Explorations in statistics: correlation

2010 ◽  
Vol 34 (4) ◽  
pp. 186-191 ◽  
Author(s):  
Douglas Curran-Everett
Keyword(s):  
Random Variables ◽  
Variable Result ◽  
Actual Experiment ◽  
Straight Line ◽  
The Relationship ◽  
Line Relationship

Learning about statistics is a lot like learning about science: the learning is more meaningful if you can actively explore. This sixth installment of Explorations in Statistics explores correlation, a familiar technique that estimates the magnitude of a straight-line relationship between two variables. Correlation is meaningful only when the two variables are true random variables: for example, if we restrict in some way the variability of one variable, then the magnitude of the correlation will decrease. Correlation cannot help us decide if changes in one variable result in changes in the second variable, if changes in the second variable result in changes in the first variable, or if changes in a third variable result in concurrent changes in the first two variables. Correlation can help provide us with evidence that study of the nature of the relationship between x and y may be warranted in an actual experiment in which one of them is controlled.

Kriging-Based Reliability Analysis and Variance-Based Sensitivity Analysis for an Idler Shaft

2015 ◽  
Author(s):  
Weimin Cui ◽  
Wei Guo ◽  
Zhongchao Sun ◽  
Tianxiang Yu
Keyword(s):  
Sensitivity Analysis ◽  
Influence Factors ◽  
Random Variables ◽  
Kriging Model ◽  
Element Analysis ◽  
Performance Function ◽  
The Finite Element Analysis ◽  
Inner Diameter ◽  
Sensitivity Method ◽  
The Relationship

In order to analyze the reason of failure and improve the reliability of the idler shaft, this paper studies the reliability and sensitivity for the idler shaft based on Kriging model and Variance Methods respectively. The finite element analysis (FEA) of idler shaft is studied in ABAQUS firstly. Then, combining the performance function and various random variables, the Kriging model of idler shaft is established and verified. Based on Kriging model which has been established, the relationship between random variables and the response value is studied, and the function reliability is calculated which explains why the failure of the idler shaft occurred frequently in service. Finally, the variance-based sensitivity method is used for sensitivity analysis of influence factors, the result shows that the reliability of idler shaft is sensitive to the inner diameter of body A and inner diameter of body B, which could contribute for the analysis and further improvement of idler shaft.

A Method for Bromine Determination in Wool Fabric by X-Ray Fluorescence Spectrometry

1976 ◽  
Vol 46 (6) ◽  
pp. 463-465 ◽  
Author(s):  
F. William Reuter ◽  
Geraldine E. Secor ◽  
Mendel Friedman
Keyword(s):  
Fluorescence Spectrometry ◽  
Wool Fabric ◽  
X Ray ◽  
Fluorescence Measurements ◽  
Straight Line ◽  
Bromine Concentration ◽  
Wet Chemical ◽  
Relationship Of ◽  
Line Relationship ◽  
Better Than

Bromine is measured in flame-resistant wool fabric by x-ray fluorescence spectrometry with a relative precision of 3 to 8% and relative accuracy of better than 10%. The method computes the bromine concentration from fluorescence measurements of the sample, and a thin film standard, and two measurements of attenuation by the sample. Deviations of 10 to 20% from a straight-line relationship of x-ray counts to bromine concentration are accounted for. X-ray fluorescence is generally useful for routine analyses of bromine in textiles and has advantages over wet chemical analysis.

scholarly journals On strict sub-Gaussianity, optimal proxy variance and symmetry for bounded random variables

2020 ◽  
Vol 24 ◽  
pp. 39-55
Author(s):  
Julyan Arbel ◽  
Olivier Marchal ◽  
Hien D. Nguyen
Keyword(s):  
Necessary Conditions ◽  
Sufficient Conditions ◽  
Random Variables ◽  
The Other ◽  
Bounded Support ◽  
Uniform Distributions ◽  
Standard Variance ◽  
Per Se ◽  
The One ◽  
The Relationship

We investigate the sub-Gaussian property for almost surely bounded random variables. If sub-Gaussianity per se is de facto ensured by the bounded support of said random variables, then exciting research avenues remain open. Among these questions is how to characterize the optimal sub-Gaussian proxy variance? Another question is how to characterize strict sub-Gaussianity, defined by a proxy variance equal to the (standard) variance? We address the questions in proposing conditions based on the study of functions variations. A particular focus is given to the relationship between strict sub-Gaussianity and symmetry of the distribution. In particular, we demonstrate that symmetry is neither sufficient nor necessary for strict sub-Gaussianity. In contrast, simple necessary conditions on the one hand, and simple sufficient conditions on the other hand, for strict sub-Gaussianity are provided. These results are illustrated via various applications to a number of bounded random variables, including Bernoulli, beta, binomial, Kumaraswamy, triangular, and uniform distributions.

