Accuracy Of Regression Equations Research Articles

An iterative approach for deriving and solving an accurate regression equation

ABSTRACT This paper introduces a method for deriving an accurate regression equation based on a set of any paired data, and a technique for solving the equation. For a practical example, we used five hundred seventy-one pairs of sediment concentration and river flow data to derive an accurate sediment rating equation. The graphs of the measured and predicted sediment concentrations matched each other, and data correlation showed Nash–Sutcliffe efficiency (NSE) of 0.9999860, coefficient of determination ( R 2 ) of 0.99998679, root mean square error (RMSE) of 0.0345, mean average error (MAE) of 0.0067, volume error (VE) of 1, and sum of square error (SSE) of 0.678631. To explain the technique of deriving and solving the accurate regression equation, separate files of video presentation and excel spreadsheet are provided as supplementary materials. In general, the method can be used to model any processes, and any calibration and validation processes can be addressed.

Effect of Sleeper-Ballast Particle Contact on Lateral Resistance of Concrete Sleepers in Ballasted Railway Tracks.

Although a sleeper makes a great contribution to the lateral resistance of ballasted tracks, in this regard, limited studies have been carried out on the effect of its contact surface with ballast aggregates. The current paper is dedicated to evaluating the effect of sleeper shape on the lateral resistance of ballasted track through discrete element modelling (DEM). For this purpose, firstly, a DEM model was validated based on the experimental results. Then, a sensitivity analysis was undertaken on the effect of the different contact areas that a standard concrete sleeper faces with the crib, shoulder and underlying ballast aggregates on lateral resistance of a single sleeper. As the main result of the current study, a high accurate regression equation for constant weight 319.2 kg and constant density 2500 kg/m3 of the sleepers was fitted between different sleeper contact areas and the maximum lateral resistance of a concrete sleeper for 3.5 mm lateral displacement in ballasted railway tracks. The obtained results showed that the effect of the sleeper's head area compared to the underlying area of the sleeper and the head area of the sleeper compared to the sleeper's side area in terms of lateral resistance are 8.2 times and 14.5 times more, respectively.

A quantitative model to predict hydraulic fracture propagating across cemented natural fracture

A quantitative model is proposed to predict hydraulic fracture propagating across cemented natural fracture based on the numerical simulation and statistical regression. The cohesive zone method is employed to capture fracture initiation and growth, and the model combining rock deformation and fluid flow is established to simulate hydraulic fracture propagation with pre-existing natural fracture. The numerical model is solved by using finite element method, and verified against the analytical solution on the classical fracture problem. The investigation of influencing factors on hydraulic fracture propagation shows that the horizontal principal stress difference, approaching angle, cementing strength of natural fracture, injection rate and fluid viscosity codetermine whether hydraulic fracture propagates across natural fracture. After identification of these influencing factors, a series of numerical cases are conducted based on different combination of factor levels. Then the logistic regression method is employed to get the quantitative relationship between the crossing result and the factors, and the accuracy of regression equation is above 99%. The crossing curves are drawn to give the threshold of injection rate for varying other influencing factors. The potential applications include the usage of crossing criterion in the numerical modeling of fracture network propagation and the optimization of injection rate in the real field.

Perbandingan Model Regresi untuk Pengukuran Luas Daun Gandum di Daerah Tropis

The growth of wheat plants can be determined by measuring leaf area index and net assimilation rate. Both measurements require leaf area data. Measurement of leaf area of wheat in Indonesia requires a method that is not only accurate, but also easier and cheaper. One of them is the regression method. The purpose of this study was to determine an accurate regression equation model in predicting wheat leaf area. This research was conducted from March to June 2021 at the Experimental Station and Plant Production Technology Laboratory, Faculty of Agriculture, UNPAD, Jatinangor, Sumedang. The materials used in this study were various leaf area printing papers from wheat plants aged 14 days after planting (DAP), 28 DAP, and 42 DAP. The regression equation was assembled from the relationship between leaf area with leaf width and length, then compared with the actual leaf area that measured by scanning. The results showed that the linear, quadratic, cubic, and logarithmic regression equations had a coefficient of determination of more than 90% to predict leaf area, at the age of 14, 28, and 42 DAP, as well as all plant ages. Quadratic regression had a limit of data that can be entered, so it needed circumspection in using the formula. Cubic regression tended to have better accuracy in predicting leaf area at 14, 28, and 42 DAP, but the accuracy was the same as other regression equations at all plant ages.

