A Modern Approach to Regression with R
This book focuses on tools and techniques for building regression models using real-world data and assessing their validity. A key theme throughout the book is that it makes sense to base inferences or conclusions only on valid models. Plots are shown to be an important tool for both building regression models and assessing their validity. We shall see that deciding what to plot and how each plot should be interpreted will be a major challenge. In order to overcome this challenge we shall need to understand the mathematical properties of the fitted regression models and associated diagnostic procedures. As such this will be an area of focus throughout the book. In particular, we shall carefully study the properties of resi- als in order to understand when patterns in residual plots provide direct information about model misspecification and when they do not. The regression output and plots that appear throughout the book have been gen- ated using R. The output from R that appears in this book has been edited in minor ways. On the book web site you will find the R code used in each example in the text.
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Added-variable plots Adjusted R-squared autocorrelation box plots Box-Cox Chapter confidence interval correlation curve data set degrees of freedom deviance diagnostic plots dummy variable equation Error t value Estimate Std example F-statistic fitted values fitting model fixed effects Food Rating freedom Multiple R-Squared given Intercept inverse response plot Kernel Density Estimate least squares estimates linear regression model lm(formula log-likelihood log(CCost log(Dwgs log(Price log(Sales log(Spans logistic regression logistic regression model marginal model plots Michelin Guide Normal Q−Q normally distributed outliers p-value parameters plot of standardized plots in Figure Pomerol prediction intervals predictor variables random effects regression coefficients regression line regression model Regression output REML Residual standard error residuals from model response variable restaurants scatter plot matrix simple linear regression standardized residuals statistically significant straight line subset Sum of Sq Theoretical Quantiles transformed valid model value Pr(>|t variable selection weighted least squares wine