Single Linear Regression Model Research Articles

Single hidden layer artificial neural network models versus multiple linear regression model in forecasting the time series of total ozone

Present paper endeavors to develop predictive artificial neural network model for forecasting the mean monthly total ozone concentration over Arosa, Switzerland. Single hidden layer neural network models with variable number of nodes have been developed and their performances have been evaluated using the method of least squares and error estimation. Their performances have been compared with multiple linear regression model. Ultimately, single-hidden-layer model with 8 hidden nodes have been identified as the best predictive model.

3‐D QSAR Studies of Microtubule Stabilizing Antimitotic Agents Towards Six Cancer Cell Lines

AbstractThe antimitotic agent paclitaxel continues to play an important role in cancer chemotherapy. However, its inefficacy on certain resistant cells and toxic side effects had led to the search for new drugs with improved biological activity. Here the QSAR models for microtubule stabilizing anticancer agents were performed to correlate their physicochemical properties with biological activity. Single and multiple linear regression models for six cancer cell lines were obtained with R2≥0.65 and q$\rm{ {_{pre}^{2}}}$≥0.6. Molecular mechanics energy and log P of the molecules account for the activity of taxanes towards B16 melanoma and breast cancer cells, respectively. The lowest unoccupied molecular orbitals and the number of nitrogen atoms in the structure account for the biological activity of epothilone derivatives and rest of the drugs towards ovarian cells. The relation between the structural properties of microtubule stabilizing antimitotic compounds and their activities on different cell lines are investigated in this paper.

Least-squares estimation in linear regression models with vague concepts

The paper is a contribution to parameter estimation in fuzzy regression models with random fuzzy sets. Here models with crisp parameters and fuzzy observations of the variables are investigated. This type of regression models may be understood as an extension of the ordinary single equation linear regression models by integrating additionally the physical vagueness of the involved items. So the significance of these regression models is to improve the empirical meaningfulness of the relationship between the items by a more sensitive attention to the fundamental adequacy problem of measurement. Concerning the parameter estimation the ordinary least-squares method is extended. The existence of estimators by the suggested method is shown, and some of their stochastic properties are surveyed.

Limit distributions of least squares estimators in linear regression models with vague concepts

Linear regression models with vague concepts extend the classical single equation linear regression models by admitting observations in form of fuzzy subsets instead of real numbers. They have lately been introduced (cf. [V. Krätschmer, Induktive Statistik auf Basis unscharfer Meßkonzepte am Beispiel linearer Regressionsmodelle, unpublished postdoctoral thesis, Faculty of Law and Economics of the University of Saarland, Saarbrücken, 2001; V. Krätschmer, Least squares estimation in linear regression models with vague concepts, Fuzzy Sets and Systems, accepted for publication]) to improve the empirical meaningfulness of the relationships between the involved items by a more sensitive attention to the problems of data measurement, in particular, the fundamental problem of adequacy. The parameters of such models are still real numbers, and a method of estimation can be applied which extends directly the ordinary least squares method. In another recent contribution (cf. [V. Krätschmer, Strong consistency of least squares estimation in linear regression models with vague concepts, J. Multivar. Anal., accepted for publication]) strong consistency and n -consistency of this generalized least squares estimation have been shown. The aim of the paper is to complete these results by an investigation of the limit distributions of the estimators. It turns out that the classical results can be transferred, in some cases even asymptotic normality holds.

Missing data estimation for 1–6 h gaps in energy use and weather data using different statistical methods

