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Linear Hypothesis Test in R: A Comprehensive Guide
Introduction:
Are you a data scientist, statistician, or R enthusiast grappling with the complexities of testing linear hypotheses? This comprehensive guide dives deep into performing linear hypothesis tests within the R programming environment. We'll move beyond basic explanations, providing practical examples, code snippets, and troubleshooting tips to empower you to confidently analyze your data and draw meaningful conclusions. This post will equip you with the knowledge to perform various linear hypothesis tests, understand the underlying theory, and interpret the results effectively. Get ready to master linear hypothesis testing in R!
1. Understanding Linear Hypothesis Tests:
Before delving into the R implementation, let's establish a solid theoretical foundation. A linear hypothesis test examines whether a linear combination of regression coefficients is equal to a specific value (typically zero). This is fundamentally important for assessing the significance of predictors in linear models, ANOVA (Analysis of Variance), and more complex models. The core concept revolves around formulating a null hypothesis (H0) – a statement about the population parameters – and an alternative hypothesis (H1) – the statement we aim to support if we reject the null. We utilize statistical tests to determine if the sample data provides enough evidence to reject H0 in favor of H1. This process hinges on the significance level (alpha), usually set at 0.05, representing the probability of rejecting H0 when it's actually true (Type I error).
2. Performing Linear Hypothesis Tests using the `lm()` and `linearHypothesis()` Functions:
R offers powerful tools for performing these tests. The `lm()` function fits linear models, providing the foundation for our hypothesis testing. The `linearHypothesis()` function from the `car` package elegantly handles the testing process. Let's illustrate this with an example.
Suppose we have a dataset where we want to investigate the relationship between house prices (`price`), square footage (`sqft`), and number of bedrooms (`bedrooms`).
```R
# Load necessary libraries
library(car)
# Sample data (replace with your actual data)
data <- data.frame(
price = c(250000, 300000, 280000, 350000, 400000),
sqft = c(1500, 1800, 1600, 2000, 2200),
bedrooms = c(3, 4, 3, 4, 5)
)
# Fit the linear model
model <- lm(price ~ sqft + bedrooms, data = data)
# Test the hypothesis: Is the effect of sqft significantly different from 0?
linearHypothesis(model, "sqft = 0")
# Test a more complex hypothesis: Is the effect of sqft equal to the effect of bedrooms?
linearHypothesis(model, "sqft - bedrooms = 0")
```
The `linearHypothesis()` function takes the model as the first argument and a character string specifying the hypothesis as the second. The output provides the F-statistic, p-value, and other relevant information to assess the significance of the hypothesis.
3. Interpreting the Results:
Understanding the output of the `linearHypothesis()` function is crucial. The F-statistic measures the variation explained by the hypothesis relative to the unexplained variation. The p-value represents the probability of observing the data (or more extreme data) if the null hypothesis were true. If the p-value is less than the significance level (e.g., 0.05), we reject the null hypothesis. The output also includes confidence intervals, which provide a range of plausible values for the linear combination of coefficients under test.
4. Advanced Techniques and Considerations:
Model Assumptions: Linear hypothesis tests rely on assumptions like linearity, independence of errors, homoscedasticity (constant variance of errors), and normality of errors. Violating these assumptions can lead to unreliable results. Diagnostic plots and tests (e.g., residual plots, Breusch-Pagan test) are essential to assess model adequacy.
Multiple Comparisons: When testing multiple hypotheses simultaneously, the risk of Type I error increases. Methods like Bonferroni correction can adjust the significance level to control the family-wise error rate.
Generalized Linear Models (GLMs): For non-normal response variables (e.g., binary, count data), GLMs are appropriate. Hypothesis testing in GLMs is slightly different but follows similar principles. Packages like `lme4` handle more complex models with random effects.
Model Selection: Including irrelevant variables can inflate the standard errors and reduce the power of the test. Techniques like stepwise regression or information criteria (AIC, BIC) can aid in selecting the best model.
