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Books on the topic 'Simple and multiple linear regression'

Author: Grafiati

Published: 4 June 2021

Last updated: 15 February 2022

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1

Shelton, Katherine Lesley. An illustration of heteroscedasticity in the multiple linear regression model. [s.l: The author], 1985.

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2

Karim, Samsul Ariffin Abdul, and Nur Fatonah Kamsani. Water Quality Index Prediction Using Multiple Linear Fuzzy Regression Model. Singapore: Springer Singapore, 2020. http://dx.doi.org/10.1007/978-981-15-3485-0.

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3

Zorn, Troy G. Utility of species-specific, multiple linear regression models for prediction of fish assemblages in rivers of Michigan's lower peninsula. Lansing, MI: Michigan Dept. of Natural Resources, Fisheries Division, 2004.

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4

Gelman, Andrew, and Deborah Nolan. Multiple regression and nonlinear models. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780198785699.003.0010.

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This chapter covers multiple regression and links statistical inference to general topics such as lurking variables that arose earlier. Many examples can be used to illustrate multiple regression, but we have found it useful to come to class prepared with a specific example, with computer output (since our students learn to run the regressions on the computer). We have found it is a good strategy to simply use a regression analysis from some published source (e.g., a social science journal) and go through the model and its interpretation with the class, asking students how the regression results would have to differ in order for the study’s conclusions to change. The chapter includes examples that revisit the simple linear model of height and income, involve the class in models of exam scores, and fit a nonlinear model (for more advanced classes) for golf putting.

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5

Miksza, Peter, and Kenneth Elpus. Regression. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780199391905.003.0010.

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This chapter presents the logic and technique of analyzing data using simple linear regression and multiple linear regression. Regression is a remarkably versatile statistical procedure that can be used not only to understand whether or not variables are related to each other (as in correlation) but also for providing estimates of the direction of the relationship and of the degree to which the variables are related. Beginning with a simple bivariate case analyzing a single predictor on a single outcome, the flexibility and ability for regression to analyze increasingly complex data, including binary outcomes, is discussed. Particular attention is paid to the ability of regression to be used to estimate the effect of a predictor on an outcome while statistically “controlling” for the values of other observed variables.

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6

Roback, Paul, and Julie Legler. Beyond Multiple Linear Regression. Chapman and Hall/CRC, 2021. http://dx.doi.org/10.1201/9780429066665.

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7

Quantitative methods in business: Unit 8 : Simple linear regression. Milton Keynes: Open University, 2003.

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8

J, Niccolucci Michael, Schuster Ervin G, and Intermountain Research Station (Ogden, Utah), eds. Identifying proxy sets in multiple linear regression: An aid to better coefficient interpretation. Ogden, UT (324 25th St., Ogden 84401): U.S. Dept. of Agriculture, Forest Service, Intermountain Research Station, 1993.

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9

Higham, Ronald P. A multiple linear regression model for predicting zone A retention by military occupational specialty. 1986.

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10

Karim, Samsul Ariffin Abdul, and Nur Fatonah Kamsani. Water Quality Index Prediction Using Multiple Linear Fuzzy Regression Model: Case Study in Perak River, Malaysia. Springer, 2020.

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11

Center, Lewis Research, ed. A multiple linear regression analysis of hot corrosion attack on a series of nickel base turbine alloys. [Cleveland, Ohio: National Aeronautics and Space Administration, Lewis Research Center, 1985.

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12

Crafton, R. Eliot. Using Multiple Linear Regression Models to Identify Factors Underlying Avian Species Imperilment in Sub-Saharan Africa and Europe. INTECH Open Access Publisher, 2011.

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13

Miles, Jeremy. General and generalised linear models. Oxford University Press, 2015. http://dx.doi.org/10.1093/med:psych/9780198527565.003.0017.

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This chapter discusses general and generalised linear models (GLM and GLZ respectively). It outlines GLMs (mean, properties of GLMs and the mean), samples and populations, comparison of two groups of data, multiple regression and the GLM, analysis of variance (ANOVA) and the GLM, GLM in SPSS, and the GLZ).

