Comparison of a class of regression equations

1984 ◽  
Vol 246 (3) ◽  
pp. R271-R276
Author(s):  
T. E. Jackson
Keyword(s):  
Linear Regression ◽  
Linear Model ◽  
Computer Analysis ◽  
Matrix Algebra ◽  
Full Rank ◽  
Confidence Regions ◽  
Regression Equation ◽  
Data Sets ◽  
Regression Equations ◽  
Testing Hypotheses

The method described in this paper offers a means of comparing linear regression equations with many parameters by utilizing joint parameter confidence regions. It is useful when comparing sets of data in which each set is represented by a similar regression equation. The method consists of establishing a full-rank linear model with the data sets to be considered and then testing hypotheses concerning parameters of the model. It is conveniently expressed in matrix algebra form and is amenable to computer analysis.

scholarly journals Comparison of Regression Equation and Friedewald’s Formula with Direct Measurement of Low-density Lipoprotein Cholesterol in Bangladeshi Population

2013 ◽  
Vol 6 (1) ◽  
pp. 143-152
Author(s):  
M. Saiedullah ◽  
N. Chowdhury ◽  
M.A.H. Khan ◽  
S. Hayat ◽  
S. Begum ◽  
...  
Keyword(s):  
Linear Regression ◽  
Low Density Lipoprotein ◽  
Density Lipoprotein ◽  
Regression Equation ◽  
Lipoprotein Cholesterol ◽  
Low Density ◽  
Regression Equations ◽  
Validation Group ◽  
Low Density Lipoprotein Cholesterol ◽  
Bangladeshi Population

Friedewald’s formula (FF) is the most widely used formula in clinical practice to calculate low-density lipoprotein cholesterol (LDLC) from total cholesterol (TC), triglyceride (TG) and high-density lipoprotein cholesterol (HDLC). But this formula frequently underestimates LDLC. The aim of this study was to derive a regression equation (RE) to abolish the underestimation and to compare the performance of RE and FF in Bangladeshi population. RE was derived from 531 lipid profiles (equation derivation group) for the calculation of LDLC by multiple linear regression analysis. The RE was then used to calculate LDLC in another 952 subjects (equation validation group). LDLC calculated by RE and FF were compared with measured LDLC by appropriate statistical analyses. In equation validation group, measured LDLC, LDLC calculated by RE and FF were 2.97±0.81, 2.91±0.80 and 2.72±0.93 mmol/L respectively. Precision (r) was 0.9525 for RE and 0.9193 for FF. Passing & Bablok linear regression equations against measured LDLC were y = 0.9792x + 0.007 for RE and y = 1.1412x – 0.6781 for FF. Accuracy within ±12% of measured LDLC was 79% and 57% for RE and FF, respectively. The derived RE is more accurate than FF for the calculation of LDLC in Bangladeshi population.  Keywords: Lipoprotein cholesterol; Friedewald’s formula; Bangladeshi population.  © 2013 JSR Publications. ISSN: 2070-0237 (Print); 2070-0245 (Online). All rights reserved.  doi: http://dx.doi.org/10.3329/jsr.v6i1.14864 J. Sci. Res. 6 (1), 143-152 (2014)

scholarly journals PENGARUH KUALITAS PRODUK TERHADAP KEPUTUSAN PEMBELIAN PAKAIAN MUSLIM PADA TOKO SEDIA PEUREULAK ACEH TIMUR

2019 ◽  
Vol 4 (2) ◽  
pp. 127-140
Author(s):  
Febi Febi ◽  
T. Muana Refi ◽  
Andi Tarlis
Keyword(s):  
Linear Regression ◽  
T Test ◽  
Regression Equations ◽  
Simple Linear Regression ◽  
Testing Hypotheses ◽  
Research Results ◽  
Test Correlation ◽  
Correlation Coeffi

This study aims to determine the effect of buying interest to the decision purchasing Muslim clothes on Sedia Toko Peureulak East Aceh. The sample in this study was 96 consumers, and the analysis equipment used simple linear regression equations, partial t-test, correlation coeffi cient, and determination coeffi cient testing. Based on the research results obtained by Y = 10.018 + 0,567X, testing coeffi cient correlation of 0.569, testing the determination coeffi cient 0.324 and testing hypotheses in the obtained tcount > ttable or 6.716 > 1.985 and tsig < 5% or 0.00 < 0.05. Thus the hypothesis of allegedly effect buying interest to decision purchasing Muslim clothes in East Aceh Peureulak Sedia Toko accepted.

scholarly journals A new uncertain linear regression model based on equation deformation

2021 ◽  
Author(s):  
Shuai Wang ◽  
Yufu Ning ◽  
Hongmei Shi
Keyword(s):  
Linear Regression ◽  
Regression Model ◽  
Linear Regression Model ◽  
Regression Equation ◽  
Elementary Transformation ◽  
Regression Equations ◽  
Linear Regression Equation ◽  
Unknown Parameters ◽  
Deformation Method ◽  
Cramer’S Rule

Abstract When the observed data are imprecise, the uncertain regression model is more suitable for the linear regression analysis. Least squares estimate can fully consider the given data and minimize the sum of squares of residual error, and can effectively solve the linear regression equation of imprecisely observed data. On the basis of uncertainty theory, this paper presents an equation deformation method for solving unknown parameters in uncertain linear regression equations. We first establish the equation deformation method of one-dimensional linear regression model, and then extend it to the case of multiple linear regression model. We also combine the equation deformation method with Cramer's rule and matrix, and propose the Cramer's rule and matrix elementary transformation method to solve the unknown parameters of the uncertain linear regression equation. Numerical examples show that the equation deformation method can effectively solve the unknown parameters of the uncertain linear regression equation.

