Applied Multivariate Data Analysis

An easy to read survey of data analysis, linear regression models and analysis of variance. The extensive development of the linear model includes the use of the linear model approach to analysis of variance provides a strong link to statistical software packages, and is complemented by a thorough overview of theory. It is assumed that the reader has the background equivalent to an introductory book in statistical inference. Can be read easily by those who have had brief exposure to calculus and linear algebra. Intended for first year graduate students in business, social and the biological sciences. Provides the student with the necessary statistics background for a course in research methodology. In addition, undergraduate statistics majors will find this text useful as a survey of linear models and their applications.

Inhalt

1 Introduction.- 1.1 Multivariate Data Analysis, Data Matrices and Measurement Scales.- 1.1.1 Data Matrices.- 1.1.2 Measurement Scales.- Quantitative Scales, Qualitative Scales, Measurement Scales and Analysis.- 1.2 The Setting.- 1.2.1 Data Collection and Statistical Inference.- Probability Samples and Random Samples, Exploratory and Confirmatory Analysis.- 1.2.2 An Outline of the Techniques to Be Studied.- Topics in Volume I.- 1.3 Review of Statistical Inference for Univariate Distributions.- 1.3.1 Populations, Samples and Sampling Distributions.- Probability Distribution and Density, Discrete Distribution, Expectation, Parameters, Sampling.- 1.3.2 Statistical Inference, Estimation and Hypothesis Testing.- Estimation, Confidence Intervals, Hypothesis Testing.- 1.3.3 Three Useful Sampling Distributions.- The?2Distribution, ThetDistribution, TheFDistribution.- 1.3.4 Some Inference Procedures for Normal Populations.- Inference for the Mean, Inference for the Variance.- 1.3.5 Inference Procedures for Non-Normal Populations.- Statistical Inference for a Population Proportion, Multinomial Distribution, Hypergeometric Distribtution, Poisson Distribution.- Exercises for Chapter 1.- Questions for Chapter 1.- 2 Univariate Data Analysis.- 2.1 Data Analysis for Univariate Samples.- 2.1.1 Stem and Leaf Plots.- Optimum Number of Intervals.- 2.1.2 Frequency Distributions.- Relative Frequency, Cumulative Frequency.- 2.1.3 Quantile Plots.- Quantile Plot for a Normal Distribution.- 2.2 Characteristics of Sample Distributions.- 2.2.1 Measures of Location.- Mean, Median and Mode, Geometric Mean, Average Rate of Change.- 2.2.2 Measures of Spread.- Variance, Standard Deviation, Median Absolute Deviation, Range, Interquartile Range, Box Plots.- 2.2.3 Measures of Skewness.- Coefficient of Skewness, A Symmetry Plot, Index of Skewness, Examples of Skewed Distributions, Sample Form of Index of Skewness.- 2.2.4 Measures of Kurtosis.- Measuring Kurtosis Using the Spread, An Index of Kurtosis, Some Examples of Distributions with Kurtosis, Sample Measures of Kurtosis.- 2.2.5 Impact of Shape on Inference forµand?.- 2.3 Outliers.- 2.3.1 Detection of Outliers.- Inference for Outliers, Tests for Outliers Using Order Statistics, Using Indices of Skewness and Kurtosis.- 2.3.2 Robust Estimation.- 2.4 Assessing Normality.- 2.4.1 K-S Test for Normality.- 2.4.2 Graphical Techniques.- The Q-Q Plot.- 2.4.3 Other Tests for Normality.- 2.5 Transformations.- 2.5.1 Removing Skewness.- Box-Cox ? Method, Approximating ?, An Alternative Approximation, Negative Observations.- 2.5.2 Removing Kurtosis.- A Modified Power Transformation.- 2.5.3 Transformations in the Presence of Other Variables.- Cited Literature for Chapter 2.- Exercises for Chapter 2.- Questions for Chapter 2.- 3 Bivariate Analysis for Qualitative Random Variables.- 3.1 Joint Distributions.- 3.1.1 Discrete Bivariate Distributions.- Moments for Joint Distributions, Linear Combinations, Conditional Distributions and Independence, Conditional Densities, Moments for Conditional Distributions.- 3.1.2 Continuous Bivariate Distributions and the Bivariate Normal.