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14

Veech, Joseph A. Habitat Ecology and Analysis. Oxford University Press, 2021. http://dx.doi.org/10.1093/oso/9780198829287.001.0001.

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Habitat is crucial to the survival and reproduction of individual organisms as well as persistence of populations. As such, species-habitat relationships have long been studied, particularly in the field of wildlife ecology and to a lesser extent in the more encompassing discipline of ecology. The habitat requirements of a species largely determine its spatial distribution and abundance in nature. One way to recognize and appreciate the over-riding importance of habitat is to consider that a young organism must find and settle into the appropriate type of habitat as one of the first challenges of life. This process can be cast in a probabilistic framework and used to better understand the mechanisms behind habitat preferences and selection. There are at least six distinctly different statistical approaches to conducting a habitat analysis – that is, identifying and quantifying the environmental variables that a species most strongly associates with. These are (1) comparison among group means (e.g., ANOVA), (2) multiple linear regression, (3) multiple logistic regression, (4) classification and regression trees, (5) multivariate techniques (Principal Components Analysis and Discriminant Function Analysis), and (6) occupancy modelling. Each of these is lucidly explained and demonstrated by application to a hypothetical dataset. The strengths and weaknesses of each method are discussed. Given the ongoing biodiversity crisis largely caused by habitat destruction, there is a crucial and general need to better characterize and understand the habitat requirements of many different species, particularly those that are threatened and endangered.

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15

Hall, Peter. Principal component analysis for functional data. Edited by Frédéric Ferraty and Yves Romain. Oxford University Press, 2018. http://dx.doi.org/10.1093/oxfordhb/9780199568444.013.8.

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This article discusses the methodology and theory of principal component analysis (PCA) for functional data. It first provides an overview of PCA in the context of finite-dimensional data and infinite-dimensional data, focusing on functional linear regression, before considering the applications of PCA for functional data analysis, principally in cases of dimension reduction. It then describes adaptive methods for prediction and weighted least squares in functional linear regression. It also examines the role of principal components in the assessment of density for functional data, showing how principal component functions are linked to the amount of probability mass contained in a small ball around a given, fixed function, and how this property can be used to define a simple, easily estimable density surrogate. The article concludes by explaining the use of PCA for estimating log-density.

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16

Klerman, Daniel. Quantitative Legal History. Edited by Markus D. Dubber and Christopher Tomlins. Oxford University Press, 2018. http://dx.doi.org/10.1093/oxfordhb/9780198794356.013.19.

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Quantitative legal history is in a rather sorry state. Only about a quarter of recent works of legal history use even simple quantitative methods (such as tables or graphs), and articles or books with more sophisticated methods, such as regression analysis, are extremely rare. The infrequent use of quantitative techniques is also a missed opportunity. Scholars from other fields, including economics, sociology, and political science, are using statistics to analyse legal history. Such analysis is particularly helpful in understanding the effect of legal change and in analysing the influence of multiple factors on legislation, judicial decision-making, and citizen behaviour. This chapter first assesses quantitatively the use of quantitative methods in legal history. It then discusses a few examples of the successful use of numbers and statistics in recent books addressing legal historical topics. Finally, it looks to the future of quantitative legal history.

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17

Edge, M. D. Statistical Thinking from Scratch. Oxford University Press, 2019. http://dx.doi.org/10.1093/oso/9780198827627.001.0001.

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In virtually every field, researchers find themselves navigating tremendous amounts of new data. Making sense of this flood of information requires much more than the rote application of traditional statistical methods. This book will train researchers to be creative and confident users of statistics by thinking hard about the application of simple methods to a small dataset. In particular, this book focuses on simple linear regression—a method with strong connections to the most important tools in applied statistics—using it as a detailed case study for teaching resampling-based, likelihood-based, and Bayesian approaches to statistical inference. This exercise imparts an idea of how statistical procedures are designed and implemented, a flavor for the philosophical positions one implicitly assumes when applying statistics, and an opportunity to probe the strengths and weaknesses of one’s statistical approach. Key to the book’s novel approach is its mathematical level, which is gentler than most texts for statisticians but more rigorous than most introductory texts for non-statisticians. Statistical Thinking from Scratch is suitable for senior undergraduate and beginning graduate students, professional researchers, and practitioners seeking to improve their understanding of statistical methods across the natural and social sciences, medicine, psychology, public health, business, and other fields.

