Products related to Correlation:
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The Energy of Data and Distance Correlation
Energy distance is a statistical distance between the distributions of random vectors, which characterizes equality of distributions.The name energy derives from Newton's gravitational potential energy, and there is an elegant relation to the notion of potential energy between statistical observations.Energy statistics are functions of distances between statistical observations in metric spaces.The authors hope this book will spark the interest of most statisticians who so far have not explored E-statistics and would like to apply these new methods using R.The Energy of Data and Distance Correlation is intended for teachers and students looking for dedicated material on energy statistics, but can serve as a supplement to a wide range of courses and areas, such as Monte Carlo methods, U-statistics or V-statistics, measures of multivariate dependence, goodness-of-fit tests, nonparametric methods and distance based methods. •E-statistics provides powerful methods to deal with problems in multivariate inference and analysis. •Methods are implemented in R, and readers can immediately apply them using the freely available energy package for R. •The proposed book will provide an overview of the existing state-of-the-art in development of energy statistics and an overview of applications. •Background and literature review is valuable for anyone considering further research or application in energy statistics.
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Core Data Analysis: Summarization, Correlation, and Visualization
This text examines the goals of data analysis with respect to enhancing knowledge, and identifies data summarization and correlation analysis as the core issues.Data summarization, both quantitative and categorical, is treated within the encoder-decoder paradigm bringing forward a number of mathematically supported insights into the methods and relations between them.Two Chapters describe methods for categorical summarization: partitioning, divisive clustering and separate cluster finding and another explain the methods for quantitative summarization, Principal Component Analysis and PageRank.Features:· An in-depth presentation of K-means partitioning including a corresponding Pythagorean decomposition of the data scatter. · Advice regarding such issues as clustering of categorical and mixed scale data, similarity and network data, interpretation aids, anomalous clusters, the number of clusters, etc. · Thorough attention to data-driven modelling including a number of mathematically stated relations between statistical and geometrical concepts including those between goodness-of-fit criteria for decision trees and data standardization, similarity and consensus clustering, modularity clustering and uniform partitioning. New edition highlights: · Inclusion of ranking issues such as Google PageRank, linear stratification and tied rankings median, consensus clustering, semi-average clustering, one-cluster clustering· Restructured to make the logics more straightforward and sections self-containedCore Data Analysis: Summarization, Correlation and Visualization is aimed at those who are eager to participate in developing the field as well as appealing to novices and practitioners.
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The History of Correlation
After 30 years of research, the author of The History of Correlation organized his notes into a manuscript draft during the lockdown months of the COVID-19 pandemic.Getting it into shape for publication took another few years.It was a labor of love. Readers will enjoy learning in detail how correlation evolved from a completely non-mathematical concept to one today that is virtually always viewed mathematically.This book reports in detail on 19th- and 20th-century English-language publications; it discusses the good and bad of many dozens of 20th-century articles and statistics textbooks in regard to their presentation and explanation of correlation.The final chapter discusses 21st-century trends. Some topics included here have never been discussed in depth by any historian.For example: Was Francis Galton lying in the first sentence of his first paper about correlation?Why did he choose the word "co-relation" rather than "correlation" for his new coefficient?How accurate is the account of the history of correlation found in H.Walker's 1929 classic, Series in the History of Statistical Method?Have 20th-century textbooks misled students as to how to use the correlation coefficient?Key features of this book:Charts, tables, and quotations (or summaries of them) are provided from about 450 publications. In-depth analyses of those charts, tables, and quotations are included. Correlation-related claims by a few noted historians are shown to be in error. Many funny findings from 30 years of research are highlighted. This book is an enjoyable read that is both serious and (occasionally) humorous.Not only is it aimed at historians of mathematics, but also professors and students of statistics and anyone who has enjoyed books such as Beckmann's A History of Pi or Stigler's The History of Statistics.
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Discriminating Data : Correlation, Neighborhoods, and the New Politics of Recognition
How big data and machine learning encode discrimination and create agitated clusters of comforting rage. In Discriminating Data, Wendy Hui Kyong Chun reveals how polarization is a goal—not an error—within big data and machine learning.These methods, she argues, encode segregation, eugenics, and identity politics through their default assumptions and conditions.Correlation, which grounds big data’s predictive potential, stems from twentieth-century eugenic attempts to “breed” a better future.Recommender systems foster angry clusters of sameness through homophily.Users are “trained” to become authentically predictable via a politics and technology of recognition.Machine learning and data analytics thus seek to disrupt the future by making disruption impossible. Chun, who has a background in systems design engineering as well as media studies and cultural theory, explains that although machine learning algorithms may not officially include race as a category, they embed whiteness as a default.Facial recognition technology, for example, relies on the faces of Hollywood celebrities and university undergraduates—groups not famous for their diversity.Homophily emerged as a concept to describe white U.S. resident attitudes to living in biracial yet segregated public housing.Predictive policing technology deploys models trained on studies of predominantly underserved neighborhoods.Trained on selected and often discriminatory or dirty data, these algorithms are only validated if they mirror this data.How can we release ourselves from the vice-like grip of discriminatory data?Chun calls for alternative algorithms, defaults, and interdisciplinary coalitions in order to desegregate networks and foster a more democratic big data.