- The Bivariate Normal, Elliptical Contours for the Bivariate Normal Distribution, Some Geometry for Elliptical Contours, Mahalanobis Distance, Conditional Density and Regression Functions, Partitioning the Variance ?y2, Regression Function forX on Y, Regression Functions, Control Variables, Alternative Linear Relationships, Determining the True Parameters.- 3.2 Statistical Inference for Bivariate Random Variables.- 3.2.1 The Correlation Coefficient.- Pearson Correlation Coefficient, Inference when? = 0, Fisher Transformation for? ? 0, Other Measures of Correlation.- 3.2.2 Goodness of Fit and Outlier Detection for a Bivariate Normal.- Elliptical Contours, An Alternative Method, Robust Estimation of Covariance and Correlation.- 3.2.3 Comparison of Marginal Distributions.- Graphical Comparisons, Paired Comparisons.- 3.3 The Simple Linear Regression Model.- 3.3.1 The Theoretical Model and Estimation.- Theory, Assumptions, Least Squares Estimation, Residuals.- 3.3.2 Inference for the Regression Coefficients.- Confidence Intervals, Joint Inferences, Bonferroni Approximation.- 3.3.3 Goodness of Fit and Prediction.- Analysis of Variance, Prediction Intervals, Confidence Interval forE[Y], Confidence Interval for a ParticularY, Confidence Band for the Entire Regression Line, Using Prediction Intervals.- 3.3.4 Repeated Observations and a Test for Lack of Fit.- 3.3.5 An Alternative Geometric Interpretation.- 3.3.6 Scatterplots, Tansformations and Smoothing.- Scatterplots, Smoothing, Simple Moving Average, Weighted Moving Average, Using Medians, Other Plots, Transformations, Estimating a Power Transformation Using the Box-Cox Family.- 3.3.7 Influence, Outliers and Leverage.- Leverage, Residuals and Deleted Residuals, Press Statistic, Standardized Residuals, Studentized Residuals, Influence Diagnostics, Cook's D, The DF Family, Robust Linear Fit.- 3.3.8 Residual Plots, Assumption Violations and Some Remedies.- Residual Plots, Heteroscedasticity, Autocorrelation, First Order Autocorrelation, Cochrane-Orcutt Procedure, Higher Order Autoregressive Models.- 3.3.9 Measurement Error in the Regression Model.- Measurement Error, Measurement Error in Bivariate Analysis, Estimator for the Simple Linear Regression Model With Measurement Error, Grouping Method.- 3.4 Regression and Correlation in a Multivariate Setting.- 3.4.1 The Partial Correlation Coefficient.- Joint Distribution of Three Variables and Partial Correlation, Sample Partial Correlation, Inference for Partial Correlation, Some Relationships Among ?XZ, ?YZ, ?XY, Supressor Variables, Possible Range for ?XY Given ?XZ and ?YZ.- 3.4.2 Partial Correlation and Regression.- Partial Regression Coefficients, Sample Relationships, Multiple Correlation, Supressor Variables and Multiple Correlation, Geometric Explanation of Supressor Variable Effect, Partial Coefficient of Determination, Sample Inference and Variance Inflation.- 3.4.3 Missing Variable Plots.- 3.4.4 Empirical vs Structural Relationships and Omitted Variable Bias.- 3.4.5 Qualitative Lurking Variables.- Cited Literature for Chapter 3.- Exercises for Chapter 3.- Questions for Chapter 3.- 4 Multiple Linear Regression.- 4.1 The Multiple Linear Regression Model.- 4.1.1 The Model, Assumptions and Least Squares Estimation.- The Model and Assumptions, Least Squares Estimation, Properties of Least Squares Estimators, Sums of Squares, Coefficient of Multiple Determination, Coefficient of Multiple Correlation, Some Population Parameters.- 4.1.2 Statistical Inference in Multiple Linear Regression.- An Additional Assumption, Inferences for Regression Coefficients, Inferences for the Model, Inference for Reduced Models, Relation to t-Test, Inferences for ? other than 0, Inferences for Linear Functions, Prediction for New Observations, Prediction Using Statistical Software.- 4.1.3 A Second Regression Example - Air Pollution Data.- Estimated Full Model, Some Reduced Models, Inferences for Linear Functions.- 4.1.4 Standardized Variables, Standardized Regression Coeffici…