5. Practical Applications and Real-World Examples:
Linear hypothesis tests find widespread application in various fields:
Economics: Testing the impact of economic policies on various indicators.
Medicine: Assessing the effectiveness of treatments in clinical trials.
Marketing: Evaluating the impact of advertising campaigns on sales.
Engineering: Optimizing processes and analyzing the performance of systems.
Sample Outline:
Title: A Deep Dive into Linear Hypothesis Testing in R
Introduction: Briefly introduce linear hypothesis tests and their importance in statistical analysis.
Chapter 1: Theoretical Foundations: Explain the core concepts of null and alternative hypotheses, significance levels, and Type I and Type II errors.
Chapter 2: Implementing Linear Hypothesis Tests in R: Detailed explanation of using `lm()` and `linearHypothesis()` functions, with code examples.
Chapter 3: Interpreting the Results: Comprehensive guide to understanding the output of the hypothesis tests, focusing on F-statistics, p-values, and confidence intervals.
Chapter 4: Advanced Topics and Considerations: Discussion of model assumptions, multiple comparisons, GLMs, and model selection techniques.
Chapter 5: Real-World Applications: Showcase applications in various fields with practical examples.
Conclusion: Summarize the key takeaways and emphasize the importance of understanding and applying linear hypothesis tests correctly.
(Detailed explanations for each chapter are provided in the main article above.)
Frequently Asked Questions (FAQs):
1. What is the difference between a t-test and a linear hypothesis test? A t-test is a specific case of a linear hypothesis test, often used to test the significance of a single coefficient. Linear hypothesis tests are more general and can test combinations of coefficients.
2. How do I handle violations of model assumptions? Transformations of variables, robust regression methods, or generalized linear models might be necessary.
3. What is the best way to choose the significance level (alpha)? 0.05 is commonly used, but the choice depends on the context and the consequences of Type I and Type II errors.
4. What if my p-value is close to the significance level? This suggests marginal significance, and further investigation or a larger sample size might be needed.
5. Can I perform linear hypothesis tests on non-linear models? Not directly. Linear hypothesis tests are designed for linear models. For non-linear models, you'll need different approaches.
6. How do I interpret the confidence intervals in the output? The confidence interval provides a range of plausible values for the linear combination of coefficients being tested.
7. What is the role of the F-statistic? The F-statistic measures the ratio of explained variance to unexplained variance, indicating the strength of the evidence against the null hypothesis.
8. What packages are necessary for performing linear hypothesis tests in R? Primarily, the `car` package is needed, but `stats` is also implicitly used.
9. Where can I find more advanced resources on this topic? Statistical textbooks and online resources focused on regression analysis and hypothesis testing are excellent sources.
Related Articles:
1. Regression Analysis in R: A comprehensive overview of regression techniques in R, including model building and interpretation.
2. Understanding p-values: A detailed explanation of p-values and their interpretation in hypothesis testing.
3. Type I and Type II Errors: A clear explanation of these errors and their implications in statistical inference.
4. Model Assumptions in Regression: A guide to assessing and addressing violations of assumptions in linear regression.
5. ANOVA in R: A tutorial on performing ANOVA (Analysis of Variance) using R.
6. GLMs in R: An introduction to Generalized Linear Models and their applications.
7. Model Selection Techniques in R: A guide to various model selection methods, including AIC and BIC.
8. Multiple Comparisons Problem: A discussion of the problem and methods for correcting for multiple comparisons.
9. Robust Regression Techniques: An overview of methods for handling outliers and violations of assumptions in regression analysis.