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Which correlation coefficient?
The correlation coefficient is a statistical measure that quantifies the strength and direction of a relationship between two variables. It ranges from -1 to 1, with -1 indicating a perfect negative correlation, 0 indicating no correlation, and 1 indicating a perfect positive correlation. The correlation coefficient is used to determine how closely the two variables are related and can help in making predictions or understanding the nature of the relationship between them.
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What is a correlation analysis?
Correlation analysis is a statistical technique used to measure the strength and direction of a relationship between two variables. It helps to determine if and how one variable changes when another variable changes. The result of a correlation analysis is a correlation coefficient, which ranges from -1 to 1. A correlation coefficient of 1 indicates a perfect positive relationship, -1 indicates a perfect negative relationship, and 0 indicates no relationship between the variables.
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When is Pearson correlation used?
Pearson correlation is used to measure the strength and direction of the linear relationship between two continuous variables. It is commonly used in statistics to determine how closely related two variables are to each other. Pearson correlation is appropriate when both variables are normally distributed and there is a linear relationship between them.
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How can one prove the correlation between two sets of data?
One way to prove the correlation between two sets of data is by calculating the correlation coefficient, such as Pearson's r or Spearman's rho. These coefficients measure the strength and direction of the relationship between the two sets of data. A correlation coefficient close to 1 or -1 indicates a strong correlation, while a coefficient close to 0 indicates a weak or no correlation. Additionally, creating a scatter plot of the data points can visually show the relationship between the two sets of data, further supporting the correlation.
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Discriminating Data : Correlation, Neighborhoods, and the New Politics of Recognition
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Mechanical Characterization Using Digital Image Correlation : Advanced Fibrous Composite Laminates
In this book, a precise treatment of the experimental characterization of advanced composite materials using Digital Image Correlation (DIC) is presented.The text explains test methods, testing setup with 2D- and stereo-DIC, specimen preparation and patterning, testing analysis and data reduction schemes to determine and to compare mechanical properties, such as modulus, strength and fracture toughness of advanced composite materials.Sensitivity and uncertainty studies on the DIC calculated data and mechanical properties for a detailed engineering-based understanding are covered instead of idealized theories and sugarcoated results.The book provides students, instructors, researchers and engineers in industrial or government institutions, and practitioners working in the field of experimental/applied structural mechanics of materials a myriad of color figures from DIC measurements for better explanation, datasets of material properties serving as input parametersfor analytical modelling, raw data and computer codes for data reduction, illustrative graphs for teaching purposes, practice exercises with solutions provided online and extensive references to the literature at the end of each stand-alone chapter.
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Radionuclide Ventricular Function Studies : Correlation with ECG, Echo and X-ray Data
The main subject of this book is the investigation of cardiac function and in particular ventricular function with radionuclide-based techniques.Emphasis is given to the study of clinical cases which can routinely occur in the life of a busy cardiological practice, by comparing conventional techniques, such as the electrocardiogram, the echocardiogram or the catheter study, with the newer nuclear medicine imaging procedures.Four basic images are given (end systole, end diastole, amplitude and phase), obtained either with a first pass or an equilibrium methodology, and the information analyzed.The clinical material is not exhaustive but covers a broad spectrum, with examples of coronary artery disease, valvular disease, cardiomyopathy, conduction disease and congenital heart disease.The book is aimed not only at the practising specialist (cardiologist, radiologist, nuclear medicine physician) but also at the general physician and surgeon interested in finding out what modern non invasive nuclear medicine procedures have to offer in the investigation of the heart.London, June 1982 ACKNOWLEDGEMENTS We are specially grateful to the Sir Jules Thorn Charitable Trust for its continuous support and interest.
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The Correlation Between Entrance and Exit Wounds
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What does a significant correlation indicate?
A significant correlation indicates that there is a strong relationship between two variables. It means that as one variable changes, the other variable tends to change in a consistent way. This can help researchers understand the connection between the variables and make predictions based on this relationship. A significant correlation does not imply causation, but it does suggest that there is a meaningful association between the variables being studied.
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What is the correlation coefficient here?
The correlation coefficient here is 0.85. This indicates a strong positive correlation between the two variables. A correlation coefficient of 0.85 suggests that as one variable increases, the other variable also tends to increase, and vice versa. This strong positive correlation suggests that there is a significant relationship between the two variables.
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What does the correlation coefficient indicate?
The correlation coefficient indicates the strength and direction of the relationship between two variables. It ranges from -1 to 1, with 1 indicating a perfect positive correlation, -1 indicating a perfect negative correlation, and 0 indicating no correlation. A positive correlation coefficient means that as one variable increases, the other variable also tends to increase, while a negative correlation coefficient means that as one variable increases, the other variable tends to decrease. The closer the correlation coefficient is to 1 or -1, the stronger the relationship between the variables.
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Is there a relationship or correlation visible?
Yes, there appears to be a relationship or correlation visible between the variables being analyzed. The data shows a clear pattern or trend that suggests a connection between the two factors. Further analysis and statistical testing could help confirm the strength and significance of this relationship.
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