Preface |
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xv | |
Acknowledgments |
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xix | |
Author |
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xxi | |
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PART I Introduction to Probability, Statistics, Time Series, and Spatial Analysis |
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3 | (26) |
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1.1 Brief History of Statistical and Probabilistic Analysis |
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3 | (1) |
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4 | (1) |
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4 | (1) |
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4 | (2) |
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5 | (1) |
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5 | (1) |
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5 | (1) |
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1.4.4 Independent vs. Dependent Variables |
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6 | (1) |
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1.5 Probability Theory and Random Variables |
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6 | (1) |
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6 | (1) |
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1.7 Descriptive Statistics |
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7 | (1) |
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1.8 Inferential Statistics |
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7 | (1) |
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1.9 Predictors, Models, and Regression |
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7 | (1) |
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8 | (1) |
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1.11 Spatial Data Analysis |
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8 | (1) |
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1.12 Matrices and Multiple Dimensions |
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8 | (1) |
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1.13 Other Approaches: Process-Based Models |
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9 | (1) |
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1.14 Baby Steps: Calculations and Graphs |
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9 | (2) |
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1.14.1 Mean, Variance, and Standard Deviation of a Sample |
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9 | (1) |
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1.14.2 Simple Graphs as Text: Stem-and-Leaf Plots |
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10 | (1) |
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11 | (1) |
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11 | (1) |
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1.16 Computer Session: Introduction to R |
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11 | (18) |
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11 | (1) |
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11 | (1) |
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1.16.3 Personalize the R GUI Shortcut |
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11 | (2) |
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13 | (1) |
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13 | (2) |
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15 | (1) |
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15 | (1) |
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16 | (1) |
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1.16.9 Downloading Data Files |
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17 | (1) |
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1.16.10 Read a Simple Text Data File |
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17 | (2) |
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1.16.11 Simple Statistics |
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19 | (1) |
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1.16.12 Simple Graphs as Text: Stem-and-Leaf Plots |
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20 | (1) |
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1.16.13 Simple Graphs to a Graphics Window |
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20 | (1) |
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1.16.14 Addressing Entries of an Array |
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20 | (2) |
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1.16.15 Example: Salinity |
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22 | (1) |
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23 | (1) |
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1.16.17 Store Your Data Files and Objects |
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24 | (1) |
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1.16.18 Command History and Long Sequences of Commands |
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25 | (1) |
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1.16.19 Editing Data in Objects |
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25 | (1) |
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1.16.20 Cleanup and Close R Session |
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26 | (1) |
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1.16.21 Computer Exercises |
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26 | (1) |
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27 | (2) |
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Chapter 2 Probability Theory |
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29 | (30) |
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2.1 Events and Probabilities |
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29 | (1) |
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29 | (2) |
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31 | (1) |
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32 | (1) |
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2.5 Conditional Probability |
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33 | (1) |
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2.6 Testing Water Quality: False Negative and False Positive |
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34 | (1) |
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35 | (1) |
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2.8 Generalization of Bayes' Rule to Many Events |
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36 | (1) |
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36 | (1) |
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37 | (2) |
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39 | (1) |
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2.12 Computer Session: Introduction to Rcmdr, Programming, and Multiple Plots |
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40 | (19) |
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40 | (1) |
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2.12.2 Package Installation and Loading |
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40 | (3) |
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2.12.3 R GUI SDI Option: Best for R Commander |
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43 | (1) |
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2.12.4 How to Import a Text Data File Using Rcmdr |
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43 | (2) |
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2.12.5 Simple Graphs on a Text Window |
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45 | (1) |
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2.12.6 Simple Graphs on a Graphics Window: Histograms |
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46 | (1) |
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2.12.7 More than One Variable: Reading Files and Plot Variables |
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47 | (1) |
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2.12.7.1 Using the R Console |
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48 | (3) |
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2.12.7.2 Using the R Commander |
