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Unit-weighted regression

About: Unit-weighted regression is a research topic. Over the lifetime, 586 publications have been published within this topic receiving 88669 citations.


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Book
01 Jan 1975
TL;DR: In this article, the Mathematical Basis for Multiple Regression/Correlation and Identification of the Inverse Matrix Elements is presented. But it does not address the problem of missing data.
Abstract: Contents: Preface. Introduction. Bivariate Correlation and Regression. Multiple Regression/Correlation With Two or More Independent Variables. Data Visualization, Exploration, and Assumption Checking: Diagnosing and Solving Regression Problems I. Data-Analytic Strategies Using Multiple Regression/Correlation. Quantitative Scales, Curvilinear Relationships, and Transformations. Interactions Among Continuous Variables. Categorical or Nominal Independent Variables. Interactions With Categorical Variables. Outliers and Multicollinearity: Diagnosing and Solving Regression Problems II. Missing Data. Multiple Regression/Correlation and Causal Models. Alternative Regression Models: Logistic, Poisson Regression, and the Generalized Linear Model. Random Coefficient Regression and Multilevel Models. Longitudinal Regression Methods. Multiple Dependent Variables: Set Correlation. Appendices: The Mathematical Basis for Multiple Regression/Correlation and Identification of the Inverse Matrix Elements. Determination of the Inverse Matrix and Applications Thereof.

29,764 citations

Journal ArticleDOI
TL;DR: In the new version, procedures to analyze the power of tests based on single-sample tetrachoric correlations, comparisons of dependent correlations, bivariate linear regression, multiple linear regression based on the random predictor model, logistic regression, and Poisson regression are added.
Abstract: G*Power is a free power analysis program for a variety of statistical tests. We present extensions and improvements of the version introduced by Faul, Erdfelder, Lang, and Buchner (2007) in the domain of correlation and regression analyses. In the new version, we have added procedures to analyze the power of tests based on (1) single-sample tetrachoric correlations, (2) comparisons of dependent correlations, (3) bivariate linear regression, (4) multiple linear regression based on the random predictor model, (5) logistic regression, and (6) Poisson regression. We describe these new features and provide a brief introduction to their scope and handling.