Application of Multiple Regression in Mathematical Model of Air Quality Calibration

Based on the existing self-built point data, state-controlled point data and wind speed, pressure, precipitation, temperature, humidity and other data, a multivariate regression mathematical model is established in this paper to optimize the self-built point data. The model is optimized via data to find out the factors that have great influence on the data of self-built points and get more accurate regression equation model. After verification, it can be seen that the calibration degree of the model to the self-built point data is high.

Prediction of Spirometric Indices Using Forced Oscillometric Indices in Patients with Asthma, COPD, and Interstitial Lung Disease.

Background and ObjectiveSpirometry is sometimes difficult to perform in elderly patients and patients with cognitive impairment. Forced oscillometry (FOT) is a simple, noninvasive technique used for measuring respiratory impedance. The aim of this study was to develop regression equations to estimate vital capacity (VC), forced vital capacity (FVC), and forced expiratory volume in 1 s (FEV1.0) on the basis of FOT indices and to evaluate the accuracy of these equations in patients with asthma, chronic obstructive pulmonary disease (COPD), and interstitial lung disease (ILD).Materials and MethodsWe retrospectively included data on 683 consecutive patients with asthma (388), COPD (128), or ILD (167) in this study. We generated regression equations for VC, FVC, and FEV1.0 by multivariate linear regression analysis and used them to estimate the corresponding values. We determined whether the estimated data reflected spirometric indices.ResultsActual and estimated VC, FVC, and FEV1.0 values showed significant correlations (all r > 0.8 and P < 0.001) in all groups. Biases between the actual data and estimated data for VC, FVC, and FEV1.0 in the asthma group were −0.073 L, −0.069 L, and 0.017 L, respectively. The corresponding values were −0.064 L, 0.027 L, and 0.069 L, respectively, in the COPD group and −0.040 L, −0.071 L, and −0.002 L, respectively, in the ILD group. The estimated data in the present study did not completely correspond to the actual data. In addition, sensitivity for an FEV1.0/FVC ratio of <0.7 and the diagnostic accuracy for the classification of COPD grade using estimated data were low.ConclusionThese results suggest that our method is not highly accurate. Further studies are needed to generate more accurate regression equations for estimating spirometric indices based on FOT measurements.

An Ecological Compensation Model for Liuxi River Basin Based on Emission Rights

Researches on standards of ecological compensation will raise awareness of protecting the ecological environment in the basin and maintain the economy&amp;rsquo;s and society&amp;rsquo;s sustainable development. This paper constructed an ecological compensation model on the Liuxi River Basin in Guangzhou, China. Data and statistics were acquired from the statistical yearbook in Guangzhou Statistical Information Network, including the total GDP, total wastewater discharge amount and total population of Guangzhou for 13 years (1995, 2000, 2005&amp;ndash;2015). Then, SPSS was used to fit the scatter plot of volume of wastewater discharged per capita and GDP per capita, and the most accurate regression equation was selected. Most importantly, an ecological compensation model was constructed based on emission rights and it was then used to calculate the annual eco-compensation fee for Conghua, where the river&amp;rsquo;s upper part is located. The results showed that the amount of ecological compensation in 2017 was 33.821 billion Chinese Yuan, which should be used to compensate Conghua for the emission rights it had given up for protecting water quality of the Liuxi River. This study provided an effective reference to the government&amp;rsquo;s decision on continuous improvement of the &amp;ldquo;Guangzhou Ecological Compensation Plan for Liuxi River Basin&amp;rdquo;.

Dry and Ash Free Dry Mass to Length Relationships and Salinity Stress Response of Rock Crayfish (Cambarus carinirostris) and Allegheny Crayfish (Faxonius obscurus)

Increasing population size and road density has lead to a dramatic increase in salt application during the cold months over the last few decades in the northeastern United States. As a result, salinity levels of freshwater streams are rising at a rapid rate. This increase in salinity has led to habitat degradation in aquatic ecosystems and a harmful effect on the health of freshwater organisms. The purpose of this project is to explore the impact of increased salinity levels on the stress levels of two common native crayfish species, the Rock Crayfish (C. carinirostris) and the Allegheny Crayfish (Faxonius obscurus), by measuring the change in respiration through the tracking of dissolved oxygen levels. This will be accomplished through the use of a respiration chamber containing various concentrations of salt solutions made from common road salt deicer. Respiration rate will be corrected for crayfish ash free dry mass and regressed against salinity. Crayfish responses to salinity may be indicative of how other freshwater macroinvertebrates react to increased salinity levels. The specimens will be dried, and their dry masses will be collected. They will be ashed to create regression equations to convert between various morphometric measurements, dry mass, and ash free dry mass. The morphometric measurements that produce the most accurate regression equation will be determined.