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51 | (2) |
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53 | (1) |
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2.12.9 Application: Bayes' Theorem |
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54 | (1) |
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2.12.10 Application: Decision Making |
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55 | (1) |
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2.12.11 More on Graphics Windows |
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55 | (1) |
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2.12.12 Editing Data in Objects |
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56 | (1) |
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2.12.13 Clean Up and Exit |
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56 | (1) |
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2.12.14 Additional GUIs to Use R |
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57 | (1) |
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2.12.15 Modifying the R Commander |
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57 | (1) |
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2.12.16 Other Packages to Be Used in the Book |
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57 | (1) |
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2.12.17 Computer Exercises |
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58 | (1) |
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58 | (1) |
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Chapter 3 Random Variables, Distributions, Moments, and Statistics |
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59 | (36) |
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59 | (1) |
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59 | (4) |
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3.2.1 Probability Mass and Density Functions (pmf and pdf) |
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59 | (3) |
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3.2.2 Cumulative Functions (cmf and cdf) |
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62 | (1) |
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62 | (1) |
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63 | (5) |
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3.3.1 First Moment or Mean |
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63 | (1) |
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3.3.2 Second Central Moment or Variance |
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64 | (2) |
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3.3.3 Population and Sample |
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66 | (1) |
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3.3.4 Other Statistics and Ways of Characterizing a Sample |
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67 | (1) |
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3.4 Some Important RV and Distributions |
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68 | (4) |
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3.5 Application Examples: Species Diversity |
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72 | (1) |
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3.6 Central Limit Theorem |
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72 | (1) |
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3.7 Random Number Generation |
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73 | (1) |
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74 | (1) |
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3.9 Computer Session: Probability and Descriptive Statistics |
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75 | (20) |
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3.9.1 Descriptive Statistics: Categorical Data, Table, and Pie Chart |
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75 | (3) |
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3.9.2 Using a Previously Generated Object or a Dataset |
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78 | (1) |
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3.9.3 Summary of Descriptive Statistics and Histogram |
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78 | (3) |
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3.9.4 Density Approximation |
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81 | (1) |
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3.9.5 Theoretical Distribution: Example Binomial Distribution |
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82 | (4) |
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3.9.6 Application Example: Species Diversity |
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86 | (1) |
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3.9.7 Random Number Generation |
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86 | (3) |
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3.9.8 Comparing Sample and Theoretical Distributions: Example Binomial |
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89 | (1) |
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3.9.9 Programming Application: Central Limit Theorem |
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90 | (2) |
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3.9.10 Sampling: Function Sample |
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92 | (1) |
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3.9.11 Cleanup and Close R Session |
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92 | (1) |
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3.9.12 Computer Exercises |
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93 | (1) |
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93 | (2) |
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Chapter 4 Exploratory Analysis and Introduction to Inferential Statistics |
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95 | (42) |
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4.1 Exploratory Data Analysis (EDA) |
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95 | (3) |
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95 | (1) |
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95 | (1) |
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4.1.3 Empirical Cumulative Distribution Function (ecdf) |
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96 | (2) |
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4.1.4 Quantile-Quantile (q - q) Plots |
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98 | (1) |
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4.1.5 Combining Plots for Exploratory Data Analysis (EDA) |
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98 | (1) |
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4.2 Relationships: Covariance and Correlation |
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98 | (4) |
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4.2.1 Serial Data: Time Series and Autocorrelation |
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101 | (1) |
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4.3 Statistical Inference |
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102 | (7) |
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103 | (2) |
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105 | (1) |
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105 | (2) |
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4.3.4 Confidence Intervals |
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107 | (2) |
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109 | (1) |
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110 | (2) |
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4.5.1 Z Test or Standard Normal |
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110 | (1) |
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110 | (1) |
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111 | (1) |
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112 | (1) |
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4.6 Nonparametric Methods |
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112 | (1) |
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4.6.1 Mann-Whitney or Wilcoxon Rank Sum Test |
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112 | (1) |