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.

scholarly journals Linear regression equations to predict β-lactam, macrolide, lincosamide and fluoroquinolone minimum inhibitory concentrations from molecular antimicrobial resistance determinants in Streptococcus pneumoniae

2021 ◽  
Author(s):  
Walter Demczuk ◽  
Irene Martin ◽  
Averil Griffith ◽  
Brigitte Lefebvre ◽  
Allison McGeer ◽  
...  
Keyword(s):  
Streptococcus Pneumoniae ◽  
Antimicrobial Resistance ◽  
Linear Regression ◽  
Training Data ◽  
Data Sets ◽  
Sequencing Analysis ◽  
Regression Equations ◽  
Validation Data ◽  
Resistance Determinants ◽  
Multiple Variable

Antimicrobial resistance in Streptococcus pneumoniae represents a threat to public health and monitoring the dissemination of resistant strains is essential to guiding health policy. Multiple-variable linear regression modeling was used to determine the contributions of molecular antimicrobial resistance determinants to antimicrobial minimum inhibitory concentration (MIC) for penicillin, ceftriaxone, erythromycin, clarithromycin, clindamycin, levofloxacin, and trimethoprim/sulfamethoxazole. Training data sets consisting of Canadian S. pneumoniae isolated from 1995 to 2019 were used to generate multiple-variable linear regression equations for each antimicrobial. The regression equations were then applied to validation data sets of Canadian (n=439) and USA (n=607 and n=747) isolates. The MIC for β-lactam antimicrobials were fully explained by amino acid substitutions in motif regions of the penicillin binding proteins PBP1a, PPB2b, and PBP2x. Accuracy of predicted MICs within one doubling dilution to phenotypically determined MICs for penicillin was 97.4%, ceftriaxone 98.2%; erythromycin 94.8%; clarithromycin 96.6%; clindamycin 98.2%; levofloxacin 100%; and trimethoprim/sulfamethoxazole 98.8%; with an overall sensitivity of 95.8% and specificity of 98.0%. Accuracy of predicted MICs to the phenotypically determined MICs was similar to phenotype-only MIC comparison studies. The ability to acquire detailed antimicrobial resistance information directly from molecular determinants will facilitate the transition from routine phenotypic testing to whole genome sequencing analysis and can fill the surveillance gap in an era of increased reliance on nucleic acid assay diagnostics to better monitor the dynamics of S. pneumoniae .

GENERATING CONCISE SETS OF LINEAR REGRESSION RULES FROM ARTIFICIAL NEURAL NETWORKS

2002 ◽  
Vol 11 (02) ◽  
pp. 189-202 ◽  
Author(s):  
RUDY SETIONO ◽  
ARNULFO AZCARRAGA
Keyword(s):  
Neural Networks ◽  
Linear Regression ◽  
Multiple Linear Regression ◽  
Function Approximation ◽  
Predictive Accuracy ◽  
Universal Function ◽  
Regression Equation ◽  
Training Data ◽  
Regression Equations ◽  
Input Variables

Neural networks with a single hidden layer are known to be universal function approximators. However, due to the complexity of the network topology and the nonlinear transfer function used in computing the hidden unit activations, the predictions of a trained network are difficult to comprehend. On the other hand, predictions from a multiple linear regression equation are easy to understand but are not accurate when the underlying relationship between the input variables and the output variable is nonlinear. We have thus developed a method for multivariate function approximation which combines neural network learning, clustering and multiple regression. This method generates a set of multiple linear regression equations using neural networks, where the number of regression equations is determined by clustering the weighted input variables. The predictions for samples of the same cluster are computed by the same regression equation. Experimental results on a number of real-world data demonstrate that this new method generates relatively few regression equations from the training data samples. Yet, drawing from the universal function approximation capacity of neural networks, the predictive accuracy is high. The prediction errors are comparable to or lower than those achieved by existing function approximation methods.

scholarly journals Estimating Aflatoxin in Farmers' Stock Peanut Lots by Measuring Aflatoxin in Various Peanut-Grade Components

1998 ◽  
Vol 81 (1) ◽  
pp. 61-67 ◽  
Author(s):  
Thomas B Whitaker ◽  
Winston M Hagler ◽  
Francis G Giesbrecht ◽  
Joe w Dorner ◽  
Floyd E Dowell ◽  
...  
Keyword(s):  
Linear Regression ◽  
Correlation Analysis ◽  
Correlation Coefficient ◽  
Test Sample ◽  
Statistical Analyses ◽  
Data Sets ◽  
Regression Equations ◽  
Total Aflatoxin ◽  
Accurate Predictor ◽  
Aflatoxin Concentration

