Estimating weights when fitting linear regression models for tree volume

1993 ◽  
Vol 23 (8) ◽  
pp. 1725-1731 ◽  
Author(s):  
Michael S. Williams ◽  
Timothy G. Gregoire
Keyword(s):  
Linear Regression ◽  
Weight Function ◽  
Loblolly Pine ◽  
Weighted Least Squares ◽  
Data Sets ◽  
Regression Equations ◽  
Linear Regression Models ◽  
White Oak ◽  
Data Set ◽  
Error Structure

The method of weighted least squares can be used to achieve homogeneity of variance with linear regression that has a heterogeneous error structure. A weight function commonly used when constructing regression equations to predict tree volume is [Formula: see text], where k1 ≈ 1.0–2.1. This paper examines the weight function [Formula: see text] for modelling the error structure in two loblolly pine (Pinustaeda L.) data sets and one white oak (Quercusalba L.) data set. The weight function [Formula: see text] is recommended for all three data sets, for which the k1 values ranged from 1.80 to 2.07.

PSVI-8 Meta-regression Analysis to Determine the Relationship Between Growing Pig Body Weight and Variation

2021 ◽  
Vol 99 (Supplement_1) ◽  
pp. 218-219
Author(s):  
Andres Fernando T Russi ◽  
Mike D Tokach ◽  
Jason C Woodworth ◽  
Joel M DeRouchey ◽  
Robert D Goodband ◽  
...  
Keyword(s):  
Body Weight ◽  
Regression Analysis ◽  
Sample Size ◽  
Polynomial Regression ◽  
Data Sets ◽  
Regression Equations ◽  
Prediction Equations ◽  
Data Set ◽  
Rate Of Increase ◽  
The Relationship

Abstract The swine industry has been constantly evolving to select animals with improved performance traits and to minimize variation in body weight (BW) in order to meet packer specifications. Therefore, understanding variation presents an opportunity for producers to find strategies that could help reduce, manage, or deal with variation of pigs in a barn. A systematic review and meta-analysis was conducted by collecting data from multiple studies and available data sets in order to develop prediction equations for coefficient of variation (CV) and standard deviation (SD) as a function of BW. Information regarding BW variation from 16 papers was recorded to provide approximately 204 data points. Together, these data included 117,268 individually weighed pigs with a sample size that ranged from 104 to 4,108 pigs. A random-effects model with study used as a random effect was developed. Observations were weighted using sample size as an estimate for precision on the analysis, where larger data sets accounted for increased accuracy in the model. Regression equations were developed using the nlme package of R to determine the relationship between BW and its variation. Polynomial regression analysis was conducted separately for each variation measurement. When CV was reported in the data set, SD was calculated and vice versa. The resulting prediction equations were: CV (%) = 20.04 – 0.135 × (BW) + 0.00043 × (BW)2, R2=0.79; SD = 0.41 + 0.150 × (BW) - 0.00041 × (BW)2, R2 = 0.95. These equations suggest that there is evidence for a decreasing quadratic relationship between mean CV of a population and BW of pigs whereby the rate of decrease is smaller as mean pig BW increases from birth to market. Conversely, the rate of increase of SD of a population of pigs is smaller as mean pig BW increases from birth to market.

scholarly journals Tolerance Intervals in a Heteroscedastic Linear Regression Context with Applications to Aerospace Equipment Surveillance

2009 ◽  
Vol 2009 ◽  
pp. 1-8 ◽  
Author(s):  
Janet Myhre ◽  
Daniel R. Jeske ◽  
Michael Rennie ◽  
Yingtao Bi
Keyword(s):  
Linear Regression ◽  
Least Squares ◽  
Performance Metrics ◽  
Weighted Least Squares ◽  
Ordinary Least Squares ◽  
Automated System ◽  
Least Squares Regression ◽  
Data Set ◽  
Tolerance Intervals ◽  
Power Of The Test

A heteroscedastic linear regression model is developed from plausible assumptions that describe the time evolution of performance metrics for equipment. The inherited motivation for the related weighted least squares analysis of the model is an essential and attractive selling point to engineers with interest in equipment surveillance methodologies. A simple test for the significance of the heteroscedasticity suggested by a data set is derived and a simulation study is used to evaluate the power of the test and compare it with several other applicable tests that were designed under different contexts. Tolerance intervals within the context of the model are derived, thus generalizing well-known tolerance intervals for ordinary least squares regression. Use of the model and its associated analyses is illustrated with an aerospace application where hundreds of electronic components are continuously monitored by an automated system that flags components that are suspected of unusual degradation patterns.