Instantaneous venous return curves in an intact canine preparation

1984 ◽  
Vol 56 (3) ◽  
pp. 765-771 ◽  
Author(s):  
M. R. Pinsky
Keyword(s):  
Venous Return ◽  
Right Atrial ◽  
Negative Slope ◽  
Positive Pressure ◽  
Similar Degree ◽  
Straight Line ◽  
Mean Systemic Pressure ◽  
Relationship Of ◽  
The Relationship ◽  
Stop Flow

The relationship between right atrial pressure (Pra) and venous return describes a venous return curve. Because changes in venous return and right ventricular stroke volume (SVRV) are similar during small tidal volume (VT) breathing, we compared the relationship of SVRV and Pra during positive-pressure ventilation (VT less than 10 ml/kg) in 17 pentobarbital-anesthetized, closed-chest, canine preparations. The SVRV-Pra relationship describes a straight line with a negative slope and a positive mean systemic pressure (Pms)-zero flow intercept (instantaneous Pms). Instantaneous Pms is similar to ventricular fibrillation-induced (stop-flow) Pms (8.1 +/- 0.8 vs. 8.4 +/- 0.7 mmHg, mean +/- SE). With volume infusion, both instantaneous and stop-flow Pms increase to a similar degree (R = 0.9014, P less than 0.001). The effect of opening an arteriovenous fistula is time dependent and variable between dogs, but by 30 s it is associated with an increase in instantaneous Pms (5.2 +/- 3.2 mmHg). Vascular compliance determined by adding and removing blood from the intravascular space displays a curvilinear hysteresis. The instantaneous venous return curve is affected by intravascular blood volume, vasomotor tone, and resistance to venous return. The relationship between SVRV and Pra during small VT breathing define instantaneous venous return curves similar to those described using right-heart bypass preparations.

Depreciation and Replacement Cost

1979 ◽  
Vol 4 (2) ◽  
pp. 125-133
Author(s):  
Ramesh Gupta
Keyword(s):  
Simulation Technique ◽  
Policy Implications ◽  
Replacement Cost ◽  
Sharp Rise ◽  
Depreciation Allowance ◽  
Straight Line ◽  
Fixed Assets ◽  
Business Income ◽  
The Relationship ◽  
Depreciation Methods

The sharp rise in prices in recent years has stirred up a brisk debate on the meaning and measurement of business income. In computing income, costs of labour and material are generally reflected in current prices, but the provision made for depreciation is generally not sufficient to replace fixed assets. This paper investigates various approaches to the oroblem of providing sufficient depreciation allowance in measuring income. The relationship between written down value and the straight line inflation adjusted method of providing depreciation has been examined. Simulation technique has been used to illustrate the problem and pertinent policy implications of the use of various depreciation methods have been highlighted.

Effects of Prey Abundance on the Development of the Spider Agelenopsis potteri (Blackwall) (Araneae: Agelenidae)

1965 ◽  
Vol 97 (2) ◽  
pp. 141-147 ◽  
Author(s):  
A. L. Turnbull
Keyword(s):  
Aedes Aegypti ◽  
Feeding Rate ◽  
Prey Capture ◽  
Prey Abundance ◽  
Feeding Rates ◽  
Live Prey ◽  
Straight Line ◽  
Line Relationship

AbstractAgelenopsis potteri (Blackwall) spiders that were reared from egg to adult on live prey (Aedes aegypti L.) supplied at different daily rates varied in the rate that they were able to capture prey, grow, and attain maturity. Mortality varied inversely with feeding rates, but some spiders matured at each feeding rate. All spiders matured in seven stages regardless of the rate of feeding. Both sexes were mature following the sixth moult. The rate of prey capture declined sharply in the adults. Males matured about four days sooner than females. A straight-line relationship exists between the rate at which prey were captured and the dry weights of the adult spiders. A straight-line relationship was also found between the numbers of prey captured per day and the daily development of the spider.

The determination of burning velocities of slow flames

1955 ◽  
Vol 228 (1174) ◽  
pp. 297-322 ◽  
Keyword(s):  
Carbon Monoxide ◽  
Burning Velocity ◽  
Flame Temperature ◽  
Excess Energy ◽  
Flat Flame ◽  
Straight Line ◽  
Flame Burner ◽  
Line Relationship ◽  
Propane Butane

