Van der Waals volume or electronegativity were also needed to predict photodynamic activity properly. Our models were able to predict the biological activities of 13 pyropheophorbide derivatives solely on the basis of their 3D molecular structures. Moreover, linear and nonlinear variable selection methods were compared in models built linearly and nonlinearly. It is expedient to use the same method (linear or nonlinear) for variable selection as for parameter estimation.

Antineoplastic Agents↗

PubMed2003

Correlation and simple linear regression.

In this tutorial article, the concepts of correlation and regression are reviewed and demonstrated. The authors review and compare two correlation coefficients, the Pearson correlation coefficient and the Spearman rho, for measuring linear and nonlinear relationships between two continuous variables. In the case of measuring the linear relationship between a predictor and an outcome variable, simple linear regression analysis is conducted. These statistical concepts are illustrated by using a data set from published literature to assess a computed tomography-guided interventional technique. These statistical methods are important for exploring the relationships between variables and can be applied to many radiologic studies.

Factor Analysis, Statistical↗

PubMed1986

Off-line removal of ocular artifacts from event-related potentials using a multiple linear regression model.

A method for correction of event-related potentials (ERP) and cortical DC shifts, disturbed by eyeblink and eye movement potentials, is described. The correcting algorithm employs a multiple linear regression model with random regressors which prevents an incorrect calculation of the propagation factor when both ocular potentials and event-related cortical potentials occur together. This propagation factor is calculated for each event-related EEG record. Segmentation of the record into 2.56 s time intervals guarantees, moreover, calculation of different propagation factors for eyeblinks and eye movements within a single trial. The correcting algorithm is executed off-line with the propagation factors calculated from the experimental data proper. A correction is carried out only when the EOG has a significant influence on ERP. The application of the procedure is illustrated by individual examples.

Blinking↗

PubMed1989

The effect of breath size and posture on calibration of the respiratory inductive plethysmograph by multiple linear regression.

The accuracy of the respiratory inductive plethysmograph (Respitrace) for estimation of lung volume changes during quiet breathing and vital capacity (VC) manoeuvres was evaluated using a variant of the multiple linear regression (MLR) technique. We applied this technique successively on quiet breathing, on the whole VC, and on each of the four quarters of the VC separately. This was carried out in six body positions. The best estimation of tidal volumes was obtained when calibration factors calculated during quiet breathing were used. The best estimation of VC was obtained when the calibration factors were adapted to the level of lung inflation. These results indicate that, using a single position MLR calibration method, the Respitrace measures tidal and VC mouth volumes very accurately. The accuracy of this MLR method for estimation of the rib cage and abdominal contributions was validated by comparison with isovolume calibration factors. Both techniques gave very similar results during tidal breathing. However, the MLR calibration factors may have no physiological meaning (i.e. for volume partitioning) when they are calculated from VC manoeuvres, in which more than two degrees of freedom are involved.

Abdomen↗

PubMed2004

Residual analysis in linear regression models with an interval-censored covariate.

Residual analysis is a useful class of techniques for the evaluation of the goodness of a fitted model. Checking the underlying assumptions is important since most linear regression estimators require a correctly specified regression function and independent and identically distributed errors to be consistent. For uncensored data, the examination of the residuals of the fitted model is a standard tool for checking whether or not the underlying model assumptions hold. Such analysis has not been widely developed for censored data. Hillis (Statistics in Medicine 1995; 14:2023-2036) developed a residual plot for model checking when the response variable of a linear model is right-censored, and Gomez et al. (Statistics in Medicine 2003; 22:409-425) proposed residuals in models with interval-censored covariates. In this paper, we propose a new definition of residuals for linear models that incorporate interval-censored covariates. This definition can be also applied when the response variable is interval-censored. These new residuals are shown to perform better in model checking than other types of residuals in this context. We illustrate them with a data set from an AIDS clinical trial study.

Anti-HIV Agents↗

PubMed1985

Linear regression: a method to accurately analyze accounts receivable.