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| linear hypothesis test in r: Parameter Estimation and Hypothesis Testing in Linear Models Karl-Rudolf Koch, 2013-03-09 A treatment of estimating unknown parameters, testing hypotheses and estimating confidence intervals in linear models. Readers will find here presentations of the Gauss-Markoff model, the analysis of variance, the multivariate model, the model with unknown variance and covariance components and the regression model as well as the mixed model for estimating random parameters. A chapter on the robust estimation of parameters and several examples have been added to this second edition. The necessary theorems of vector and matrix algebra and the probability distributions of test statistics are derived so as to make this book self-contained. Geodesy students as well as those in the natural sciences and engineering will find the emphasis on the geodetic application of statistical models extremely useful. |
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| linear hypothesis test in r: An R Companion to Linear Statistical Models Christopher Hay-Jahans, 2011-10-19 Focusing on user-developed programming, An R Companion to Linear Statistical Models serves two audiences: those who are familiar with the theory and applications of linear statistical models and wish to learn or enhance their skills in R; and those who are enrolled in an R-based course on regression and analysis of variance. For those who have never used R, the book begins with a self-contained introduction to R that lays the foundation for later chapters. This book includes extensive and carefully explained examples of how to write programs using the R programming language. These examples cover methods used for linear regression and designed experiments with up to two fixed-effects factors, including blocking variables and covariates. It also demonstrates applications of several pre-packaged functions for complex computational procedures. |
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| linear hypothesis test in r: Handbook of Regression Modeling in People Analytics Keith McNulty, 2021-07-29 Despite the recent rapid growth in machine learning and predictive analytics, many of the statistical questions that are faced by researchers and practitioners still involve explaining why something is happening. Regression analysis is the best ‘swiss army knife’ we have for answering these kinds of questions. This book is a learning resource on inferential statistics and regression analysis. It teaches how to do a wide range of statistical analyses in both R and in Python, ranging from simple hypothesis testing to advanced multivariate modelling. Although it is primarily focused on examples related to the analysis of people and talent, the methods easily transfer to any discipline. The book hits a ‘sweet spot’ where there is just enough mathematical theory to support a strong understanding of the methods, but with a step-by-step guide and easily reproducible examples and code, so that the methods can be put into practice immediately. This makes the book accessible to a wide readership, from public and private sector analysts and practitioners to students and researchers. Key Features: 16 accompanying datasets across a wide range of contexts (e.g. academic, corporate, sports, marketing) Clear step-by-step instructions on executing the analyses Clear guidance on how to interpret results Primary instruction in R but added sections for Python coders Discussion exercises and data exercises for each of the main chapters Final chapter of practice material and datasets ideal for class homework or project work. |
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| linear hypothesis test in r: Regression Analysis with R Giuseppe Ciaburro, 2018-01-31 Build effective regression models in R to extract valuable insights from real data Key Features Implement different regression analysis techniques to solve common problems in data science - from data exploration to dealing with missing values From Simple Linear Regression to Logistic Regression - this book covers all regression techniques and their implementation in R A complete guide to building effective regression models in R and interpreting results from them to make valuable predictions Book Description Regression analysis is a statistical process which enables prediction of relationships between variables. The predictions are based on the casual effect of one variable upon another. Regression techniques for modeling and analyzing are employed on large set of data in order to reveal hidden relationship among the variables. This book will give you a rundown explaining what regression analysis is, explaining you the process from scratch. The first few chapters give an understanding of what the different types of learning are – supervised and unsupervised, how these learnings differ from each other. We then move to covering the supervised learning in details covering the various aspects of regression analysis. The outline of chapters are arranged in a way that gives a feel of all the steps covered in a data science process – loading the training dataset, handling missing values, EDA on the dataset, transformations and feature engineering, model building, assessing the model fitting and performance, and finally making predictions on unseen datasets. Each