scholarly journals Individual Tree Volume Equations for Red Pine in Michigan

1997 ◽  
Vol 14 (2) ◽  
pp. 53-58 ◽  
Author(s):  
Gary W. Fowler
Keyword(s):  
Red Pine ◽  
Data Sets ◽  
Regression Equations ◽  
Independent Data ◽  
Data Set ◽  
Individual Tree ◽  
Standing Trees ◽  
Pine Stands ◽  
Volume Estimates ◽  
Volume Equations

Abstract New total, pulpwood, sawtimber, and residual pulpwood cubic foot individual tree volume equations were developed for red pine in Michigan using nonlinear and multiple linear regression. Equations were also developed for Doyle, International 1/4 in., and Scribner bd ft volume, and a procedure for estimating pulpwood and residual pulpwood rough cord volumes from the appropriate cubic foot equations was described. Average ratios of residual pulpwood (i.e., topwood, cubic foot or cords) to mbf were developed for 7.6 and 9.6 in. sawtimber. Data used to develop these equations were collected during May-August 1983-1985 from 3,507 felled and/or standing trees from 27 stands in Michigan. Sixteen and 11 stands were located in the Upper and Lower Peninsulas, respectively. All equations were validated on an independent data set. Rough cord volume estimates based on the new pulpwood equation were compared with contemporary tables for 2 small cruise data sets. The new equations can be used to more accurately estimate total volume and volume per acre when cruising red pine stands. North. J. Appl. For. 14(2):53-58.

scholarly journals Controlling the outcome of SN2 reactions in ionic liquids: from rational data set design to predictive linear regression models

2020 ◽  
Vol 22 (40) ◽  
pp. 23009-23018
Author(s):  
Alexandra Schindl ◽  
Rebecca R. Hawker ◽  
Karin S. Schaffarczyk McHale ◽  
Kenny T.-C. Liu ◽  
Daniel C. Morris ◽  
...  
Keyword(s):  
Ionic Liquids ◽  
Linear Regression ◽  
Regression Models ◽  
Reaction Rate ◽  
Computational Approach ◽  
Set Design ◽  
Linear Regression Models ◽  
Data Set ◽  
Reaction Rate Constants ◽  
Sn2 Reactions

An iterative, combined experimental and computational approach towards predicting reaction rate constants in ionic liquids is presented.

A Ccomparison of sedigraph and pipette methods for soil particle-size analysis

Soil Research ◽  
1993 ◽  
Vol 31 (4) ◽  
pp. 407 ◽  
Author(s):  
GD Buchan ◽  
KS Grewal ◽  
JJ Claydon ◽  
RJ Mcpherson
Keyword(s):  
Particle Size ◽  
New Zealand ◽  
Particle Size Analysis ◽  
Size Analysis ◽  
Data Sets ◽  
Regression Equations ◽  
Total Iron Content ◽  
Data Set ◽  
X Ray ◽  
The Difference

The X-ray attenuation (Sedigraph) method for particle-size analysis is known to consistently estimate a finer size distribution than the pipette method. The objectives of this study were to compare the two methods, and to explore the reasons for their divergence. The methods are compared using two data sets from measurements made independently in two New Zealand laboratories, on two different sets of New Zealand soils, covering a range of textures and parent materials. The Sedigraph method gave systematically greater mass percentages at the four measurement diameters (20, 10, 5 and 2 �m). For one data set, the difference between clay (<2 �m) percentages from the two methods is shown to be positively correlated (R2 = 0.625) with total iron content of the sample, for all but one of the soils. This supports a novel hypothesis that the typically greater concentration of Fe (a strong X-ray absorber) in smaller size fractions is the major factor causing the difference. Regression equations are presented for converting the Sedigraph data to their pipette equivalents.

scholarly journals Technical Note: Regression Analysis of Proximal Hyperspectral Data to Predict Soil pH and Olsen P

Agriculture ◽  
2019 ◽  
Vol 9 (3) ◽  
pp. 55 ◽  
Author(s):  
Miles Grafton ◽  
Therese Kaul ◽  
Alan Palmer ◽  
Peter Bishop ◽  
Michael White
Keyword(s):  
Soil Nutrient ◽  
Large Data ◽  
Technical Note ◽  
Soil Samples ◽  
Hyperspectral Data ◽  
Data Sets ◽  
Regression Equations ◽  
Data Set ◽  
Hill Country ◽  
Olsen P

This work examines two large data sets to demonstrate that hyperspectral proximal devices may be able to measure soil nutrient. One data set has 3189 soil samples from four hill country pastoral farms and the second data set has 883 soil samples taken from a stratified nested grid survey. These were regressed with spectra from a proximal hyperspectral device measured on the same samples. This aim was to obtain wavelengths, which may be proxy indicators for measurements of soil nutrients. Olsen P and pH were regressed with 2150 wave bands between 350 nm and 2500 nm to find wavebands, which were significant indicators. The 100 most significant wavebands for each proxy were used to regress both data sets. The regression equations from the smaller data set were used to predict the values of pH and Olsen P to validate the larger data set. The predictions from the equations from the smaller data set were as good as the regression analyses from the large data set when applied to it. This may mean that, in the future, hyperspectral analysis may be a proxy to soil chemical analysis; or increase the intensity of soil testing by finding markers of fertility cheaply in the field.

