## Linear Regression Analysis: Theory and ComputingThis volume presents in detail the fundamental theories of linear regression analysis and diagnosis, as well as the relevant statistical computing techniques so that readers are able to actually model the data using the methods and techniques described in the book. It covers the fundamental theories in linear regression analysis and is extremely useful for future research in this area. The examples of regression analysis using the Statistical Application System (SAS) are also included. This book is suitable for graduate students who are either majoring in statistics/biostatistics or using linear regression analysis substantially in their subject fields. |

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### Contents

1 Introduction | 1 |

2 Simple Linear Regression | 9 |

3 Multiple Linear Regression | 41 |

4 Detection of Outliers and Inuential Observations in Multiple Linear Regression | 129 |

5 Model Selection | 157 |

6 Model Diagnostics | 195 |

8 Generalized Linear Models | 269 |

9 Bayesian Linear Regression | 297 |

317 | |

325 | |

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### Common terms and phrases

algorithm Bayesian linear collinearity column Compute confidence interval Consider correlation data points data set degrees of freedom denote density discuss DPROS dummy variables equation error term error variance example F test fitted values function given heteroscedasticity idempotent matrix independent variables influential observation interaction Intercept inverse ith observation lasso least squares estimation linear model linear regression model log-likelihood logistic mean shift outlier method model diagnosis model selection multiple linear regression multiple regression nonlinear null orthogonal P-Value Parameter Estimates population posterior predictors PRESS residual proc reg procedure projection matrix quadratic form Quasar Quasar Data random forests regression analysis regression coefficients regression line regression model regression parameters regression prediction regressors residual plot response variable ridge regression sample simple linear regression standard stepwise studentized residual sum of squares Table test statistic Theorem transformation variance inflation vector space versus Wald Wald test