chapter starts with explaining the theoretical concepts and once the reader gets comfortable with the theory, we move to the practical examples to support the understanding. The practical examples are illustrated using R code including the different packages in R such as R Stats, Caret and so on. Each chapter is a mix of theory and practical examples. By the end of this book you will know all the concepts and pain-points related to regression analysis, and you will be able to implement your learning in your projects. What you will learn Get started with the journey of data science using Simple linear regression Deal with interaction, collinearity and other problems using multiple linear regression Understand diagnostics and what to do if the assumptions fail with proper analysis Load your dataset, treat missing values, and plot relationships with exploratory data analysis Develop a perfect model keeping overfitting, under-fitting, and cross-validation into consideration Deal with classification problems by applying Logistic regression Explore other regression techniques – Decision trees, Bagging, and Boosting techniques Learn by getting it all in action with the help of a real world case study. Who this book is for This book is intended for budding data scientists and data analysts who want to implement regression analysis techniques using R. If you are interested in statistics, data science, machine learning and wants to get an easy introduction to the topic, then this book is what you need! Basic understanding of statistics and math will help you to get the most out of the book. Some programming experience with R will also be helpful |
| linear hypothesis test in r: Applied Statistics Using R Mehmet Mehmetoglu, Matthias Mittner, 2021-11-10 If you want to learn to use R for data analysis but aren’t sure how to get started, this practical book will help you find the right path through your data. Drawing on real-world data to show you how to use different techniques in practice, it helps you progress your programming and statistics knowledge so you can apply the most appropriate tools in your research. It starts with descriptive statistics and moves through regression to advanced techniques such as structural equation modelling and Bayesian statistics, all with digestible mathematical detail for beginner researchers. The book: Shows you how to use R packages and apply functions, adjusting them to suit different datasets. Gives you the tools to try new statistical techniques and empowers you to become confident using them. Encourages you to learn by doing when running and adapting the authors’ own code. Equips you with solutions to overcome the potential challenges of working with real data that may be messy or imperfect. Accompanied by online resources including screencast tutorials of R that give you step by step guidance and R scripts and datasets for you to practice with, this book is a perfect companion for any student of applied statistics or quantitative research methods courses. |
| linear hypothesis test in r: Regression Analysis and Linear Models Richard B. Darlington, Andrew F. Hayes, 2016-08-22 Emphasizing conceptual understanding over mathematics, this user-friendly text introduces linear regression analysis to students and researchers across the social, behavioral, consumer, and health sciences. Coverage includes model construction and estimation, quantification and measurement of multivariate and partial associations, statistical control, group comparisons, moderation analysis, mediation and path analysis, and regression diagnostics, among other important topics. Engaging worked-through examples demonstrate each technique, accompanied by helpful advice and cautions. The use of SPSS, SAS, and STATA is emphasized, with an appendix on regression analysis using R. The companion website (www.afhayes.com) provides datasets for the book's examples as well as the RLM macro for SPSS and SAS. Pedagogical Features: *Chapters include SPSS, SAS, or STATA code pertinent to the analyses described, with each distinctively formatted for easy identification. *An appendix documents the RLM macro, which facilitates computations for estimating and probing interactions, dominance analysis, heteroscedasticity-consistent standard errors, and linear spline regression, among other analyses. *Students are guided to practice what they learn in each chapter using datasets provided online. *Addresses topics not usually covered, such as ways to measure a variable’s importance, coding systems for representing categorical variables, causation, and myths about testing interaction. |
| linear hypothesis test in r: Panel Data Econometrics with R Yves Croissant, Giovanni Millo, 2018-08-10 Panel Data Econometrics with R provides a tutorial for using R in the field of panel data econometrics. Illustrated throughout with examples in econometrics, political science, agriculture and epidemiology, this book presents classic methodology and applications as well as more advanced topics and recent developments in this field including error component models, spatial panels and dynamic models. They have developed the software programming in R and host replicable material on the book’s accompanying website. |