20,778 citations

Book
01 Jan 1978
TL;DR: In this article, the authors compare two straight line regression models and conclude that the Straight Line Regression Equation does not measure the strength of the Straight-line Relationship, but instead is a measure of the relationship between two straight lines.
Abstract: 1. CONCEPTS AND EXAMPLES OF RESEARCH. Concepts. Examples. Concluding Remarks. References. 2. CLASSIFICATION OF VARIABLES AND THE CHOICE OF ANALYSIS. Classification of Variables. Overlapping of Classification Schemes. Choice of Analysis. References. 3. BASIC STATISTICS: A REVIEW. Preview. Descriptive Statistics. Random Variables and Distributions. Sampling Distributions of t, ?O2, and F. Statistical Inference: Estimation. Statistical Inference: Hypothesis Testing. Error Rate, Power, and Sample Size. Problems. References. 4. INTRODUCTION TO REGRESSION ANALYSIS. Preview. Association versus Causality. Statistical versus Deterministic Models. Concluding Remarks. References. 5. STRAIGHT-LINE REGRESSION ANALYSIS. Preview. Regression with a Single Independent Variable. Mathematical Properties of a Straight Line. Statistical Assumptions for a Straight-line Model. Determining the Best-fitting Straight Line. Measure of the Quality of the Straight-line Fit and Estimate ?a2. Inferences About the Slope and Intercept. Interpretations of Tests for Slope and Intercept. Inferences About the Regression Line ?YY|X = ?O0 + ?O1X . Prediction of a New Value of Y at X0. Problems. References. 6. THE CORRELATION COEFFICIENT AND STRAIGHT-LINE REGRESSION ANALYSIS. Definition of r. r as a Measure of Association. The Bivariate Normal Distribution. r and the Strength of the Straight-line Relationship. What r Does Not Measure. Tests of Hypotheses and Confidence Intervals for the Correlation Coefficient. Testing for the Equality of Two Correlations. Problems. References. 7. THE ANALYSIS-OF-VARIANCE TABLE. Preview. The ANOVA Table for Straight-line Regression. Problems. 8. MULTIPLE REGRESSION ANALYSIS: GENERAL CONSIDERATIONS. Preview. Multiple Regression Models. Graphical Look at the Problem. Assumptions of Multiple Regression. Determining the Best Estimate of the Multiple Regression Equation. The ANOVA Table for Multiple Regression. Numerical Examples. Problems. References. 9. TESTING HYPOTHESES IN MULTIPLE REGRESSION. Preview. Test for Significant Overall Regression. Partial F Test. Multiple Partial F Test. Strategies for Using Partial F Tests. Tests Involving the Intercept. Problems. References. 10. CORRELATIONS: MULTIPLE, PARTIAL, AND MULTIPLE PARTIAL. Preview. Correlation Matrix. Multiple Correlation Coefficient. Relationship of RY|X1, X2, !KXk to the Multivariate Normal Distribution. Partial Correlation Coefficient. Alternative Representation of the Regression Model. Multiple Partial Correlation. Concluding Remarks. Problems. References. 11. CONFOUNDING AND INTERACTION IN REGRESSION. Preview. Overview. Interaction in Regression. Confounding in Regression. Summary and Conclusions. Problems. References. 12. DUMMY VARIABLES IN REGRESSION. Preview. Definitions. Rule for Defining Dummy Variables. Comparing Two Straight-line Regression Equations: An Example. Questions for Comparing Two Straight Lines. Methods of Comparing Two Straight Lines. Method I: Using Separate Regression Fits to Compare Two Straight Lines. Method II: Using a Single Regression Equation to Compare Two Straight Lines. Comparison of Methods I and II. Testing Strategies and Interpretation: Comparing Two Straight Lines. Other Dummy Variable Models. Comparing Four Regression Equations. Comparing Several Regression Equations Involving Two Nominal Variables. Problems. References. 13. ANALYSIS OF COVARIANCE AND OTHER METHODS FOR ADJUSTING CONTINUOUS DATA. Preview. Adjustment Problem. Analysis of Covariance. Assumption of Parallelism: A Potential Drawback. Analysis of Covariance: Several Groups and Several Covariates. Comments and Cautions. Summary Problems. Reference. 14. REGRESSION DIAGNOSTICS. Preview. Simple Approaches to Diagnosing Problems in Data. Residual Analysis: Detecting Outliers and Violations of Model Assumptions. Strategies of Analysis. Collinearity. Scaling Problems. Diagnostics Example. An Important Caution. Problems. References. 