Page 8 - Applied Statistics Using SPSS, STATISTICA, MATLAB and R

Contents ix

5.2.3 The Chi-Square Test of Independence ......................................195
5.2.4 Measures of Association Revisited............................................197
5.3 Inference on Two Populations ................................................................200
5.3.1 Tests for Two Independent Samples..........................................201
5.3.2 Tests for Two Paired Samples...................................................205
5.4 Inference on More Than Two Populations..............................................212
5.4.1 The Kruskal-Wallis Test for Independent Samples...................212
5.4.2 The Friedmann Test for Paired Samples ...................................215
5.4.3 The Cochran Q test....................................................................217
Exercises...............................................................................................................218

6 Statistical Classification 223

6.1 Decision Regions and Functions.............................................................223
6.2 Linear Discriminants...............................................................................225
6.2.1 Minimum Euclidian Distance Discriminant ..............................225
6.2.2 Minimum Mahalanobis Distance Discriminant.........................228
6.3 Bayesian Classification...........................................................................234
6.3.1 Bayes Rule for Minimum Risk..................................................234
6.3.2 Normal Bayesian Classification ................................................240
6.3.3 Dimensionality Ratio and Error Estimation...............................243
6.4 The ROC Curve ......................................................................................246
6.5 Feature Selection.....................................................................................253
6.6 Classifier Evaluation...............................................................................256
6.7 Tree Classifiers .......................................................................................259
Exercises...............................................................................................................268

7 Data Regression 271

7.1 Simple Linear Regression .......................................................................272
7.1.1 Simple Linear Regression Model ..............................................272
7.1.2 Estimating the Regression Function..........................................273
7.1.3 Inferences in Regression Analysis.............................................279
7.1.4 ANOVA Tests ...........................................................................285
7.2 Multiple Regression................................................................................289
7.2.1 General Linear Regression Model.............................................289
7.2.2 General Linear Regression in Matrix Terms .............................289
7.2.3 Multiple Correlation ..................................................................292
7.2.4 Inferences on Regression Parameters ........................................294
7.2.5 ANOVA and Extra Sums of Squares.........................................296
7.2.6 Polynomial Regression and Other Models ................................300
7.3 Building and Evaluating the Regression Model......................................303
7.3.1 Building the Model....................................................................303
7.3.2 Evaluating the Model ................................................................306
7.3.3 Case Study.................................................................................308
7.4 Regression Through the Origin...............................................................314