| linear hypothesis test in r: Introductory Statistics with R Peter Dalgaard, 2008-06-27 This book provides an elementary-level introduction to R, targeting both non-statistician scientists in various fields and students of statistics. The main mode of presentation is via code examples with liberal commenting of the code and the output, from the computational as well as the statistical viewpoint. Brief sections introduce the statistical methods before they are used. A supplementary R package can be downloaded and contains the data sets. All examples are directly runnable and all graphics in the text are generated from the examples. The statistical methodology covered includes statistical standard distributions, one- and two-sample tests with continuous data, regression analysis, one-and two-way analysis of variance, regression analysis, analysis of tabular data, and sample size calculations. In addition, the last four chapters contain introductions to multiple linear regression analysis, linear models in general, logistic regression, and survival analysis. |
| linear hypothesis test in r: Biostatistical Methods John M. Lachin, 2009-09-25 Comprehensive coverage of classical and modern methods of biostatistics Biostatistical Methods focuses on the assessment of risks and relative risks on the basis of clinical investigations. It develops basic concepts and derives biostatistical methods through both the application of classical mathematical statistical tools and more modern likelihood-based theories. The first half of the book presents methods for the analysis of single and multiple 2x2 tables for cross-sectional, prospective, and retrospective (case-control) sampling, with and without matching using fixed and two-stage random effects models. The text then moves on to present a more modern likelihood- or model-based approach, which includes unconditional and conditional logistic regression; the analysis of count data and the Poisson regression model; and the analysis of event time data, including the proportional hazards and multiplicative intensity models. The book contains a technical appendix that presents the core mathematical statistical theory used for the development of classical and modern statistical methods. Biostatistical Methods: The Assessment of Relative Risks: * Presents modern biostatistical methods that are generalizations of the classical methods discussed * Emphasizes derivations, not just cookbook methods * Provides copious reference citations for further reading * Includes extensive problem sets * Employs case studies to illustrate application of methods * Illustrates all methods using the Statistical Analysis System(r) (SAS) Supplemented with numerous graphs, charts, and tables as well as a Web site for larger data sets and exercises, Biostatistical Methods: The Assessment of Relative Risks is an excellent guide for graduate-level students in biostatistics and an invaluable reference for biostatisticians, applied statisticians, and epidemiologists. |
| linear hypothesis test in r: Modeling Dose-Response Microarray Data in Early Drug Development Experiments Using R Dan Lin, Ziv Shkedy, Daniel Yekutieli, Dhammika Amaratunga, Luc Bijnens, 2012-08-27 This book focuses on the analysis of dose-response microarray data in pharmaceutical settings, the goal being to cover this important topic for early drug development experiments and to provide user-friendly R packages that can be used to analyze this data. It is intended for biostatisticians and bioinformaticians in the pharmaceutical industry, biologists, and biostatistics/bioinformatics graduate students. Part I of the book is an introduction, in which we discuss the dose-response setting and the problem of estimating normal means under order restrictions. In particular, we discuss the pooled-adjacent-violator (PAV) algorithm and isotonic regression, as well as inference under order restrictions and non-linear parametric models, which are used in the second part of the book. Part II is the core of the book, in which we focus on the analysis of dose-response microarray data. Methodological topics discussed include: • Multiplicity adjustment • Test statistics and procedures for the analysis of dose-response microarray data • Resampling-based inference and use of the SAM method for small-variance genes in the data • Identification and classification of dose-response curve shapes • Clustering of order-restricted (but not necessarily monotone) dose-response profiles • Gene set analysis to facilitate the interpretation of microarray results • Hierarchical Bayesian models and Bayesian variable selection • Non-linear models for dose-response microarray data • Multiple contrast tests • Multiple confidence intervals for selected parameters adjusted for the false coverage-statement rate All methodological issues in the book are illustrated using real-world examples of dose-response microarray datasets from early drug development experiments. |