15. POLYNOMIAL REGRESSION. Preview. Polynomial Models. Least-squares Procedure for Fitting a Parabola. ANOVA Table for Second-order Polynomial Regression. Inferences Associated with Second-order Polynomial Regression. Example Requiring a Second-order Model. Fitting and Testing Higher-order Model. Lack-of-fit Tests. Orthogonal Polynomials. Strategies for Choosing a Polynomial Model. Problems. 16. SELECTING THE BEST REGRESSION EQUATION. Preview. Steps in Selecting the Best Regression Equation. Step 1: Specifying the Maximum Model. Step 2: Specifying a Criterion for Selecting a Model. Step 3: Specifying a Strategy for Selecting Variables. Step 4: Conducting the Analysis. Step 5: Evaluating Reliability with Split Samples. Example Analysis of Actual Data. Issues in Selecting the Most Valid Model. Problems. References. 17. ONE-WAY ANALYSIS OF VARIANCE. Preview. One-way ANOVA: The Problem, Assumptions, and Data Configuration. for One-way Fixed-effects ANOVA. Regression Model for Fixed-effects One-way ANOVA Fixed-effects Model for One-way ANOVA. Random-effects Model for One-way ANOVA. -comparison Procedures for Fixed-effects One-way ANOVA. a Multiple-comparison Technique. Orthogonal Contrasts and Partitioning an ANOVA Sum of Squares. Problems. References. 18. RANDOMIZED BLOCKS: SPECIAL CASE OF TWO-WAY ANOVA. Preview. Equivalent Analysis of a Matched-pairs Experiment. Principle of Blocking. Analysis of a Randomized-blocks Experiment. ANOVA Table for a Randomized-blocks Experiment. Models for a Randomized-blocks Experiment. Fixed-effects ANOVA Model for a Randomized-blocks Experiment. Problems. References. 19. TWO-WAY ANOVA WITH EQUAL CELL NUMBERS. Preview. Using a Table of Cell Means. General Methodology. F Tests for Two-way ANOVA. Regression Model for Fixed-effects Two-way ANOVA. Interactions in Two-way ANOVA. Random- and Mixed-effects Two-way ANOVA Models. Problems. References. 20. TWO-WAY ANOVA WITH UNEQUAL CELL NUMBERS. Preview. Problem with Unequal Cell Numbers: Nonorthogonality. Regression Approach for Unequal Cell Sample Sizes. Higher-way ANOVA. Problems. References. 21. THE METHOD OF MAXIMUM LIKELIHOOD. Preview. The Principle of Maximum Likelihood. Statistical Inference Using Maximum Likelihood. Summary. Problems. 22. LOGISTIC REGRESSION ANALYSIS. Preview. The Logistic Model. Estimating the Odds Ratio Using Logistic Regression. A Numerical Example of Logistic Regression. Theoretical Considerations. An Example of Conditional ML Estimation Involving Pair-matched Data with Unmatched Covariates. Summary. Problems. References. 23. POLYTOMOUS AND ORDINAL LOGISTIC REGRESSION. Preview. Why Not Use Binary Regression? An Example of Polytomous Logistic Regression: One Predictor, Three Outcome Categories. An Example: Extending the Polytomous Logistic Model to Several Predictors. Ordinal Logistic Regression: Overview. A "Simple" Hypothetical Example: Three Ordinal Categories and One Dichotomous Exposure Variable. Ordinal Logistic Regression Example Using Real Data with Four Ordinal Categories and Three Predictor Variables. Summary. Problems. References. 24. POISSON REGRESSION ANALYSIS. Preview. The Poisson Distribution. Example of Poisson Regression. Poisson Regression: General Considerations. Measures of Goodness of Fit. Continuation of Skin Cancer Data Example. A Second Illustration of Poisson Regression Analysis. Summary. Problems. References. 25. ANALYSIS OF CORRELATED DATA PART 1: THE GENERAL LINEAR MIXED MODEL. Preview. Examples. General Linear Mixed Model Approach. Example: Study of Effects of an Air Polluion Episode on FEV1 Levels. Summary!XAnalysis of Correlated Data: Part 1. Problems. References. 26. ANALYSIS OF CORRELATED DATA PART 2: RANDOM EFFECTS AND OTHER ISSUES. Preview. Random Effects Revisited. Results for Random Effects Models Applied to Air Pollution Study Data. Second Example!XAnalysis of Posture Measurement Data. Recommendations about Choice of Correlation Structure. Analysis of Data for Discrete Outcomes. Problems. References. 27. SAMPLE SIZE PLANNING FOR LINEAR AND LOGISTIC REGRESSION AND ANALYSIS OF VARIANCE. Preview. Review: Sample Size Calculations for Comparisons of Means and Proportions. Sample Size Planning for Linear Regression. Sample Size Planning for Logistic Regression. Power and Sample Size Determination for Linear Models: A General Approach. Sample Size Determination for Matched Case-control Studies with a Dichotomous Outcome. Practical Considerations and Cautions. Problems. References. Appendix A. Appendix B. Appendix C. Solutions to Exercises. Index.