Present methods of analysis of accounts receivable can result in information that is accurate. What is needed, therefore, is an improvement in those methods. Linear regression analysis is one improvement that can help the patient accounts manager. Its use of a standard coefficient and elimination of annualization of revenue and division of total annual revenue by accounts receivable can create more accurate and reliable information.

Accounting↗

PubMed1990

Using linear and non-linear regression to fit biochemical data.

For biochemists or chemists the most common form of data analysis is likely to be regression analysis. This is a technique to find the 'best' values for various experimental parameters; defined as those values which, when used in an appropriate equation, result in the minimum deviation of the calculated results from the experimental data. Despite the widespread application of regression analysis, the basis of the technique and the underlying assumptions are often poorly understood or appreciated. This article describes the basics of linear and non-linear regression, the role of 'weighting' and the potential pitfalls of such analyses.

Biochemical Phenomena↗

PubMed2001

Using segmented linear regression models with unknown change points to analyze strategy shifts in cognitive tasks.

Some years ago, Beem (1993, 1995) described a program for fitting two regression lines with an unknown change point (Segcurve). He suggested that such models are useful for the analysis of a variety of phenomena and gave an example of an application to the study of strategy shifts in a mental rotation task. This technique has also proven to be very fruitful for investigating strategy use and strategy shifts in other cognitive tasks. Recently, Beem (1999) developed SegcurvN, which fits n regression lines with (n - 1) unknown change points. In the present article we present this new technique and demonstrate the usefulness of a three-phase segmented linear regression model for the identification of strategies and strategy shifts in cognitive tasks by applying it to data from a numerosity judgment experiment. The advantages and shortcomings of this technique are evaluated.

Attention↗

PubMed1992

Rumen protein degradation rates estimated by non-linear regression analysis of Michaelis-Menten in vitro data.

An in vitro method applying Michaelis-Menten saturation kinetics was developed as an alternative approach for estimating protein degradation rates in the rumen. Non-linear regression (NLR) analysis of the integrated Michaelis-Menten equation yielded fractional degradation rates, kd, from direct estimates of the maximum velocity: Michaelis constant ratio (kd = Vmax:Km). Degradation rates obtained using data from a series of 2 h inhibitor in vitro incubations were respectively 0.989, 0.134, and 0.037/h for casein, solvent soya-bean meal (SSBM) and expeller soya-bean meal (ESBM). Degradation rates obtained from 2 h incubations had lower standard errors than those obtained using 1 h incubations; 2 h rates were not significantly different from 1 h rates, suggesting end-product inhibition was not significant at 2 h. The NLR Michaelis-Menten method was used to determine degradation rates for twelve protein sources: casein, bovine serum albumin, two samples of lucerne (Medicago sativa) hay, and four samples each of SSBM and ESBM. Statistical analysis of NLR results revealed significant differences among the twelve protein sources. Casein was degraded most rapidly (0.827/h), and the four ESBM samples most slowly (0.050-0.098/h). Degradation rate for serum albumin was 0.135/h; rates for SSBM and lucerne hays ranged from 0.160 to 0.208/h. Degradation rates estimated using the NLR method were more rapid than those obtained with a limited substrate approach; NLR rates were more consistent with in vivo estimates of rumen protein escape. Greater concentrations of slowly degraded proteins were needed with the NLR method to define curvilinearity of the degradation curve more accurately.

Animals↗

PubMed2005

Linear and nonlinear modeling of antifungal activity of some heterocyclic ring derivatives using multiple linear regression and Bayesian-regularized neural networks.