Analysing hourly energy use to determine retrofit savings or diagnose system problems frequently requires rehabilitation of short periods of missing data. This paper evaluates four methods for rehabilitating short periods of missing data. Single variable regression, polynomial models, Lagrange interpolation, and linear interpolation models are developed, demonstrated, and used to fill 1–6 h gaps in weather data, heating data and cooling data for commercial buildings. The methodology for comparing the performance of the four different methods for filling data gaps uses 11 1-year data sets to develop different models and fill over 500 000 ‘pseudo-gaps’ 1–6 h in length for each model. These pseudo-gaps are created within each data set by assuming data is missing, then these gaps are filled and the ‘filled’ values compared with the measured values. Comparisons are made using four statistical parameters: mean bias error (MBE), root mean square error, sum of the absolute errors, and coefficient of variation of the sum of the absolute errors. Comparison based on frequency within specified error limits is also used. A linear interpolation model or a polynomial model with hour-of-day as the independent variable both fill 1–6 missing hours of cooling data, heating data or weather data, with accuracy clearly superior to the single variable linear regression model and to the Lagrange model. The linear interpolation model is the simplest and most convenient method, and generally showed superior performance to the polynomial model when evaluated using root mean square error, sum of the absolute errors, or frequency of filling within set error limits as criteria. The eighth-order polynomial model using time as the independent variable is a relatively simple, yet powerful approach that provided somewhat superior performance for filling heating data and cooling data if MBE is the criterion as is often the case when evaluating retrofit savings. Likewise, a tenth-order polynomial model provided the best performance when filling dew-point temperature data when MBE is the criterion. It is possible that the results would differ somewhat for other data sets, but the strength of the linear and polynomial models relative to the other models evaluated seems quite robust. Copyright © 2006 John Wiley & Sons, Ltd.

Strong consistency of least-squares estimation in linear regression models with vague concepts

Linear regression models with vague concepts extend the classical single equation linear regression models by admitting observations in form of fuzzy subsets instead of real numbers. They have recently been introduced [cf. Krätschmer, Induktive statistik auf basis unscharfer meßkonzepte am beispiel linearer regressionsmodelle, Unpublished Habilitation Monograph, Faculty of Law and Economics of the University of Saarland, Saarbrücken, 2001] to improve the empirical meaningfulness of the relationship between the involved items by a more sensitive attention to the problems of data measurement, in particular the fundamental problem of adequacy. The parameters of such models are still real numbers, and a method of estimation can be applied which extends directly the ordinary least-squares method. This paper deals with some first asymptotic properties of estimators obtained by the method. Firstly, strong consistency will be shown, and secondly, the convergence rate will be investigated. The later result will be the starting point for a future study which will calculate the limit distributions of the estimators.

The transfer between instruments of a reflectance near-infrared assay for paracetamol in intact tablets.

This study compares several correction methods to facilitate the transfer of a validated near-infrared (NIR) assay for paracetamol in intact tablets between two reflectance NIR instruments of the same type. Transfer was defined as the ability to accurately predict the true assay value of a sample measured on a NIR system using an assay developed on a different system, and was assessed using a comprehensive set of statistical tests. Direct electronic transfer of the calibration models, representing the NIR assay, was not possible as a result of a definite residual spectrum between instruments. The use of a correction method based on the standardisation of the material used to record the reference spectrum also proved ineffective. Two methods investigated did succeed, the first employed a response surface calculated between the reflectance values of a set of six certified photometric standards measured on both instruments, with all full range partial least square (PLS) regression models subsequently transferred. The next was correction of the spectra from the second instrument utilising the residual spectrum between the mean sample of the validation set measured on both instruments. Through this approach all PLS regression models and also a single multiple linear regression (MLR) model were transferred. As an outcome of this study guidelines are suggested for the transfer of NIR assays along with the criteria deemed necessary to conclusively prove transfer and justify any correction method utilised. The significant criteria were determined to be the paired t-test with both the UV reference assay data and the original NIR assay data, and comparison of the coefficient of multiple determinations.

Assessment of coral reef bathymetric mapping using visible Landsat Thematic Mapper data

Bathymetry estimations in shallow areas using satellite multispectral scanners have been used preferentially in areas with clear water and homogeneous bottoms. Reef environments have high water transparency, but also have a rich bottom diversity which introduces several difficulties into water depth accuracy estimations. The aim of the present study was to assess the accuracy in a coral reef system of four bathymetric approaches based on a Landsat Thematic Mapper (TM) image, namely (1) a single linear regression model using the first principal component; (2) a multiple linear regression; (3) a two-step non-supervised classification with multiple linear regression; and (4) a supervised classification. Given the natural patchiness, and cover type and depth variability in the study area (Alacranes Reef ), 473 echosounded profiles were selected under radiometric and topographic criteria, in order to delineate homogeneous areas that allow a better relationship between radiometric and depth data. One thousand and eighty-five profiles that did not meet the criteria were used to assess the model's response in areas where the bottom exhibits high variability. Differences provided by residual analysis and rms. error were used to evaluate the water depth accuracy estimations of the models. A two-step non-supervised approach produced the lowest overall rms. error (2 m), and exhibited balanced over/under error residuals.