Statistical Models for the Twinning Rate

1987 ◽  
Vol 36 (3) ◽  
pp. 297-312 ◽  
Author(s):  
J.O. Fellman ◽  
A.W. Eriksson
Keyword(s):  
Linear Regression ◽  
Statistical Models ◽  
Maternal Age ◽  
Regression Models ◽  
Model Building ◽  
Data Sets ◽  
Linear Regression Models ◽  
Linear Regression Technique ◽  
Secular Decline ◽  
Disaggregated Data

AbstractLinear regression models are used to explain the variations in the twinning rates. Data sets from different countries are analysed and maternal age, parity and marital status are the main regressors. The model building technique is also used in order to study the secular decline in the twinning rate. Linear regression technique makes it possible to compare the effect of different factors but the method requires sufficiently disaggregated data.

scholarly journals Regression models for estimating chick hatchling weight from some egg geometry traits

2018 ◽  
Vol 34 (3) ◽  
pp. 323-334
Author(s):  
Nadya Mincheva ◽  
Mitko Lalev ◽  
Magdalena Oblakova ◽  
Pavlina Hristakieva
Keyword(s):  
Linear Regression ◽  
Surface Area ◽  
Regression Models ◽  
Linear Models ◽  
Geometric Mean ◽  
Coefficient Of Determination ◽  
Regression Equations ◽  
Linear Regression Models ◽  
Egg Weight ◽  
Mean Diameter

The prediction of chicks? weight before hatching is an important element of selection, aimed at improving the uniformity rate and productivity of birds. With this regards, our goal was to develop and evaluate optimum models for similar prediction in two White Plymouth Rock chickens lines - line L and line K on the basis of the incubation egg weight and egg geometry characteristics - egg maximum breadth (B), egg length (L), geometric mean diameter (Dg), egg volume (V), egg surface area (S). A total of 280 eggs (140 from each line) laid by 40-weekold hens were randomly selected. Mean arithmetic values, standard deviations and coefficients of variation of studied parameters were determined for each line. Correlation coefficients between the weight of hatchlings and predictors were the highest for egg weight, geometric mean diameter, volume and surface area of eggs (r=0.731-0.779 for line L; r=0.802-0.819 for line ?). Nine linear regression models were developed and their accuracy evaluated. The regression equations of hatchlings? weight vs egg length had the lowest coefficient of determination (0.175 for line K and 0.291 for line L), but when egg length and breadth entered the model together, its value increased significantly up to 0.541 and 0.665 for lines L and K, respectively. The weight of day-old chicks from line L could be predicted with higher accuracy with a model involving egg surface area apart egg weight (ChW=0.513EW+0.282S - 10.345; R2=0.620). In line ? a more accurate prognosis was attained by adding egg breadth as an additional predictor to the weight in the model (ChW=0.587EW+0.566? - 19.853; R2=0.692). The study demonstrated that multiple linear regression models were more precise that single linear models.

scholarly journals Comparison of Sediment Rating Curves Developed on Load and on Concentration

1997 ◽  
Vol 28 (3) ◽  
pp. 189-200 ◽  
Author(s):  
Margareta B. Jansson
Keyword(s):  
Linear Regression ◽  
Bias Correction ◽  
Water Discharge ◽  
Regression Equations ◽  
Rating Curve ◽  
Weighted Mean ◽  
Data Set ◽  
Sediment Rating Curve ◽  
Rating Curves ◽  
Linear Regressions

A sediment rating curve developed as a linear regression on logged values which is back-transformed must be corrected for the bias introduced by the log transformation. This article shows that the variances are identical for linear regressions based on values of logged load and logged concentration from the same data set. This means that the bias correction factoss 101.1513σ2 for the back-transformed regressions are equivalent. Therefore a back-tranoformed log regression based on loads corrected for bias gives identical sedimett discharges to a back-transformed log regression on concentrations corrected for bias. Regression equations from gauging stations in two neighbouring basins in Costa Rica confirm this conclusion. Mean loads for individual discharge classes were plotted on diagrams in log scales to find the points where the sedimett rating curve changes direction. When sediment rating curves were developed on logged mean concentrations, water discharge weighted mean concentrations had to be determined in order to produce equations comparable to those on logged mean loads. Consequently, discharge weighted mean concentrations must be used in a plot to determine the change in direction of a sedimett rating curve and to check the goodnsss of fit of a regression developed by any model employing concentration as the dependent variabe.

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