Measurements of the burning velocities of methane, ethane, propane, butane, ethylene, carbon monoxide and cyanogen mixtures with air, in the range about 4 to 8 cm, are made by the flat-flame burner method with an accuracy of 2 to 3%. The results can be represented by a straight-line relationship between composition and burning velocity except for carbon monoxide which is sensitive to the percentage of water vapour present. Extrapolated values agree well with recent measurements of faster flames. Measurements are also made on binary mixtures with air of the gases, including hydrogen. The mixture law holds except with mixtures containing carbon monoxide. Limits of inflammability are also determined and the burning velocities at the limits average 3⋅6 cm/s. The mixtures obey the Le Chatelier rule accurately, except for carbon monoxide mixtures. The burning velocities of the hydrocarbons can be represented approximately by a straight-line relationship with the heat generated and with the maximum flame temperature, but correlation is best when thermal conductivity is introduced. At a given velocity the excess energy maintained by the flame appears to be constant for all the hydrocarbons investigated, except methane, which behaves slightly differently. The burning velocities of the hydrocarbons are controlled by a reaction which provides reasonable values of the activation energies and probably precedes the sudden development of chain branching.

Relationship Between Running Velocity of 2 Distances and Various Lactate Parameters

2006 ◽  
Vol 1 (3) ◽  
pp. 270-283 ◽  
Author(s):  
Charilaos Papadopoulos ◽  
J. Andrew Doyle ◽  
Brian D. LaBudde
Keyword(s):  
Lactate Threshold ◽  
Lactate Concentration ◽  
Correlation Coefficients ◽  
Time Trial ◽  
Venous Catheter ◽  
Maximal Exercise Test ◽  
Straight Line ◽  
The Mean ◽  
The Relationship ◽  
Trained Runners

Purpose:The purpose of this study was to determine the relationship between various lactate-threshold (LT) definitions and the average running velocity during a 10-km and a 21.1-km time trial (TT).Methods:Thirteen well-trained runners completed an incremental maximal exercise test, a 10-km TT, and a 21.1-km TT on a motorized treadmill. Blood samples were collected through a venous catheter placed in an antecubital vein. Pearson's correlation coefficients were used to determine the relationship between the running velocity at the different LT definitions and the average running velocity during each TT. A dependent t test was used to determine statistical differences for the mean lactate response between the 2 running distances.Results:The LTDmax, the point on the regression curve that yielded the maximal perpendicular distance to the straight line formed by the 2 endpoints, was the LT definition with the highest correlation for both 10-km (r = .844) and 21.1-km TTs (r = .783). The velocity at the LTDmax was not, however, the velocity closest to the performance velocity for either distance. The mean running velocity at each LT was significantly different and tended to overestimate the mean TT performance velocities. The mean lactate concentration during the 10-km TT (3.52 ± 1.58 mmol) was significantly higher than during the 21.1-km TT (1.86 ± 0.90 mmol).Conclusion:These results indicate that a single LT point cannot be reliably associated with different running distances. Furthermore, these data suggest that a different methodology for estimating the LT that considers individual responses might be required for different running distances.

Comparative studies of meat V. Factors affecting the iodine number of the fat from the fatty and muscular tissues of cattle

1956 ◽  
Vol 48 (1) ◽  
pp. 61-73 ◽  
Author(s):  
E. H. Callow ◽  
S. R. Searle
Keyword(s):  
Iodine Number ◽  
Comparative Studies ◽  
Analysis Of Covariance ◽  
Muscular Tissue ◽  
Fatty Tissue ◽  
Factors Affecting ◽  
Rectangular Hyperbola ◽  
Straight Line ◽  
Line Relationship ◽  
Muscular Tissues

1. Carcasses of twenty-one fat cattle (from six cows, ten steers and five heifers, aged from 12 months to 12 years and representing seven breeds) have been dissected into nine joints, and the fatty and muscular tissue from each joint dissected and analysed for fat. The iodine number of each sample of fat has been determined.2. The fat in fatty tissues ranged from 28·3 to 96·7%, and in muscular tissues from 1·3 to 14·2%. Iodine numbers of fat from fatty tissues ranged from 34·0 to 69·0 and those of fat from muscular tissues from 45·9 to 73·2.3. By an analysis of covariance it has been possible to reduce these data to two families of regression lines—those for fatty tissue and those for muscular tissue.4. The equations for fatty tissue have the following generalized form:I.N. = AFT + CFT + JFT + b1F/FT,where AFT = 55·6 ± 1·7 and is a general constant,CFT is a series of constants for the various carcasses and ranges from +12·6 to −6·7,JFT is a series of constants for the various joints and ranges from +6·6 to −10·3,b1 is a general constant with the value −0·052(± 0·025),F/FT is the percentage of fat in any given sample of fatty tissue, and I.N. is its iodine number.5. A similar set of equations has been deduced for muscular tissue. Here, however, the relation between iodine number and percentage of fat is a rectangular hyperbola. Consequently, the inverse (Z) of the percentage of fat (in order to get a straight-line relationship) has been used.

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