Antifungal activity was modeled for a set of 96 heterocyclic ring derivatives (2,5,6-trisubstituted benzoxazoles, 2,5-disubstituted benzimidazoles, 2-substituted benzothiazoles and 2-substituted oxazolo(4,5-b)pyridines) using multiple linear regression (MLR) and Bayesian-regularized artificial neural network (BRANN) techniques. Inhibitory activity against Candida albicans (log(1/C)) was correlated with 3D descriptors encoding the chemical structures of the heterocyclic compounds. Training and test sets were chosen by means of k-Means Clustering. The most appropriate variables for linear and nonlinear modeling were selected using a genetic algorithm (GA) approach. In addition to the MLR equation (MLR-GA), two nonlinear models were built, model BRANN employing the linear variable subset and an optimum model BRANN-GA obtained by a hybrid method that combined BRANN and GA approaches (BRANN-GA). The linear model fit the training set (n = 80) with r2 = 0.746, while BRANN and BRANN-GA gave higher values of r2 = 0.889 and r2 = 0.937, respectively. Beyond the improvement of training set fitting, the BRANN-GA model was superior to the others by being able to describe 87% of test set (n = 16) variance in comparison with 78 and 81% the MLR-GA and BRANN models, respectively. Our quantitative structure-activity relationship study suggests that the distributions of atomic mass, volume and polarizability have relevant relationships with the antifungal potency of the compounds studied. Furthermore, the ability of the six variables selected nonlinearly to differentiate the data was demonstrated when the total data set was well distributed in a Kohonen self-organizing neural network (KNN).

Antifungal Agents↗

PubMedDate not supplied

Comparative study of QSAR/QSPR correlations using support vector machines, radial basis function neural networks, and multiple linear regression.

Support vector machines (SVMs) were used to develop QSAR models that correlate molecular structures to their toxicity and bioactivities. The performance and predictive ability of SVM are investigated and compared with other methods such as multiple linear regression and radial basis function neural network methods. In the present study, two different data sets were evaluated. The first one involves an application of SVM to the development of a QSAR model for the prediction of toxicities of 153 phenols, and the second investigation deals with the QSAR model between the structures and the activities of a set of 85 cyclooxygenase 2 (COX-2) inhibitors. For each application, the molecular structures were described using either the physicochemical parameters or molecular descriptors. In both studied cases, the predictive ability of the SVM model is comparable or superior to those obtained by MLR and RBFNN. The results indicate that SVM can be used as an alternative powerful modeling tool for QSAR studies.

Animals↗

PubMed1983

A new biometrical procedure for testing the equality of measurements from two different analytical methods. Application of linear regression procedures for method comparison studies in clinical chemistry, Part I.

Procedures for the statistical evaluation of method comparisons and instrument tests often have a requirement for distributional properties of the experimental data, but this requirement is frequently not met. In our paper we propose a new linear regression procedure with no special assumptions regarding the distribution of the samples and the measurement errors. The result does not depend on the assignment of the methods (instruments) to X and Y. After testing a linear relationship between X and Y confidence limits are given for the slope beta and the intercept alpha; they are used to determine whether there is only a chance difference between beta and 1 and between alpha and 0. The mathematical background is amplified separately in an appendix.

Biometry↗

PubMed1986

Estimating enzyme kinetic parameters: a computer program for linear regression and non-parametric analysis.

An IBM computer program, WILMAN4, is described which calculates the estimates, Km, V and Km/V from initial velocity measurements according to one of four statistical methods. Three of these methods involve linear regression analysis using weights given by assuming: (i) constant absolute error (G.N. Wilkinson, 1961, Biochem J., 80, 324-332), (ii) constant relative error (G. Johansen and R. Lumry, 1961, C.R. Trav. Lab. Carlsberg, 32, 185-214) and (iii) an error function in between the above two cases. (A. Cornish-Bowden, 1976, Principles of Enzyme Kinetics, Butterworths Inc, Boston, Mass., pp. 168-193). The fourth method is a non-parametric procedure derived by Eisenthal and Cornish-Bowden (Biochim. Biophys. Acta, 532 (1974) 268-272). Residuals are obtained by subtracting the experimental and the calculated velocities. Outliers, or residuals which are greater than two experimental standard deviations, can be identified and removed from the data set. If the sequence of positive and negative signs of the residuals is random as determined by a statistical probability calculation, the data set is assumed to obey the Michaelis-Menten equation.

Biometry↗