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Foundations of Linear and Generalized Linear Models
A valuable overview of the most important ideas and results in statistical modeling Written by a highly-experienced author, Foundations of Linear and Generalized Linear Models is a clear and comprehensive guide to the key concepts and results of linearstatistical models.The book presents a broad, in-depth overview of the most commonly usedstatistical models by discussing the theory underlying the models, R software applications,and examples with crafted models to elucidate key ideas and promote practical modelbuilding. The book begins by illustrating the fundamentals of linear models, such as how the model-fitting projects the data onto a model vector subspace and how orthogonal decompositions of the data yield information about the effects of explanatory variables.Subsequently, the book covers the most popular generalized linear models, which include binomial and multinomial logistic regression for categorical data, and Poisson and negative binomial loglinear models for count data.Focusing on the theoretical underpinnings of these models, Foundations ofLinear and Generalized Linear Models also features: An introduction to quasi-likelihood methods that require weaker distributional assumptions, such as generalized estimating equation methodsAn overview of linear mixed models and generalized linear mixed models with random effects for clustered correlated data, Bayesian modeling, and extensions to handle problematic cases such as high dimensional problemsNumerous examples that use R software for all text data analysesMore than 400 exercises for readers to practice and extend the theory, methods, and data analysisA supplementary website with datasets for the examples and exercises An invaluable textbook for upper-undergraduate and graduate-level students in statistics and biostatistics courses, Foundations of Linear and Generalized Linear Models is also an excellent reference for practicing statisticians and biostatisticians, as well as anyone who is interested in learning about the most important statistical models for analyzing data.
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Aegean Linear Script(s) : Rethinking the Relationship Between Linear A and Linear B
When does a continuum become a divide? This book investigates the genetic relationship between Linear A and Linear B, two Bronze Age scripts attested on Crete and Mainland Greece and understood to have developed one out of the other.By using an interdisciplinary methodology, this research integrates linguistic, epigraphic, palaeographic and archaeological evidence, and places the writing practice in its sociohistorical setting.By challenging traditional views, this work calls into question widespread assumptions and interpretative schemes on the relationship between these two scripts, and opens up new perspectives on the ideology associated with the retention, adaptation and transmission of a script, and how identity was negotiated at a moment of closer societal interaction between Cretans and Greek-speaking Mainlanders in the Late Bronze Age.By delving deeper into the structure and inner workings of these two writing systems, this book will make us rethink the relationship between Linear A and B.
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Linear Systems
This textbook provides a mathematical introduction to linear systems, with a focus on the continuous-time models that arise in engineering applications such as electrical circuits and signal processing.The book introduces linear systems via block diagrams and the theory of the Laplace transform, using basic complex analysis. The book mainly covers linear systems with finite-dimensional state spaces.Graphical methods such as Nyquist plots and Bode plots are presented alongside computational tools such as MATLAB.Multiple-input multiple-output (MIMO) systems, which arise in modern telecommunication devices, are discussed in detail.The book also introduces orthogonal polynomials with important examples in signal processing and wireless communication, such as Telatar’s model for multiple antenna transmission.One of the later chapters introduces infinite-dimensional Hilbert space as a state space, with the canonical model of a linear system.The final chapter covers modern applications to signal processing, Whittaker’s sampling theorem for band-limited functions, and Shannon’s wavelet. Based on courses given for many years to upper undergraduate mathematics students, the book provides a systematic, mathematical account of linear systems theory, and as such will also be useful for students and researchers in engineering.The prerequisites are basic linear algebra and complex analysis.
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Linear Algebra
Linear Algebra is intended for a one-term course at the junior or senior level.It begins with an exposition of the basic theory of vector spaces and proceeds to explain the fundamental structure theorems for linear maps, including eigenvectors and eigenvalues, quadric and hermitian forms, diagonalization of symmetric, hermitian, and unitary linear maps and matrices, triangulation, and Jordan canonical form.The book also includes a useful chapter on convex sets and the finite-dimensional Krein-Milman theorem.The presentation is aimed at the student who has already had some exposure to the elementary theory of matrices, determinants, and linear maps.However, the book is logically self-contained. In this new edition, many parts of the book have been rewritten and reorganized, and new exercises have been added.
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Is it linear or non-linear?
The relationship between the variables is non-linear.
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How are linear equations used in real-life applications?
Linear equations are used in real-life applications to model various situations such as calculating costs, predicting sales, and analyzing trends. For example, businesses use linear equations to determine pricing strategies based on production costs and desired profit margins. Engineers use linear equations to design structures and systems by analyzing forces and stresses. Additionally, linear equations are used in physics to describe motion, electricity, and other natural phenomena. Overall, linear equations provide a mathematical framework to solve practical problems and make informed decisions in various fields.
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What are linear functions in a real-world context?