9,433 citations

Book
09 Oct 2001
TL;DR: The second edition of the Second Edition of the Logistic regression model as discussed by the authors is the most complete version of the first edition and includes a discussion of the relationship between linear regression and logistic regression.
Abstract: Series Editor's Introduction Author's Introduction to the Second Edition 1. Linear Regression and Logistic Regression Model 2. Summary Statistics for Evaluating the Logistic Regression Model 3. Interpreting the Logistic Regression Coefficients 4. An Introduction to Logistic Regression Diagnosis Ch 5. Polytomous Logistic Regression and Alternatives to Logistic Regression 6. Notes Appendix A References Tables Figures

4,046 citations

Book
01 Apr 2005
TL;DR: In this article, the authors present a set of confidence limits of the geometric mean for a log-normal distribution for a given value and the confidence limits for a large sample for a small sample.
Abstract: 1 Introduction 11 Analytical problems 12 Errors in qunatitative analysis 13 Types of error 14 Random and systematic errors in titrimetric analysis 15 Handling systematic errors 16 Planning and design of experiments 17 Calculators and computers in statistical calculations 2 Statistics of Repeated Measurements 21 Mean and standard deviation 22 The distribution of repeated measurements 23 Log-normal distribution 24 Definition of a 'sample' 25 The sampling distribution of the mean 26 Confidence limits of the mean for large samples 27 Confidence limits of the mean for small samples 28 Presentation of results 29 Other uses of confidence limits 210 Confidence limits of the geometric mean for a log-normal distribution 211 Propagation of random errors 212 Propagation of systematic errors 3 Significance Tests 31 Introduction 32 Comparison of an experimental mean with a known value 33 Comparison of two experimental means 34 Paired t-test 35 One-sided and two-sided tests 36 F-test for the comparison of standard deviations 37 Outliers 38 Analysis of variance 39 Comparison of several means 310 The arithmetic of ANOVA calculations 311 The chi-squared test 312 Testing for normality of distribution 313 Conclusions from significance tests 314 Bayesian Statistics 4 The Quality of Analytical Measurements 41 Introduction 42 Sampling 43 Separation and estimation of variances using ANOVA 44 Sampling strategy 45 Quality control methods - Introduction 46 Stewhart charts for mean values 47 Stewhart charts for ranges 48 Establishing the process capability 49 Average run length: cusum charts 410 Zone control charts (J-charts) 411 Proficiency testing schemes 412 Method performance studies (collaborative trials) 413 Uncertainty 414 Acceptable sampling 415 Method validation 5 Calibration Methods in Instumental Analysis 51 Introduction: instrumentational analysis 52 Calibration graphs in instrumental analysis 53 The product-moment correlation coefficient 54 The line of regression of y on x 55 Errors in the slope and intercept of the regression line 56 Calculation of a concentration and its random error 57 Limits of detection 58 The method of standard additions 59 Use of regression lines for comparing analytical methods 510 Weighted regression lines 511 Intersection of two straight lines 512 ANOVA and regression calculations 513 Curvilinear regression methods - Introduction 514 Curve fitting 515 Outliers in regression 6 Non-parametric and Robust Methods 61 Introduction 62 The median: initial data analysis 63 The sign test 64 The Wald-Wolfowitz runs test 65 The Wilcoxon signed rank test 66 Simple tests for two independent samples 67 Non-parametric tests for more than two samples 68 Rank correlation 69 Non-parametric regression methods 610 Robust methods: introduction 611 Simple robust methods: trimming and winsorization 612 Further robust estimates of location and spread 613 Robust ANOVA 614 Robust regression methods 615 Re-sampling statistics 616 Conclusions 7 Experiimental Design and Optimization 71 Introduction 72 Randomization and blocking 73 Two-way ANOVA 74 Latin squares and other designs 75 Interactions 76 Identifying the important factors: factorial designs 77 Fractional factorial designs 78 Optimization: basic principles and univariate methods 79 Optimization using the alternating variable search method 710 The method of steepest ascent 711 Simplex optimization 712 Simulated annealing 8 Multivariate Analysis 81 Introduction 82 Initial analysis 83 Prinicipal component analysis 84 Cluster analysis 85 Discriminant analysis 86 K-nearest neighbour method 87 Disjoint class modelling 88 Regression methods 89 Multiple linear regression 810 Principal component regression 811 Partial least squares regression 812 Natural computation methods artificial neural networks 813 Conclusions Solutions to Exercises Appendix 1 Commonly used statistical significance tests Appendix 2 Statistical tables Index

3,668 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202124
202019
201923
201819
201727
201621