Learning Regression Analysis by Simulation

Kunio Takezawa is senior research scientist at the National Agricultural Research Center of Japan and an associate professor in the Graduate School of Life and Environmental Sciences at the University of Tsukuba. He received B.A. and M.A. degrees in applied physics from Nagoya University and a Ph.D. in agricultural science from the University of Tokyo. Dr.Takezawa has served as a researcher at the National Institute of Agro-Environmental Sciences and as a senior researcher at the Hokuriku Agricultural Experiment Station. He and H. Omori (Tokyo University) translated Jeffrey S. Simonoff’s Smoothing Methodsin Statistics (Springer, 1996), which was published as Heikatsuka to nonparametric kaiki heno syotai by Norintokei-kyokaiin 1999 as the first Japanese textbook on nonparametric regression. He was recognized with awards from the Japan Science and Technology Agency in 1997 and the Japanese Agricultural Systems Society in 2002. Dr. Takezawa holds several patents for his inventions.

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 χ2 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 mixedmodel. Generalized additive mixed model.