The standard approach of most introductory books for practical statistics is that readers first learn the minimum mathematical basics of statistics and rudimentary concepts of statistical methodology. They then are given examples of analyses of data obtained from natural and social phenomena so that they can grasp practical definitions of statistical methods. Finally they go on to acquaint themselves with statistical software for the PC and analyze similar data to expand and deepen their understanding of statistical methods.

Chapter 1 Linear algebra. Starting up and executing R. Vectors. Matrices. Addition of two matrices. Multiplying two matrices. Identity and inverse matrices. Simultaneous equations. Diagonalization of a symmetric matrix. Quadratic forms.- Chapter 2 Distributions and tests. Sampling and random variables. Probability distribution. Normal distribution and the central limit theorem. Interval estimation by t distribution. t-test. Intervalestimation of population variance and the ¿2 distribution. Fdistribution and F-test. Wilcoxon signed-rank sum test.- Chapter 3 Simple regression. Derivation of regression coefficients. Exchange between predictor variable and target variable. Regression to the mean. Confidence interval of regression coefficients in simple regression. t-Test in simple regression. F-teston simple regression. Selection between constant and nonconstant regression equations. Prediction error of simple regression. Weighted regression. Least squares method and prediction error.- Chapter 4 Multiple regression. Derivation of regression coefficients. Test on multiple regression. Prediction error on multiple regression. Notes on model selection using prediction error. Polynomial regression. Variance of regression coefficient and multicollinearity. Detection of multicollinearity using Variance Inflation Factors. Hessian matrix of log-likelihood.- Chapter 5 Akaike's Information Criterion (AIC) and the third variance. Cp and FPE. AIC of a multiple regression equation with independent and identical normal distribution. Derivation of AIC for multiple regression. AIC with unbiased estimator for error variance. Error variance by maximizing expectation of log-likelihood in light of the data in the future and the "third variance." Relationship between AIC (or GCV) and F-test. AIC on Poisson regression.- Chapter 6 Linear mixed model. Random-effects model. Random intercept model. Random intercept and slope model. Generalized linear mixed model. Generalized additive mixed model.