Applied Regression Modeling

ISBN-13: 9781119615866 / Angielski / Twarda / 2020 / 336 str.

Iain Pardoe

Spis treści

Preface xiAcknowledgments xvIntroduction xviiI.1 Statistics in Practice xviiI.2 Learning Statistics xixAbout the Companion Website xxi1 Foundations 11.1 Identifying and Summarizing Data 21.2 Population Distributions 51.3 Selecting Individuals at Random--Probability 91.4 Random Sampling 111.4.1 Central limit theorem--normal version 121.4.2 Central limit theorem--t-version 141.5 Interval Estimation 161.6 Hypothesis Testing 201.6.1 The rejection region method 201.6.2 The p-value method 231.6.3 Hypothesis test errors 271.7 Random Errors and Prediction 281.8 Chapter Summary 31Problems 312 Simple Linear Regression 392.1 Probability Model for X and Y 402.2 Least Squares Criterion 452.3 Model Evaluation 502.3.1 Regression standard error 512.3.2 Coefficient of determination--R² 532.3.3 Slope parameter 572.4 Model Assumptions 652.4.1 Checking the model assumptions 662.4.2 Testing the model assumptions 722.5 Model Interpretation 722.6 Estimation and Prediction 742.6.1 Confidence interval for the population mean, E(Y) 742.6.2 Prediction interval for an individual Y -value 752.7 Chapter Summary 792.7.1 Review example 80Problems 833 Multiple Linear Regression 953.1 Probability Model for (X1, X2, . . .) and Y 963.2 Least Squares Criterion 1003.3 Model Evaluation 1063.3.1 Regression standard error 1063.3.2 Coefficient of determination--R² 1083.3.3 Regression parameters--global usefulness test 1153.3.4 Regression parameters--nested model test 1203.3.5 Regression parameters--individual tests 1273.4 Model Assumptions 1373.4.1 Checking the model assumptions 1373.4.2 Testing the model assumptions 1433.5 Model Interpretation 1453.6 Estimation and Prediction 1463.6.1 Confidence interval for the population mean, E(Y ) 1473.6.2 Prediction interval for an individual Y -value 1483.7 Chapter Summary 151Problems 1524 Regression Model Building I 1594.1 Transformations 1614.1.1 Natural logarithm transformation for predictors 1614.1.2 Polynomial transformation for predictors 1674.1.3 Reciprocal transformation for predictors 1714.1.4 Natural logarithm transformation for the response 1754.1.5 Transformations for the response and predictors 1794.2 Interactions 1844.3 Qualitative Predictors 1914.3.1 Qualitative predictors with two levels 1924.3.2 Qualitative predictors with three or more levels 2014.4 Chapter Summary 210Problems 2115 Regression Model Building II 2215.1 Influential Points 2235.1.1 Outliers 2235.1.2 Leverage 2285.1.3 Cook's distance 2305.2 Regression Pitfalls 2345.2.1 Nonconstant variance 2345.2.2 Autocorrelation 2375.2.3 Multicollinearity 2425.2.4 Excluding important predictor variables 2465.2.5 Overfitting 2495.2.6 Extrapolation 2505.2.7 Missing data 2525.2.8 Power and sample size 2555.3 Model Building Guidelines 2565.4 Model Selection 2595.5 Model Interpretation Using Graphics 2635.6 Chapter Summary 270Problems 272Notation and Formulas 287Univariate Data 287Simple Linear Regression 288Multiple Linear Regression 289Bibliography 293Glossary 299Index 3056 Case studies 5336.1 Home prices 5336.1.1 Data description 5336.1.2 Exploratory data analysis 5366.1.3 Regression model building 5396.1.4 Results and conclusions 5426.1.5 Further questions 5516.2 Vehicle fuel efficiency 5526.2.1 Data description 5526.2.2 Exploratory data analysis 5546.2.3 Regression model building 5566.2.4 Results and conclusions 5576.2.5 Further questions 5676.3 Pharmaceutical patches 5686.3.1 Data description 5686.3.2 Exploratory data analysis 5696.3.3 Regression model building 5706.3.4 Model diagnostics 5736.3.5 Results and conclusions 5746.3.6 Further questions 5787 Extensions 5797.1 Generalized linear models 5817.1.1 Logistic regression 5827.1.2 Poisson regression 5947.2 Discrete choice models 6027.3 Multilevel models 6097.4 Bayesian modeling 6147.4.1 Frequentist inference 6147.4.2 Bayesian inference 616Problems 620A Computer software help 623Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 626B Critical values for t-distributions 631C Notation and formulas 635C.1 Univariate data 635C.2 Simple linear regression 637C.3 Multiple linear regression 639D Mathematics refresher 643D.1 The natural logarithm and exponential functions 643D.2 Rounding and accuracy 644E Multiple Linear Regression Using Matrices 647E.1 Vectors and matrices 647E.2 Matrix multiplication 649E.3 Matrix addition 652E.4 Transpose of a matrix 654E.5 Inverse of a matrix 656E.6 Estimated multiple linear regression model equation 657E.7 Least squares regression parameter estimates 659E.8 Predicted or fitted values 661E.9 Residuals and the regression standard error 663E.10 Coefficient of determination 664E.11 Regression parameter standard errors and t-statistics 665E.12 Estimation and prediction 666E.13 Leverages, standardized and studentized residuals, and Cook's distances 668F Answers for selected problems 673

O autorze

Iain Pardoe, PhD, received his PhD in Statistics from the University of Minnesota. He is an Online Instructor of the "Regression Methods" graduate course at Pennsylvania State University. He also teaches "Biostatistics," "Mathematics for Computing Science," and "Mathematics for Teachers" at Thompson Rivers University and was previously an Associate Professor at the University of Oregon.