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4.6.2 Wilcoxon Signed Rank Test |
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112 | (1) |
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4.6.3 Spearman Correlation |
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112 | (1) |
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113 | (1) |
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4.8 Computer Session: Exploratory Analysis and Inferential Statistics |
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113 | (24) |
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4.8.1 Create an Example Dataset |
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113 | (1) |
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113 | (1) |
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114 | (1) |
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4.8.4 Empirical Cumulative Plot |
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114 | (1) |
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115 | (1) |
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4.8.6 Building a Function: Example |
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115 | (1) |
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4.8.7 More on the Standard Normal |
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116 | (2) |
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4.8.8 Quantile-Quantile (q-q) Plots |
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118 | (1) |
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4.8.9 Function to Plot Exploratory Data Analysis (EDA) Graphs |
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119 | (1) |
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4.8.10 Time Series and Autocorrelation Plots |
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120 | (1) |
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4.8.11 Additional Functions for the Rconsole and the R Commander |
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121 | (1) |
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4.8.12 Parametric: One Sample t-Test or Means Test |
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122 | (2) |
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4.8.13 Power Analysis: One Sample t-Test |
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124 | (2) |
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4.8.14 Parametric: Two-Sample t-Test |
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126 | (2) |
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4.8.15 Power Analysis: Two Sample t-Test |
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128 | (1) |
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4.8.16 Using Data Sets from Packages |
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129 | (1) |
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4.8.17 Nonparametric: Wilcoxon Test |
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130 | (2) |
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4.8.18 Bivariate Data and Correlation Test |
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132 | (3) |
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4.8.19 Computer Exercises |
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135 | (1) |
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136 | (1) |
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Chapter 5 More on Inferential Statistics: Goodness of Fit, Contingency Analysis, and Analysis of Variance |
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137 | (40) |
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5.1 Goodness of Fit (GOF) |
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137 | (4) |
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5.1.1 Qualitative: Exploratory Analysis |
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137 | (1) |
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5.1.2 x2 (Chi-Square) Test |
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137 | (3) |
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5.1.3 Kolmogorov-Smirnov (K-S) |
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140 | (1) |
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140 | (1) |
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5.2 Counts and Proportions |
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141 | (1) |
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5.3 Contingency Tables and Cross-Tabulation |
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141 | (3) |
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144 | (7) |
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145 | (3) |
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148 | (1) |
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5.4.3 Factor Interaction in ANOVA Two-Way |
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149 | (1) |
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5.4.4 Nonparametric Analysis of Variance |
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150 | (1) |
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151 | (2) |
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5.6 Computer Session: More on Inferential Statistics |
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153 | (24) |
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5.6.1 GOF: Exploratory Analysis |
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153 | (1) |
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5.6.2 GOF: Chi-Square Test |
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154 | (1) |
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5.6.3 GOF: Kolmogorov-Smirnov Test |
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155 | (1) |
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156 | (1) |
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5.6.5 Count Tests and the Binomial |
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156 | (1) |
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5.6.6 Obtaining a Single Element of a Test Result |
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157 | (1) |
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5.6.7 Comparing Proportions: prop.test |
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158 | (1) |
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5.6.8 Contingency Tables: Direct Input |
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159 | (1) |
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5.6.9 Contingency Tables: Cross-Tabulation |
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160 | (2) |
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162 | (4) |
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166 | (3) |
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5.6.12 ANOVA Nonparametric: Kruskal-Wallis |
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169 | (3) |
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5.6.13 ANOVA Nonparametric: Friedman |
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172 | (1) |
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5.6.14 ANOVA: Generating Fictional Data for Further Learning |
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172 | (3) |
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5.6.15 Computer Exercises |
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175 | (1) |
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176 | (1) |
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177 | (48) |
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6.1 Simple Linear Least Squares Regression |
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177 | (18) |
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6.1.1 Derivatives and Optimization |
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178 | (2) |
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6.1.2 Calculating Regression Coefficients |
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180 | (3) |
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6.1.3 Interpreting the Coefficients Using Sample Means, Variances and Covariance |
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183 | (1) |
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6.1.4 Regression Coefficients from Expected Values |
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184 | (1) |
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6.1.5 Interpretation of the Error Terms |