| linear hypothesis test in r: R Cookbook Paul Teetor, 2011-03-03 With more than 200 practical recipes, this book helps you perform data analysis with R quickly and efficiently. The R language provides everything you need to do statistical work, but its structure can be difficult to master. This collection of concise, task-oriented recipes makes you productive with R immediately, with solutions ranging from basic tasks to input and output, general statistics, graphics, and linear regression. Each recipe addresses a specific problem, with a discussion that explains the solution and offers insight into how it works. If you’re a beginner, R Cookbook will help get you started. If you’re an experienced data programmer, it will jog your memory and expand your horizons. You’ll get the job done faster and learn more about R in the process. Create vectors, handle variables, and perform other basic functions Input and output data Tackle data structures such as matrices, lists, factors, and data frames Work with probability, probability distributions, and random variables Calculate statistics and confidence intervals, and perform statistical tests Create a variety of graphic displays Build statistical models with linear regressions and analysis of variance (ANOVA) Explore advanced statistical techniques, such as finding clusters in your data Wonderfully readable, R Cookbook serves not only as a solutions manual of sorts, but as a truly enjoyable way to explore the R language—one practical example at a time.—Jeffrey Ryan, software consultant and R package author |
| linear hypothesis test in r: Environmental and Ecological Statistics with R, Second Edition Song S. Qian, 2016-11-03 Emphasizing the inductive nature of statistical thinking, Environmental and Ecological Statistics with R, Second Edition, connects applied statistics to the environmental and ecological fields. Using examples from published works in the ecological and environmental literature, the book explains the approach to solving a statistical problem, covering model specification, parameter estimation, and model evaluation. It includes many examples to illustrate the statistical methods and presents R code for their implementation. The emphasis is on model interpretation and assessment, and using several core examples throughout the book, the author illustrates the iterative nature of statistical inference. The book starts with a description of commonly used statistical assumptions and exploratory data analysis tools for the verification of these assumptions. It then focuses on the process of building suitable statistical models, including linear and nonlinear models, classification and regression trees, generalized linear models, and multilevel models. It also discusses the use of simulation for model checking, and provides tools for a critical assessment of the developed models. The second edition also includes a complete critique of a threshold model. Environmental and Ecological Statistics with R, Second Edition focuses on statistical modeling and data analysis for environmental and ecological problems. By guiding readers through the process of scientific problem solving and statistical model development, it eases the transition from scientific hypothesis to statistical model. |
| linear hypothesis test in r: Goodness-of-Fit Tests and Model Validity C. Huber-Carol, N. Balakrishnan, M. Nikulin, M. Mesbah, 2012-12-06 The 37 expository articles in this volume provide broad coverage of important topics relating to the theory, methods, and applications of goodness-of-fit tests and model validity. The book is divided into eight parts, each of which presents topics written by expert researchers in their areas. Key features include: * state-of-the-art exposition of modern model validity methods, graphical techniques, and computer-intensive methods * systematic presentation with sufficient history and coverage of the fundamentals of the subject * exposure to recent research and a variety of open problems * many interesting real life examples for practitioners * extensive bibliography, with special emphasis on recent literature * subject index This comprehensive reference work will serve the statistical and applied mathematics communities as well as practitioners in the field. |
| linear hypothesis test in r: Fuzzy Statistical Decision-Making Cengiz Kahraman, Özgür Kabak, 2016-07-15 This book offers a comprehensive reference guide to fuzzy statistics and fuzzy decision-making techniques. It provides readers with all the necessary tools for making statistical inference in the case of incomplete information or insufficient data, where classical statistics cannot be applied. The respective chapters, written by prominent researchers, explain a wealth of both basic and advanced concepts including: fuzzy probability distributions, fuzzy frequency distributions, fuzzy Bayesian inference, fuzzy mean, mode and median, fuzzy dispersion, fuzzy p-value, and many others. To foster a better understanding, all the chapters include relevant numerical examples or case studies. Taken together, they form an excellent reference guide for researchers, lecturers and postgraduate students pursuing research on fuzzy statistics. Moreover, by extending all the main aspects of classical statistical decision-making to its fuzzy counterpart, the book presents a dynamic snapshot of the field that is expected to stimulate new directions, ideas and developments. |