Application Of L1- Regularization Approach In QSAR Problem. Linear Regression And Artificial Neural Networks

One of the primary tasks of analytical chemistry and QSAR/QSPR researches is building of prognostic regression equations based on descriptors sets. The one of the most important problems here is to decrease the number of descriptors in the initial descriptor set which is usually way too big. In current investigation the descriptor set is proposed to be reduced employing the least absolute shrinkage and selection operator (LASSO) approach. Decreased descriptor sets were used for calculations with application of the following QSAR/QSPR methods: ordinary least squares (OLS), the least absolute deviation (LAD) regressions and artificial neural networks (ANN). Contrary to aforementioned methods principal component regression (PCR) and partial least squares (PLS) approaches can produce solutions containing numerous descriptors. In this article we compared the viability of these two different descriptor handling ideologies in application to molecular chemical and physical properties prediction. From the obtained results it is possible to see that there are tasks for which PCR and PLS approaches can fail to produce accurate regression equations. At the same time, methods OLS and LAD that use small amount of descriptors can provide viable solutions for the same cases. It was shown that these small sets of descriptors selected with LASSO approach can be used in ANN to obtain models with even better internal validation characteristics.

Lower limb sagittal kinematic and kinetic modeling of very slow walking for gait trajectory scaling.

Lower extremity powered exoskeletons (LEPE) are an emerging technology that assists people with lower-limb paralysis. LEPE for people with complete spinal cord injury walk at very slow speeds, below 0.5m/s. For the able-bodied population, very slow walking uses different neuromuscular, locomotor, postural, and dynamic balance control. Speed dependent kinetic and kinematic regression equations in the literature could be used for very slow walking LEPE trajectory scaling; however, kinematic and kinetic information at walking speeds below 0.5 m/s is lacking. Scaling LEPE trajectories using current reference equations may be inaccurate because these equations were produced from faster than real-world LEPE walking speeds. An improved understanding of how able-bodied people biomechanically adapt to very slow walking will provide LEPE developers with more accurate models to predict and scale LEPE gait trajectories. Full body motion capture data were collected from 30 healthy adults while walking on an instrumented self-paced treadmill, within a CAREN-Extended virtual reality environment. Kinematic and kinetic data were collected for 0.2 m/s—0.8 m/s, and self-selected walking speed. Thirty-three common sagittal kinematic and kinetic gait parameters were identified from motion capture data and inverse dynamics. Gait parameter relationships to walking speed, cadence, and stride length were determined with linear and quadratic (second and third order) regression. For parameters with a non-linear relationship with speed, cadence, or stride-length, linear regressions were used to determine if a consistent inflection occurred for faster and slower walking speeds. Group mean equations were applied to each participant’s data to determine the best performing equations for calculating important peak sagittal kinematic and kinetic gait parameters. Quadratic models based on walking speed had the strongest correlations with sagittal kinematic and kinetic gait parameters, with kinetic parameters having the better results. The lack of a consistent inflection point indicated that the kinematic and kinetic gait strategies did not change at very slow gait speeds. This research showed stronger associations with speed and gait parameters then previous studies, and provided more accurate regression equations for gait parameters at very slow walking speeds that can be used for LEPE joint trajectory development.

Use of the forced-oscillation technique to estimate spirometry values.