Normal Linear Regression Models With Recursive Graphical Markov Structure

A multivariate normal statistical model defined by the Markov properties determined by an acyclic digraph admits a recursive factorization of its likelihood function (LF) into the product of conditional LFs, each factor having the form of a classical multivariate linear regression model (≡WMANOVA model). Here these models are extended in a natural way to normal linear regression models whose LFs continue to admit such recursive factorizations, from which maximum likelihood estimators and likelihood ratio (LR) test statistics can be derived by classical linear methods. The central distribution of the LR test statistic for testing one such multivariate normal linear regression model against another is derived, and the relation of these regression models to block-recursive normal linear systems is established. It is shown how a collection of nonnested dependent normal linear regression models (≡Wseemingly unrelated regressions) can be combined into a single multivariate normal linear regression model by imposing a parsimonious set of graphical Markov (≡Wconditional independence) restrictions.

The U. S.-Canada Free Trade Agreement: Impact on the U. S. Steel Industry

This study empirically estimates the impact of the U. S.-Canada FTA on specific iron and steel exports and imports using quarterly data for the period January 1981 to December 1990. A single equation multiple linear regression model is used to quantify at the industry and industry segment levels the impact of the agreement. The dependent variables are the quantities of major steel products traded between the two nations. The explanatory variables include foreign price adjusted for the exchange rate and tariff rate, domestic price, and the industrial production index. Results include calculation of price and income elasticities, which vary considerably by industry segments. The impact of free trade, as modeled, varies widely from product to product. As such it has important implications not only for government policy and employment but also for the adjustment problems faced by both the large integrated steel mill and the minimill producers.

Pooled time series regression analysis in longitudinal studies

Many longitudinal studies attempt to examine changes in outcome measures over time in groups of patients. Applying conventional analytic techniques, such as a single classical linear regression model, to these data will often not result in minimum variance estimates, and may affect the results of tests of significance. Pooled time series regression analyses comprise a set of techniques that may be used in these instances to model changes in outcome measures over time. Pooling of time series data from many individuals may be done using two types of models: fixed effect models, which specify differences among individuals in separate intercept terms, and random effects models, which allow for differences among individuals by including an additional error component in the model. The choice between these alternative model specifications is guided by both theoretical and statistical considerations. This paper describes the use of pooled time series analysis, contrasts these methods with two classical linear regression approaches, and demonstrates these differences using two examples: a hypothetical study of serum glucose measurements in patients with diabetic ketoacidosis, and a longitudinal study of the development of functional disability in a cohort of patients with rheumatoid arthritis. These methods may be applicable to the study of outcomes in many chronic illnesses.

A robust method of estimation based on the MML estimators for a single linear regression model

We adopt the modified maximum likelihood approach (based on symmetrically Type-II censored normal samples) of Tiku (1967, 1970) and obtain a robust method of estimation of the parameters in a simple linear regression model. By simulating the bias and mean square error of these estimators under both normal and mixture-normal models for the error component and then comparing them with the corresponding values of the ordinary least-square estimators (or the MLE's under normality), we display their efficiency and robustness features. We also obtain the asymptotic variances and covariances under normality of these estimators via the information matrix. Finally, we consider a numerical example and illustrate the method of estimation developed in this paper.

Eddy transport of sensible heat and the life history of synoptic systems: A statistical analysis for the Southern Hemisphere winter