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18

Ferreira, Eliel Alves, and João Vicente Zamperion. Excel: Uma ferramenta estatística. Brazil Publishing, 2021. http://dx.doi.org/10.31012/978-65-5861-400-5.

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This study aims to present the concepts and methods of statistical analysis using the Excel software, in a simple way aiming at a greater ease of understanding of students, both undergraduate and graduate, from different areas of knowledge. In Excel, mainly Data Analysis Tools will be used. For a better understanding, there are, in this book, many practical examples applying these tools and their interpretations, which are of paramount importance. In the first chapter, it deals with introductory concepts, such as introduction to Excel, the importance of statistics, concepts and definitions. Being that in this will be addressed the subjects of population and sample, types of data and their levels of measurement. Then it brings a detailed study of Descriptive Statistics, where it will be studied percentage, construction of graphs, frequency distribution, measures of central tendency and measures of dispersion. In the third chapter, notions of probability, binomial and normal probability distribution will be studied. In the last chapter, Inferential Statistics will be approached, starting with the confidence interval, going through the hypothesis tests (F, Z and t tests), ending with the statistical study of the correlation between variables and simple linear regression. It is worth mentioning that the statistical knowledge covered in this book can be useful for, in addition to students, professionals who want to improve their knowledge in statistics using Excel.

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19

Witkov, Carey, and Keith Zengel. Chi-Squared Data Analysis and Model Testing for Beginners. Oxford University Press, 2019. http://dx.doi.org/10.1093/oso/9780198847144.001.0001.

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This book is the first to make chi-squared model testing, one of the data analysis methods used to discover the Higgs boson and gravitational waves, accessible to undergraduate students in introductory physics laboratory courses. By including uncertainties in the curve fitting, chi-squared data analysis improves on the centuries old ordinary least squares and linear regression methods and combines best fit parameter estimation and model testing in one method. A toolkit of essential statistical and experimental concepts is developed from the ground up with novel features to interest even those familiar with the material. The presentation of one- and two-parameter chi-squared model testing, requiring only elementary probability and algebra, is followed by case studies that apply the methods to simple introductory physics lab experiments. More challenging topics, requiring calculus, are addressed in an advanced topics chapter. This self-contained and student-friendly introduction to chi-squared analysis and model testing includes a glossary, end-of-chapter problems with complete solutions, and software scripts written in several popular programming languages, that the reader can use for chi-squared model testing. In addition to introductory physics lab students, this accessible introduction to chi-squared analysis and model testing will be of interest to all who need to learn chi-squared model testing, e.g. beginning researchers in astrophysics and particle physics, beginners in data science, and lab students in other experimental sciences.

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20

Sahay, Sundeep, T. Sundararaman, and Jørn Braa. Complexity and Public Health Informatics in Low and Middle-Income Countries. Oxford University Press, 2017. http://dx.doi.org/10.1093/med/9780198758778.003.0007.

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This chapter enriches the Expanded PHI perspective through the lens of complexity. Current technical health systems and institutional developments, including the increasing inter-connections between them, and the uncertainities associated with both context and goals are enhancing complexity exponentially. Simple linear approaches to design and develop systems can no longer work, as they imply trying to bring order into processes which by definition defy them. Cloud computing and big data are offered as examples to depict this rising complexity, providing rich opportunities to materialize them. Many organizations are adopting outsourcing models as a means to manage this complexity. However, outsourcing comes in multiple hues and shades, from a simple use of third party hardware to the externalization of the whole value chain of activities, including the analysis and use of data. Public health informatics in LMICs, which are population-based and taking place in largely resource-constrained and unstructured settings, are by definition problematic to outsource and should be approached with caution. An incremental approach where a ‘cultivation strategy’ addresses uncertainities, and ‘attractors’ draw in user-participants are more likely to succeed.

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