Abstract Five, 2 kg test samples were taken from each of 120 farmers' stock peanut lots contaminated with aflatoxin. Kernels from each 2 kg sample were divided into the following grade components: sound mature kernels plus sound splits (SMKSS), other kernels (OK), loose shelled kernels (LSK), and damaged kernels (DAM). Kernel mass, aflatoxin mass, and aflatoxin concentration were measured for each of the 2400 component samples. For 120 lots tested, average aflatoxin concentrations in SMKSS, OK, LSK, and DAM components were 235, 2543, 11 775, and 69 775 ng/g, respectively. Aflatoxins in SMKSS, OK, LSK, and DAM components represented 6.9, 7.9, 33.3, and 51.9% of the total aflatoxin mass, respectively. Cumulatively, 3 aflatoxin risk components—OK, LSK, and DAM—accounted for 93.1% of total aflatoxin, but only 18.4% percent of test sample mass. Correlation analysis suggests that the most accurate predictor of aflatoxin concentration in the lot is the cumulative aflatoxin mass in the high 3 risk corn ponents OK + LSK + DAM (correlation coefficient, r = 0.996). If the aflatoxin in the combined OK + LSK + DAM components is expressed in concentration units, r decreases to 0.939. Linear regression equations relating aflatoxin in OK + LSK + DAM to aflatoxin concentration in the lot were developed. The cumulative aflatoxin in the OK + LSK + DAM components was not an accurate predictor (r = 0.539) of aflatoxin in the SMKSS component. Statistical analyses of 3 other data sets published previously yielded similar results.

Note on Cognitive Factors Related to Factor B of the 16 Pf Test

1971 ◽  
Vol 29 (3_suppl) ◽  
pp. 1075-1077 ◽  
Author(s):  
Joseph J. Fleishman ◽  
Bernard J. Fine
Keyword(s):  
Linear Regression ◽  
Multiple Linear Regression ◽  
Regression Equation ◽  
Cognitive Factors ◽  
Cognitive Tests ◽  
Regression Equations ◽  
Linear Regression Equation ◽  
Factor B ◽  
Enlisted Men ◽  
Selection Of

A selection of 21 tests from the French, Ekstrom, and Price battery of cognitive tests and the Cattell 16 PF Test were administered to 54 Army enlisted men. Product-moment correlations and multiple linear regression equations were computed between 16 PF Factor B scores (considered a measure of intelligence) and the 21 cognitive tests. The multiple linear regression equation indicated that 70% of the variance of Factor B scores could be accounted for by the selected cognitive tests.

scholarly journals THE RELIABILITY OF FORECASTS IN TRANSPORTATION

Transport ◽  
2002 ◽  
Vol 17 (6) ◽  
pp. 219-222
Author(s):  
Mindaugas Mazūra ◽  
Olga Fadina
Keyword(s):  
Linear Regression ◽  
Correlation Analysis ◽  
Mathematical Models ◽  
Nonlinear Regression ◽  
Empirical Data ◽  
Turnover Rate ◽  
Regression Equation ◽  
Regression Equations ◽  
Linear Regression Equation ◽  
Linear And Nonlinear

Major problems of forecasting the economic characteristics of transportation (i.e. the amount of freight and passengers carried, the turnover rate of freight and passengers, etc. in transportation as a whole and in particular areas using various transport facilities) are demonstrated. Methods for predicting the development of transportation based on multidimensional regression and correlation analysis and realizing mathematical models for choosing linear and nonlinear regression equations, more accurately approximating the empirical data, are presented. The research conducted has demonstrated that the most reliable forecasts may be made when the methods of choosing the proper non-linear regression equation described in Section 2 of the present paper are used.

EVALUATING RELATIONSHIPS AMONG SOIL PROPERTIES BY COMPUTER ANALYSIS

1971 ◽  
Vol 51 (1) ◽  
pp. 105-111 ◽  
Author(s):  
J. A. McKEAGUE ◽  
J. H. DAY ◽  
J. A. SHIELDS
Keyword(s):  
Organic Matter ◽  
Linear Regression ◽  
Correlation Analysis ◽  
Soil Properties ◽  
Cation Exchange ◽  
Computer Analysis ◽  
Cation Exchange Capacity ◽  
Exchange Capacity ◽  
Regression Equations ◽  
Ph Dependent

Data for 16 measured and seven calculated properties of 461 samples from 115 soils occurring in various parts of Canada were coded, and a correlation analysis was run on the data for various groups of samples. In general, correlations of color value and organic matter were moderately high (|r| > 0.5) and significant, but for 21 Podzol Ae horizons the correlation was very low (r = −0.13) and not significant. Chroma and dithionite Fe were significantly correlated for several groups of samples but not for Podzolic B (spodic) horizons or Bm horizons. Linear regression equations expressing cation exchange capacity and pH-dependent charge as functions of organic matter and other variables fitted the data reasonably well. The danger of generalizing from presumed relationships among soil properties was indicated but, for some groups of samples, useful relationships existed between visible soil properties and properties measured in the laboratory.

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