Linear functions in a real-world context represent relationships that have a constant rate of change. They are often used to model situations where there is a direct proportionality between two variables. For example, the relationship between distance and time when traveling at a constant speed can be represented by a linear function. In real-world applications, linear functions are useful for predicting outcomes, making decisions, and analyzing trends based on the given data.
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How are linear equations used in real-life situations?
Linear equations are used in real-life situations to model and solve problems involving relationships that are directly proportional. For example, they can be used in calculating costs, determining rates of change, predicting future values, and analyzing trends in various fields such as economics, engineering, physics, and business. By representing real-world scenarios with linear equations, individuals and organizations can make informed decisions and optimize their resources.
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New Style Mini Telescopic Linear Actuator High Thrust DIY Mini Linear Push Rod Refitted Mini Linear
New Style Mini Telescopic Linear Actuator High Thrust DIY Mini Linear Push Rod Refitted Mini Linear
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Further Linear Algebra
Most of the introductory courses on linear algebra develop the basic theory of finite dimensional vector spaces, and in so doing relate the notion of a linear mapping to that of a matrix.Generally speaking, such courses culminate in the diagonalisation of certain matrices and the application of this process to various situations.Such is the case, for example, in our previous SUMS volume Basic Linear Algebra.The present text is a continuation of that volume, and has the objective of introducing the reader to more advanced properties of vector spaces and linear mappings, and consequently of matrices.For readers who are not familiar with the contents of Basic Linear Algebra we provide an introductory chapter that consists of a compact summary of the prerequisites for the present volume.In order to consolidate the student's understanding we have included a large num ber of illustrative and worked examples, as well as many exercises that are strategi cally placed throughout the text.Solutions to the exercises are also provided. Many applications of linear algebra require careful, and at times rather tedious, calculations by hand.Very often these are subject to error, so the assistance of a com puter is welcome.As far as computation in algebra is concerned, there are several packages available.Here we include, in the spirit of a tutorial, a chapter that gives 1 a brief introduction to the use of MAPLE in dealing with numerical and algebraic problems in linear algebra.
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Linear Regression Analysis
Concise, mathematically clear, and comprehensive treatment of the subject. * Expanded coverage of diagnostics and methods of model fitting. * Requires no specialized knowledge beyond a good grasp of matrix algebra and some acquaintance with straight-line regression and simple analysis of variance models. * More than 200 problems throughout the book plus outline solutions for the exercises. * This revision has been extensively class-tested.
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Linear Planter - Double
Our contemporary style Linear Planters are ideally sized for a variety of decorative shrubs such as box, standards, miniature firs and will look beautiful when filled with flowering plants. Choose a planter – or more than one – that will suit your garden size and style from the Linear range: square, double, long and tall. The planters have a modern look, with strong horizontal lines and natural timber colouring, they're sure to add interest and structure to any garden. This Linear Double Planter will add a focal point to a patio, terrace or balcony. For a superior finish, the timber used is smooth-planed and Pressure Treated with a preservative to protect it against rot. The planter is kept off the ground by Pressure Treated battens. The planters each come with a porous lining to keep soil and moisture in and ensure your plants thrive. Delivered flat packed for easy self-assembly. If using to grow food produce we recommend lining the bed/planter with a membrane before adding the soil.
Price: 109.03 € | Shipping*: 0.00 €
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What is a linear equation over the real numbers?
A linear equation over the real numbers is an equation that can be written in the form ax + b = 0, where a and b are real numbers and x is a variable. The solution to a linear equation is a real number that makes the equation true when substituted for x. The graph of a linear equation is a straight line, and the solutions to the equation represent the x-coordinate of the points where the line intersects the x-axis. Linear equations are fundamental in mathematics and have many applications in various fields such as physics, engineering, and economics.
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What is the difference between a linear term, a linear equation, and a linear function?
A linear term is a single variable or constant raised to the power of 1, such as 3x or 5. A linear equation is an equation that can be written in the form y = mx + b, where x is the independent variable, y is the dependent variable, m is the slope, and b is the y-intercept. A linear function is a mathematical relationship between two variables that can be represented by a straight line on a graph, and it can be expressed in the form f(x) = mx + b, where f(x) represents the dependent variable, x is the independent variable, m is the slope, and b is the y-intercept.
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What is the linear span of a linear space?
The linear span of a linear space is the set of all possible linear combinations of the vectors in that space. In other words, it is the collection of all possible vectors that can be obtained by scaling and adding the vectors in the space. The linear span forms a subspace of the original space and is often used to describe the "space" that is covered by the original set of vectors. It is a fundamental concept in linear algebra and is used to understand the properties and structure of vector spaces.
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Is my proof on linear independence in linear algebra correct?
To provide accurate feedback on the correctness of your proof on linear independence in linear algebra, I would need to review the specific details and steps of your proof. Please share your proof or key arguments so that I can assess its validity and provide you with constructive feedback.
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