PurposeSpirometry is sometimes difficult to perform in elderly patients and in those with severe respiratory distress. The forced-oscillation technique (FOT) is a simple and noninvasive method of measuring respiratory impedance. The aim of this study was to determine if FOT data reflect spirometric indices.Patients and methodsPatients underwent both FOT and spirometry procedures prior to inclusion in development (n=1,089) and validation (n=552) studies. Multivariate linear regression analysis was performed to identify FOT parameters predictive of vital capacity (VC), forced VC (FVC), and forced expiratory volume in 1 second (FEV1). A regression equation was used to calculate estimated VC, FVC, and FEV1. We then determined whether the estimated data reflected spirometric indices. Agreement between actual and estimated spirometry data was assessed by Bland–Altman analysis.ResultsSignificant correlations were observed between actual and estimated VC, FVC, and FEV1 values (all r>0.8 and P<0.001). These results were deemed robust by a separate validation study (all r>0.8 and P<0.001). Bias between the actual data and estimated data for VC, FVC, and FEV1 in the development study was 0.007 L (95% limits of agreement [LOA] 0.907 and −0.893 L), −0.064 L (95% LOA 0.843 and −0.971 L), and −0.039 L (95% LOA 0.735 and −0.814 L), respectively. On the other hand, bias between the actual data and estimated data for VC, FVC, and FEV1 in the validation study was −0.201 L (95% LOA 0.62 and −1.022 L), −0.262 L (95% LOA 0.582 and −1.106 L), and −0.174 L (95% LOA 0.576 and −0.923 L), respectively, suggesting that the estimated data in the validation study did not have high accuracy.ConclusionFurther studies are needed to generate more accurate regression equations for spirometric indices based on FOT measurements.

CUF scaling effect on contact angle and threshold pressure

PurposeThis paper aims to present experimental and finite volume method (FVM)-based simulation studies on the scaling effect on the capillary contact angle and entrant pressure for a three-dimensional encapsulation process of ball-grid array (BGA).Design/methodology/approachWith the development of various sizes of BGA packages, the scaling effect of BGA model on capillary underfill (CUF) process is investigated together with the influences of different industrial standard solder bump arrangements and dispensing methods used as case study.FindingsThe experimental results agree well to the simulation findings with minimal deviation in filling time and similar flow front profiles for all setups. The results revealed that the capillary contact angle of flow front decreases in scale-up model with larger gap height observed and lengthens the encapsulation process. Statistical correlation studies are conducted and accurate regression equations are obtained to relate the gap height to the completion filling time and contact angle. CUF threshold capillary pressures were computed based on Leverett-J function and found to be increasing with the scale size of the package.Practical implicationsThese statistical data provide accurate insights into the impact of BGA’s scale sizes to the CUF process that will be benefiting the future design of BGA package. This study provided electronic designers with profound understanding on the scaling effect in CUF process of BGA, which may be extended to the future development of miniature-sized BGA and multi-stack device.Originality/valueThis study relates the flow behaviour of encapsulant to its capillary contact angle and Leverett-J pressure threshold, in the CUF process of different BGA and dispensing conditions. To date, no research has been found to predict the threshold pressure on the gap between the chip and substrate.

Development and evaluation of models to estimate body chemical composition of young Nellore bulls

ABSTRACT The objective of this study was to develop accurate regression equations to predict body composition of Nellore cattle using chemical composition of the 9th, 10th, and 11th ribs and to evaluate the models proposed by analyzing mean and linear bias. Sixty-seven Nellore bulls were slaughtered and slaughter body weight (SBW), hot carcass weight (HCW), and 9th-, 10th-, and 11th-rib-cut weight (RCW) were measured. Empty body composition was obtained after grinding, homogenizing, sampling, chemical analysis, and pooling (blood, skin, head [...]

Performance study of parallel kanban-base stock for a high-mix multi-stage production system with the entrance of rework

The present study evaluates the performance of parallel kanban-base stock (PKB) system to regulate the production of high-mix items in a multi-stage shared-machine facility with the entrance of rework. The high-runner products are handled using a kanban system and low-runner products using a base stock system. The PKB systems were differentiated in terms of the model driver, loading rule, and rework entrance policy. The performance measures adopted the total output, average work-in-process, flow times and average machine utilisations. Discrete-event simulations were conducted with an analysis constituted of multi-factor ANOVA and response surface methodology. From the analysis, there is a specific R(LR) value that gives desired performance, and at the same time, its dependency is solely on accuracy of regression equation. Between rework policies, predominantly merge rework entrance policy yields more desirable results as observed within performance measures, compared to original rework entrance policy.