The efficiency of successive satellite-observed stages in the development of extratropical frontal cyclones for transporting eddy sensible heat at 850 mb on the Southern Hemisphere, is determined for the five winters (June through September) of 1973–1977. An inventory of cloud vortex data is allied with independent estimates of the zonally-averaged transient eddy heat flux,\([\overline {v' T'} ]\), using a statistical technique known aspath analysis. Path analysis is an improvement over single equation linear regression models since it controls for the temporally continuous nature of cyclone evolution. The results indicate that different cloud vortex types are associated with characteristic regimes of\(\overline {v' T'} \). The quite strong poleward flux of heat effected in the cyclogenetic stages weakens substantially by the onset of dissipation. These results are in general agreement with those for the summer and transition seasons derived using linear regression by Tucker (1979). However, a significant netequatorward flux of\(\overline {v' T'} \) is found to be connected with the short-lived mature (spiral) cloud vortex type. In association with a southward displacement of the maximum latitude of cyclogenesis and a reduced crosslatitude motion of systems in winter, this apparently results in the strong lower-level heat flux convergence characteristic of the circumpolar trough at that time. A systematic error, by year, in the statistical model specification of heat transport related to cloud vortex type is found to be associated with phase of the Southern Oscillation (SO). Incorporating this effect into the model greatly improves the goodness-of-fit of the heat flux estimates and indicates that the efficiency of the mcridional eddy heat transport by cyclones is greatest (least) when the SOI is low (high). The implications of these results in the context of other, related studies are discussed.

Estimation of Thompson Seedless Grapevine Leaf Area

Leaves were sampled from Thompson Seedless grapevine shoots three times during a two year period at two widely different locations in order to make estimates of leaf area. Linear length and width measurements were made of all leaves from each of 94, 36 and 23 shoots collected respectively at bloom and véraison, 1981 in Davis and bloom, 1982 in Fresno County. Linear regressions were calculated for each shoot with leaf area as the dependent variable and several linear leaf measurements as the independent variables. All independent variables were highly correlated to leaf area (P < .001); however, the product of leaf length and width consistently gave the highest r values. An analysis of variance of the regression coefficients using length x width as the independent variable indicated that vine to vine variance was usually not significant (P > .05). Cane variation within vines was also not significant. Mean slope and intercept values were calculated for each data set resulting in a single linear regression model for each of the three samples. A Bonferroni general multiple comparison procedure showed no significant differences among the three models. Calculated leaf area found using the ratio of fresh weight-to-unit leaf area was not significantly different than predicted leaf area based on foliometer measurements.

Measuring the Impacts of Solid Waste Disposal Site Location on Property Values

T HE large and growing quantity of solid wastes poses an increasingly complex disposal problem for rural and urban areas. One important effect of the location of disposal sites is the external effect on adjacent property values. This paper attempts to estimate external effects on property prices resulting from the location of landfill types of solid waste disposal sites. This has important implications for public policy on site location and possible compensation to internalize the resultant external effects. A single equation linear regression model for price estimation is hypothesized. The data sample is 182 observations of single-unit house sales over the period 1962-1970 in the neighborhoods around five solid waste disposal sites in Fort Wayne, Indiana. Date and price of sale, as well as location of the property and detailed information about dwelling characteristics, were obtained. Three general categories of predetermined variables are used: (1) Physical attributes of residential property-size of house and lot, number of bathrooms and bedrooms, age of house, amount of encumbrance and ownership-tenant occupancy (the key features of the quantity and quality of living service provided by a piece of residential property); (2) year of sale-the best available measure of the general level of cost of housing; (3) factors representing amenities and disamenities associated with solid waste disposal sites and neighborhood characteristics. Based on a diffusion phenomenon, the impacts of solid waste disposal sites on residential property prices were measured by distance from the nearest disposal site and the absolute degrees that the resiential property is away from downwind (prevailing) of the disposal site. Zero-one variables were used to represent differences among disposal sites. The predetermined variables in the linear model explained approximately 78 percent of the variation in residential property prices. Coefficients of the physical attribute variables were all s g ificantly different from zero at the .05 level and all had the hypothesized sign except the number of bedrooms. The distance and angle v riables are key policy variables in the model. Both coefficients were positive as hypothesized, suggesting that a premium is placed on being a g eater distance away and being away from downwind of disposal sites. The estimated coefficients indicate that on the average the price of residential property increases 61 cents per foot of distance and $10.30 per degree away from downwind of a disposal site. This first attempt to measure external effects f solid waste disposal sites on adjacent property values has important implications for community development and policy. The empirical results suggest magnitudes of costs imposed and indicate the nature of their distribution around solid waste disposal sites. In decisions concerning disposal site location, external social cost and benefit are an integral and possibly major factor. Further research is therefore warranted in refining the model and its variables to more accuately measure these effects.