| linear hypothesis test in r: An R Companion to Applied Regression John Fox, Sanford Weisberg, 2018-09-27 An R Companion to Applied Regression is a broad introduction to the R statistical computing environment in the context of applied regression analysis. John Fox and Sanford Weisberg provide a step-by-step guide to using the free statistical software R, an emphasis on integrating statistical computing in R with the practice of data analysis, coverage of generalized linear models, and substantial web-based support materials. The Third Edition has been reorganized and includes a new chapter on mixed-effects models, new and updated data sets, and a de-emphasis on statistical programming, while retaining a general introduction to basic R programming. The authors have substantially updated both the car and effects packages for R for this edition, introducing additional capabilities and making the software more consistent and easier to use. They also advocate an everyday data-analysis workflow that encourages reproducible research. To this end, they provide coverage of RStudio, an interactive development environment for R that allows readers to organize and document their work in a simple and intuitive fashion, and then easily share their results with others. Also included is coverage of R Markdown, showing how to create documents that mix R commands with explanatory text. An R Companion to Applied Regression continues to provide the most comprehensive and user-friendly guide to estimating, interpreting, and presenting results from regression models in R. –Christopher Hare, University of California, Davis |
| linear hypothesis test in r: Data Analysis for the Life Sciences with R Rafael A. Irizarry, Michael I. Love, 2016-10-04 This book covers several of the statistical concepts and data analytic skills needed to succeed in data-driven life science research. The authors proceed from relatively basic concepts related to computed p-values to advanced topics related to analyzing highthroughput data. They include the R code that performs this analysis and connect the lines of code to the statistical and mathematical concepts explained. |
| linear hypothesis test in r: An R and S-Plus Companion to Applied Regression John Fox, 2002-06-05 This book fits right into a needed niche: rigorous enough to give full explanation of the power of the S language, yet accessible enough to assign to social science graduate students without fear of intimidation. It is a tremendous balance of applied statistical firepower and thoughtful explanation. It meets all of the important mechanical needs: each example is given in detail, code and data are freely available, and the nuances of models are given rather than just the bare essentials. It also meets some important theoretical needs: linear models, categorical data analysis, an introduction to applying GLMs, a discussion of model diagnostics, and useful instructions on writing customized functions. —JEFF GILL, University of Florida, Gainesville |
| linear hypothesis test in r: Data Analytics for the Social Sciences G. David Garson, 2021-11-30 Data Analytics for the Social Sciences is an introductory, graduate-level treatment of data analytics for social science. It features applications in the R language, arguably the fastest growing and leading statistical tool for researchers. The book starts with an ethics chapter on the uses and potential abuses of data analytics. Chapters 2 and 3 show how to implement a broad range of statistical procedures in R. Chapters 4 and 5 deal with regression and classification trees and with random forests. Chapter 6 deals with machine learning models and the caret package, which makes available to the researcher hundreds of models. Chapter 7 deals with neural network analysis, and Chapter 8 deals with network analysis and visualization of network data. A final chapter treats text analysis, including web scraping, comparative word frequency tables, word clouds, word maps, sentiment analysis, topic analysis, and more. All empirical chapters have two Quick Start exercises designed to allow quick immersion in chapter topics, followed by In Depth coverage. Data are available for all examples and runnable R code is provided in a Command Summary. An appendix provides an extended tutorial on R and RStudio. Almost 30 online supplements provide information for the complete book, books within the book on a variety of topics, such as agent-based modeling. Rather than focusing on equations, derivations, and proofs, this book emphasizes hands-on obtaining of output for various social science models and how to interpret the output. It is suitable for all advanced level undergraduate and graduate students learning statistical data analysis. |
| linear hypothesis test in r: Advanced Statistics with Applications in R Eugene Demidenko, 2019-11-12 Advanced Statistics with Applications in R fills the gap between several excellent theoretical statistics textbooks and many applied statistics books where teaching reduces to using existing packages. This book looks at what is under the hood. Many statistics issues including the recent crisis with p-value are caused by misunderstanding of statistical concepts due to poor theoretical background of practitioners and applied statisticians. This book is the product of a forty-year experience in teaching of probability and statistics and their applications for solving real-life problems. There are more than 442 examples in the book: basically every probability or statistics concept is illustrated with an example accompanied with an R code. Many examples, such as Who said π? What team is better? The fall of the Roman empire, James Bond chase problem, Black Friday shopping, Free fall equation: Aristotle or Galilei, and many others are intriguing. These examples cover biostatistics, finance, physics and engineering, text and image analysis, epidemiology, spatial statistics, sociology, etc. Advanced Statistics with Applications in R teaches students to use theory for solving real-life problems through computations: there are about 500 R codes and 100 datasets. These data can be freely downloaded from the author's website dartmouth.edu/~eugened. This book is suitable as a text for senior undergraduate students with major in statistics or data science or graduate students. Many researchers who apply statistics on the regular basis find explanation of many fundamental concepts from the theoretical perspective illustrated by concrete real-world applications. |