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185 | (3) |
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6.1.6 Evaluating Regression Models |
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188 | (4) |
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6.1.7 Regression through the Origin |
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192 | (3) |
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6.2 ANOVA as Predictive Tool |
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195 | (1) |
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196 | (4) |
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197 | (1) |
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6.3.2 Nonlinear Optimization |
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197 | (1) |
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6.3.3 Polynomial Regression |
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198 | (1) |
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6.3.4 Predicted vs. Observed Plots |
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198 | (2) |
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6.4 Computer Session: Simple Regression |
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200 | (25) |
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200 | (2) |
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6.4.2 Simple Linear Regression |
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202 | (4) |
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6.4.3 Nonintercept Model or Regression through the Origin |
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206 | (2) |
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6.4.4 ANOVA One Way: As Linear Model |
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208 | (3) |
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6.4.5 Linear Regression: Lack-of-Fit to Nonlinear Data |
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211 | (3) |
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6.4.6 Nonlinear Regression by Transformation |
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214 | (2) |
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6.4.7 Nonlinear Regression by Optimization |
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216 | (3) |
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6.4.8 Polynomial Regression |
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219 | (2) |
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6.4.9 Predicted vs. Observed Plots |
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221 | (1) |
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6.4.10 Computer Exercises |
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221 | (2) |
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223 | (2) |
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Chapter 7 Stochastic or Random Processes and Time Series |
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225 | (34) |
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7.1 Stochastic Processes and Time Series: Basics |
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225 | (1) |
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225 | (2) |
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7.3 Autocovariance and Autocorrelation |
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227 | (4) |
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7.4 Periodic Series, Filtering, and Spectral Analysis |
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231 | (7) |
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238 | (3) |
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7.6 Marked Poisson Process |
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241 | (6) |
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247 | (2) |
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249 | (1) |
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7.9 Computer Session: Random Processes and Time Series |
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250 | (9) |
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7.9.1 Gaussian Random Processes |
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250 | (2) |
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252 | (1) |
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252 | (1) |
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7.9.4 Filtering and Spectrum |
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253 | (1) |
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254 | (1) |
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255 | (1) |
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7.9.7 Poisson Process Simulation |
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255 | (1) |
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7.9.8 Marked Poisson Process Simulation: Rainfall |
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256 | (1) |
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257 | (1) |
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258 | (1) |
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Chapter 8 Spatial Point Patterns |
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259 | (50) |
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8.1 Types of Spatially Explicit Data |
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259 | (1) |
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8.2 Types of Spatial Point Patterns |
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259 | (1) |
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259 | (1) |
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8.4 Testing Spatial Patterns: Cell Count Methods |
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260 | (4) |
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8.4.1 Testing Uniform Patterns |
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260 | (1) |
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8.4.2 Testing for Spatial Randomness |
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261 | (2) |
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263 | (1) |
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8.5 Nearest-Neighbor Analysis |
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264 | (4) |
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8.5.1 First-Order Analysis |
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264 | (2) |
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8.5.2 Second-Order Analysis |
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266 | (2) |
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8.6 Marked Point Patterns |
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268 | (1) |
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8.7 Geostatistics: Regionalized Variables |
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269 | (1) |
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8.8 Variograms: Covariance and Semivariance |
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270 | (4) |
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271 | (1) |
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272 | (2) |
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274 | (2) |
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276 | (5) |
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276 | (2) |
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278 | (1) |
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278 | (1) |
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8.10.4 Linear and Power Models |
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279 | (1) |
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8.10.5 Modeling the Empirical Variogram |
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280 | (1) |
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281 | (3) |
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8.12 Computer Session: Spatial Analysis |
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284 | (25) |
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8.12.1 Packages and Functions |
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284 | (1) |
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284 | (1) |
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8.12.3 Creating a Pattern: Location-Only |
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285 | (1) |
