Probability and Statistics with R

What Is R? Introduction to R Downloading and Installing R Vectors Mode and Class of an Object Getting Help External Editors RStudio Packages R Data Structures Reading and Saving Data in R Working with Data Using Logical Operators with Data Frames Tables Summarizing Functions Probability Functions Flow Control Creating Functions Simple Imputation Using plot() Coordinate Systems and Traditional Graphic's States Exploring Data What Is Statistics? Data Displaying Qualitative Data Displaying Quantitative Data Summary Measures of Location Summary Measures of Spread Bivariate Data Complex Plot Arrangements Multivariate Data General Probability and Random Variables Introduction Counting Techniques Axiomatic Probability Random Variables Moment Generating Functions Univariate Probability Distributions Introduction Discrete Univariate Distributions Continuous Univariate Distributions Multivariate Probability Distributions Joint Distribution of Two Random Variables Independent Random Variables Several Random Variables Conditional Distributions Expected Values, Covariance, and Correlation Multinomial Distribution Bivariate Normal Distribution Sampling and Sampling Distributions Sampling Parameters Estimators Sampling Distribution of the Sample Mean Sampling Distribution for a Statistic from an Infinite Population Sampling Distributions Associated with the Normal Distribution Point Estimation Introduction Properties of Point Estimators Point Estimation Techniques Confidence Intervals Introduction Confidence Intervals for Population Means Confidence Intervals for Population Variances Confidence Intervals Based on Large Samples Hypothesis Testing Introduction Type I and Type II Errors Power Function Uniformly Most Powerful Test rho-Value or Critical Level Tests of Significance Hypothesis Tests for Population Means Hypothesis Tests for Population Variances Hypothesis Tests for Population Proportions Nonparametric Methods Introduction Sign Test Wilcoxon Signed-Rank Test The Wilcoxon Rank-Sum or the Mann-Whitney U-Test The Kruskal-Wallis Test Friedman Test for Randomized Block Designs Goodness-of-Fit Tests Categorical Data Analysis Nonparametric Bootstrapping Permutation Tests Experimental Design Introduction Fixed Effects Model Analysis of Variance (ANOVA) for the One-Way Fixed Effects Model Power and the Non-Central F Distribution Checking Assumptions Fixing Problems Multiple Comparisons of Means Other Comparisons among the Means Summary of Comparisons of Means Random Effects Model (Variance Components Model) Randomized Complete Block Design Two-Factor Factorial Design Regression Introduction Simple Linear Regression Multiple Linear Regression Ordinary Least Squares Properties of the Fitted Regression Line Using Matrix Notation with Ordinary Least Squares The Method of Maximum Likelihood The Sampling Distribution of ss ANOVA Approach to Regression General Linear Hypothesis Model Building Model Validation Interpreting a Logarithmically Transformed Model Qualitative Predictors Estimation of the Mean Response for New Values Xh Prediction and Sampling Distribution of New Observations Yh(new) Simultaneous Confidence Intervals Appendix A: R Commands Appendix B: Quadratic Forms and Random Vectors and Matrices Bibliography Index Problems appear at the end of each chapter.