Reconstruction of Length of Humerus from its Fragments and its Medicolegal Importance

Objective : In Medicolegal cases, the skeletal remains presented to Anatomists and Forensic experts are often fragmentary and asked to pronounce an opinion in order to establish a possible identity. For this reason the present study is undertaken on the samples of vidarbha region of Maharashtra with the object to estimate the length of the humerus from its various fragments and then the stature can be estimated by using the multiplication factor. Material&Method : The material consists of 167 adult human humeri from dissection hall cadavers of Govt. Medical College, Nagpur. Measurements of total length of humerus and its various fragments were taken on the osteometric board. In order to compare the measurements the humerus was divided in to four segments: A-B, A-C, C-E and D- E. The Range, Mean, S.D. , percentile length, co-efficient of correlation and Regression equations for each segments were calculated. With the help of regression equation, the length of humerus was estimated. Results : The co-efficient of correlation obtained for all the segments is statistically significant. The total length of humerus calculated from segment I (A-B) and segment IV (D-E) by regression equations showed an average error of 1.5 cms. and from segment II (A-C) and segment III (C-E) showed an error less than 1 cm. Conclusion : The Regression formulae can be used to estimate the length of humerus from its segments. The accuracy of regression equations of each segment in calculating the length of humerus in this region is very high.

MODELLING OF INTERNAL COMBUSTION ENGINES’ EMISSION THROUGH THE USE OF TRAFFIC FLOW MATHEMATICAL MODELS

Road traffic flows on a straight road segment are modelled in this article. The mathematical model of traffic flows has been constructed by using the method of lumped parameters. CO2, CO, CH, NOx, PM regression equations of internal combustion engines’ (ICE) emission has been developed. The accuracy of regression equations is 0.98÷0.99. The article presents assumptions for constructing the mathematical model, description of the mathematical model and gives simulation results. Traffic flow parameters, such as traffic flow concentration and traffic flow speed are presented as modelling results. ICE emission depending on the concentration and traffic flow speed are presented as well.

Estimation of carcass composition by ultrasound measurements in 4 anatomical locations of 3 commercial categories of lamb1

The objectives were to study the relationship between in vivo ultrasound measurements and cold carcass measurements at 4 anatomical points along the backbone of lambs and to determine appropriate regression equations to estimate carcass composition by using ultrasonic measurements at each anatomical point. The lambs (n = 114) used were suckling lambs (BW = 11.09 kg), light lambs (BW = 22.43 kg), and wethers (BW = 32.03 kg), representing a wide range of BW. Measurements of subcutaneous fat and skin thickness and of muscle depth and muscle width were taken over the 10th to 11th and 12th to 13th thoracic vertebrae and over the first to second and third to fourth lumbar vertebrae. These measurements were taken at one-third of the musculus longissimus thoracis et lumborum (LMT) width with the probe perpendicular to the backbone. The left sides of the carcasses were dissected into muscle, fat, and bone. The weight of lean tissue increased (P < 0.001) at a rate of approximately 500 g for each kilogram of carcass weight increase. Pelvic fat weight increased (P < 0.001) slightly with increasing carcass weight (11.8 g), whereas kidney fat and subcutaneous fat showed great gains (P < 0.001; 40.3 and 134.4 g, respectively). Ultrasound LMT width of light lambs remained constant along the backbone, whereas LMT width of suckling lambs and wethers increased (P < 0.001) from the cranial to the caudal direction. Ultrasound LMT depth and fat thickness between the 10th and 11th thoracic vertebrae were greater (P < 0.01) than measurements taken at other backbone locations. The greatest difference between ultrasound and carcass measurements was in LMT width, with differences between ultrasound and carcass measurements always being greater in LMT depth than in fat thickness. Carcass LMT width was more closely correlated with carcass lean than with other tissues, especially at both thoracic locations (r = 0.80 and r = 0.71). In general, skin thickness measured by ultrasound was poorly correlated (from r = 0.19 to r = 0.33) with all carcass tissues because of slight variations in skin thickness. Ultrasound LMT depth was more closely correlated with carcass tissues than was carcass LMT depth (from r = 0.53 for bone to r = 0.71 for lean), whereas ultrasound fat depth and carcass fat depth presented similar correlations (from r = 0.49 for bone to r = 0.72 for intermuscular fat). Regression coefficients for predicting lean were 0.95 to 0.96, for predicting subcutaneous fat were 0.67 to 0.75, for predicting intermuscular fat were 0.81 to 0.84, and for predicting bone were 0.78 to 0.88. This study was not conclusive regarding predicting carcass composition in relation to an optimal anatomical position, given that all the anatomical locations studied allowed accurate regression equations. Body weight was the most important predictor of carcass composition, with a slight improvement in regression equations when using ultrasound. However, ultrasound muscle and fat depths were correlated with carcass muscle and fat depths and with the tissular composition of carcass.