| linear hypothesis test in r: The Theory and Practice of Econometrics George G. Judge, William E. Griffiths, R. Carter Hill, Helmut Lütkepohl, Tsoung-Chao Lee, 1991-01-16 This broadly based graduate-level textbook covers the major models and statistical tools currently used in the practice of econometrics. It examines the classical, the decision theory, and the Bayesian approaches, and contains material on single equation and simultaneous equation econometric models. Includes an extensive reference list for each topic. |
| linear hypothesis test in r: Modern Statistics with R Måns Thulin, 2024 The past decades have transformed the world of statistical data analysis, with new methods, new types of data, and new computational tools. Modern Statistics with R introduces you to key parts of this modern statistical toolkit. It teaches you: Data wrangling - importing, formatting, reshaping, merging, and filtering data in R. Exploratory data analysis - using visualisations and multivariate techniques to explore datasets. Statistical inference - modern methods for testing hypotheses and computing confidence intervals. Predictive modelling - regression models and machine learning methods for prediction, classification, and forecasting. Simulation - using simulation techniques for sample size computations and evaluations of statistical methods. Ethics in statistics - ethical issues and good statistical practice. R programming - writing code that is fast, readable, and (hopefully!) free from bugs. No prior programming experience is necessary. Clear explanations and examples are provided to accommodate readers at all levels of familiarity with statistical principles and coding practices. A basic understanding of probability theory can enhance comprehension of certain concepts discussed within this book. In addition to plenty of examples, the book includes more than 200 exercises, with fully worked solutions available at: www.modernstatisticswithr.com. |
| linear hypothesis test in r: Computational Statistics with R , 2014-11-27 R is open source statistical computing software. Since the R core group was formed in 1997, R has been extended by a very large number of packages with extensive documentation along with examples freely available on the internet. It offers a large number of statistical and numerical methods and graphical tools and visualization of extraordinarily high quality. R was recently ranked in 14th place by the Transparent Language Popularity Index and 6th as a scripting language, after PHP, Python, and Perl. The book is designed so that it can be used right away by novices while appealing to experienced users as well. Each article begins with a data example that can be downloaded directly from the R website. Data analysis questions are articulated following the presentation of the data. The necessary R commands are spelled out and executed and the output is presented and discussed. Other examples of data sets with a different flavor and different set of commands but following the theme of the article are presented as well. Each chapter predents a hands-on-experience. R has superb graphical outlays and the book brings out the essentials in this arena. The end user can benefit immensely by applying the graphics to enhance research findings. The core statistical methodologies such as regression, survival analysis, and discrete data are all covered. - Addresses data examples that can be downloaded directly from the R website - No other source is needed to gain practical experience - Focus on the essentials in graphical outlays |
| linear hypothesis test in r: Linear Models And Regression With R: An Integrated Approach Debasis Sengupta, S Rao Jammalamadaka, 2019-07-30 Starting with the basic linear model where the design and covariance matrices are of full rank, this book demonstrates how the same statistical ideas can be used to explore the more general linear model with rank-deficient design and/or covariance matrices. The unified treatment presented here provides a clearer understanding of the general linear model from a statistical perspective, thus avoiding the complex matrix-algebraic arguments that are often used in the rank-deficient case. Elegant geometric arguments are used as needed.The book has a very broad coverage, from illustrative practical examples in Regression and Analysis of Variance alongside their implementation using R, to providing comprehensive theory of the general linear model with 181 worked-out examples, 227 exercises with solutions, 152 exercises without solutions (so that they may be used as assignments in a course), and 320 up-to-date references.This completely updated and new edition of Linear Models: An Integrated Approach includes the following features: |
