西南交通大学：《管理统计学》（双语版） 第17章 多元分析简介

第17章多元分析简介 Introduction to Multivariate Data analysis

Introduction to Multivariate Data Analysis 第17章 多元分析简介

本章概要 To define multivariate analysis To describe multiple regression analysis and multiple discriminant analysis To learn about factor analysis and cluster analySIs To gain an appreciation of perceptual mapping To develop an understanding of conjoint analySIs

本章概要 • To define multivariate analysis. • To describe multiple regression analysis and multiple discriminant analysis. • To learn about factor analysis and cluster analysis. • To gain an appreciation of perceptual mapping. • To develop an understanding of conjoint analysis

Multivariate analysis 多变量分析 The term multivariate analysis is used to analyze multiple measurements on each individual or object being studied

Multivariate Analysis 多变量分析 The term multivariate analysis is used to analyze multiple measurements on each individual or object being studied

Multivariate Techniques 多变量技术 Multiple regression analysis(多重回归分析) Multiple discriminant analysis(多重判别分析) Cluster analysis(聚类分析) Factor analysis(因子分析) - Perceptual mapping(感知图) Conjoint analysis(结合分析)

Multivariate Techniques 多变量技术 - Multiple regression analysis（多重回归分析） - Multiple discriminant analysis（多重判别分析） - Cluster analysis（聚类分析） - Factor analysis（因子分析） - Perceptual mapping（感知图） - Conjoint analysis（结合分析）

Multivariate software 多变量分析软件 The computational requirements for the various multivariate procedures discussed in this chapter are substantial. As a practical matter, running the various types of analyses presented requires a computer and appropriate software g

Multivariate Software 多变量分析软件 The computational requirements for the various multivariate procedures discussed in this chapter are substantial. As a practical matter, running the various types of analyses presented requires a computer and appropriate software

Multiple regression Analysis 多重回归分析 Multiple regression analysis defined Multiple regression analysis enables the researcher to predict the level of magnitude of a dependent variable based on the levels of more than one independent variable

Multiple Regression Analysis 多重回归分析 • Multiple Regression Analysis Defined – Multiple regression analysis enables the researcher to predict the level of magnitude of a dependent variable based on the levels of more than one independent variable

Multiple regression Analysis Basic equation(方程) Y=a+b1XI+ b2X2 +b3X3+.+ BnXn where dependent or criterion variable X estimated constant b I-n= coefficients associated with the predictor variables so that a change of one unit in X will cause a change of bl units in Y: the values for the coefficients are estimated from the regression analysis X I-n= predictor (independent) variables that influence the dependent variable

Multiple Regression Analysis • Basic Equation（方程） Y = a + b1X1 + b2X2 + b3X3 + …+ BnXn where Y = dependent or criterion variable X = estimated constant b 1-n = coefficients associated with the predictor variables so that a change of one unit in X will cause a change of b1 units in Y; the values for the coefficients are estimated from the regression analysis X 1-n = predictor (independent) variables that influence the dependent variable

Multiple regression analysis Measures(多量) Coefficient of Determination R-square This statistic can assume values from o to 1 and provides a measure of the percentage of the variation in the dependent variable that is explained by variation in the independent variables The b values Or regression coefficients, indicate the effect of the individual independent variables on the dependent variable

Multiple Regression Analysis • Measures（多量） – Coefficient of Determination R-square • This statistic can assume values from 0 to 1 and provides a measure of the percentage of the variation in the dependent variable that is explained by variation in the independent variables. • The b Values • Or regression coefficients, indicate the effect of the individual independent variables on the dependent variable

Multiple regression Analysis Measures(continued) Dummy variables(哑变量) In some situations, the anal yst needs to include nominally scaled independent variables such as gender, marital status, occupation, or race in a multiple regression analysis. Dummy variables can be created for this purpose Dichotomous nominally scaled independent variables can be transformed into dummy variables by coding one value(e.g. female) as 0 and the other (e.g. male)as 1

Multiple Regression Analysis • Measures (continued) – Dummy Variables（哑变量） • In some situations, the analyst needs to include nominally scaled independent variables such as gender, marital status, occupation, or race in a multiple regression analysis. Dummy variables can be created for this purpose. • Dichotomous nominally scaled independent variables can be transformed into dummy variables by coding one value (e.g. female) as 0 and the other (e.g. male) as 1

Multiple regression Analysis Potential Problems in Using and Interpreting Multiple regression analysis C ollineari iy(共线性) Occurs when the independent variables are correlated Collinearity leads to unstable regression coefficients Scaling of Coefficients(系数尺度 The magnitude of the regression coefficients associated with the various independent variables can be compared directly only if they are scaled in the same units of if the data have been standardized

Multiple Regression Analysis • Potential Problems in Using and Interpreting Multiple Regression Analysis – Collinearity（共线性） • Occurs when the independent variables are correlated. Collinearity leads to unstable regression coefficients. – Scaling of Coefficients（系数尺度） • The magnitude of the regression coefficients associated with the various independent variables can be compared directly only if they are scaled in the same units of if the data have been standardized