Prediction of digestible energy content across feed ingredients and fish species by linear regression

In an attempt to develop predictive relationships, apparent digestible energy (ADE) content (n = 361) as biological dependent variable and dietary contents of crude protein (CP), lipid, ash and gross energy (GE) as independent variables, obtained in 40 studies with 65 different feed ingredients and evaluated with 26 fish species, were subjected to linear correlation and multiple linear regression analysis. With dietary CP and GE contents identified as significant predictors, only 58% of the variation in ADE content could be explained. No improvement in accuracy of regression equations was gained by classification of values according to either feed ingredient (animal proteins, plant proteins, cereals) or fish species (water type, water temperature, feed habit). An R (2)-value of 0.4570 and mean prediction error (MPE) of 0.2085 between predicted and observed ADE values from eight independent studies (n = 37) illustrated the inability of the derived regression equation to accurately predict ADE contents of feed ingredients. Inclusion of dietary crude fibre and nitrogen-free extract (NFE) contents as independent variables did not improve the accuracy of prediction equations. The inadequacy of the use of linear regression to predict DE content from dietary composition across feed ingredients and fish species with high accuracy is discussed.

Improvement of organic matter digestibility along with changes of physical properties of rice straw by chemical treatments

This study was carried out to study the effects of different chemical treatments on physical properties and digestion of rice straw. Rice straw was treated with sodium hydroxide (NaOH) at 15, 30, 45, 60 or 75 g/kg dry matter, ammonia bicarbonate (NH 4 HCO 3 ) at 30, 60, 90, 120 or 150 g/kg or their combinations (10 or 20 g NaOH/kg and 30, 60 or 90 g NH 4 HCO 3 /kg), respectively. The relationship between straw digestion and its physical properties was analysed. Treatment with NaOH increased the volumetric weight (VW), swelling capacity (SC), water-holding capacity (WHC), and in vitro organic matter digestibility (OMD), and decreased specific porosity (SP) of rice straw linearly. Treatment with NH 4 HCO 3 did not significantly affect VW, SC, or SP, but increase OMD linearly and tended decrease WHC. For the combination treatment of NaOH and NH 4 HCO 3 , there existed significant interactions on SC, SP and OMD. A significant linear correlation was found between OMD and VW, SC, SP, or WHC, when the data for all treatments were analysed. The accuracy of regression equation could be improved by including multiple physical property parameters. It is inferred that change in all physical properties is indicative of improvement in straw digestion after treatment.

Using Soil Physical and Chemical Properties to Estimate Bulk Density

A stepwise multiple regression procedure was developed to predict oven-dried bulk density from soil properties using the 1997 USDA-NRCS National Soil Survey Characterization Data. The database includes both subsoil and topsoil samples. An overall regression equation for predicting oven-dried bulk density from soil properties (R2 = 0.45, P < 0.001) was developed using almost 47000 soil samples. Partitioning the database by soil suborders improved regression relationships (R2 = 0.62, P < 0.001). Of the soil properties considered, the stepwise multiple regression analysis indicated that organic C content was the strongest contributor to bulk density prediction. Other significant variables included clay content, water content and to a lesser extent, silt content and depth. In general, the accuracy of regression equations was better for suborders containing more organic C (most Inceptisols, Spodosols, Ultisols, and Mollisols). Bulk density was poorly predicted for suborders of the Aridisol and Vertisol orders which contain little or no organic C. Although organic C was an important variable in the suborder analysis, water content explained most (>30%) of the variation in bulk density for Udox, Xererts, Ustands, Aquands, and Saprists. Relationships between bulk density with soil volume measured on oven-dried natural clods and bulk density with soil volume measured at field-moisture content and one-third bar were also determined (R2 = 0.70 and 0.69, respectively; P < 0.001). Utilizing the regression equations developed in this study, oven-dried bulk density predictions were obtained for 71% of the 85608 samples in the database without bulk density measurements. While improving on methods of previous analyses, this study illustrates that regression equations are a feasible alternative for bulk-density estimation.