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8.12.4 Generating Patterns with Random Numbers |
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286 | (2) |
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8.12.5 Grid or Quadrat Analysis: Chi-Square Test for Uniformity |
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288 | (1) |
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8.12.6 Grid or Quadrat Analysis: Randomness, Poisson Model |
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289 | (1) |
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8.12.7 Nearest-Neighbor Analysis: G and K Functions |
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290 | (3) |
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8.12.8 Monte Carlo: Nearest-Neighbor Analysis of Uniformity |
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293 | (1) |
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8.12.9 Marked Spatial Patterns: Categorical Marks |
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294 | (4) |
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8.12.10 Marked Spatial Patterns: Continuous Values |
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298 | (3) |
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8.12.11 Marked Patterns: Use Sample Data from sgeostat |
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301 | (4) |
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8.12.12 Computer Exercises |
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305 | (1) |
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306 | (3) |
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PART II Matrices, Tempral and Spatial Autoregressive Processes, and Multivariate Analysis |
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Chapter 9 Matrices and Linear Algebra |
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309 | (24) |
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309 | (1) |
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9.2 Dimension of a Matrix |
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309 | (1) |
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310 | (1) |
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310 | (2) |
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311 | (1) |
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9.4.2 Symmetric Matrices: Covariance Matrix |
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311 | (1) |
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312 | (1) |
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312 | (7) |
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9.5.1 Addition and Subtraction |
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312 | (1) |
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9.5.2 Scalar Multiplication |
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313 | (1) |
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313 | (1) |
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9.5.4 Matrix Multiplication |
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313 | (2) |
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9.5.5 Determinant of a Matrix |
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315 | (1) |
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9.5.6 Matrix Transposition |
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316 | (1) |
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316 | (1) |
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317 | (2) |
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9.6 Solving Systems of Linear Equations |
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319 | (2) |
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9.7 Linear Algebra Solution of the Regression Problem |
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321 | (2) |
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9.8 Alternative Matrix Approach to Linear Regression |
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323 | (2) |
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325 | (1) |
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9.10 Computer Session: Matrices and Linear Algebra |
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326 | (7) |
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326 | (1) |
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327 | (3) |
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330 | (1) |
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9.10.4 Solving System of Linear Equations |
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331 | (1) |
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331 | (1) |
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9.10.6 Computer Exercises |
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332 | (1) |
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332 | (1) |
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Chapter 10 Multivariate Models |
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333 | (36) |
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10.1 Multiple Linear Regression |
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333 | (9) |
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333 | (5) |
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10.1.2 Population Concepts and Expected Values |
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338 | (1) |
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10.1.3 Evaluation and Diagnostics |
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339 | (1) |
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10.1.4 Variable Selection |
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340 | (2) |
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10.2 Multivariate Regression |
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342 | (2) |
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10.3 Two-Group Discriminant Analysis |
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344 | (5) |
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10.4 Multiple Analysis of Variance (MANOVA) |
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349 | (4) |
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353 | (2) |
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10.6 Computer Session: Multivariate Models |
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355 | (14) |
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10.6.1 Multiple Linear Regression |
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355 | (4) |
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10.6.2 Multivariate Regression |
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359 | (2) |
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10.6.3 Two-Group Linear Discriminant Analysis |
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361 | (2) |
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363 | (2) |
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10.6.5 Computer Exercises |
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365 | (1) |
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365 | (2) |
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367 | (2) |
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Chapter 11 Dependent Stochastic Processes and Time Series |
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369 | (36) |
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369 | (9) |
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11.1.1 Dependent Models: Markov Chain |
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369 | (2) |
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11.1.2 Two-Step Rainfall Generation: First Step Markov Sequence |
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371 | (1) |
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11.1.3 Combining Dry/Wet Days with Amount on Wet Days |
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371 | (3) |
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374 | (4) |
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11.2 Semi-Markov Processes |
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378 | (3) |
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11.3 Autoregressive (AR) Process |
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381 | (6) |
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11.4 ARMA and ARIMA Models |
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387 | (2) |
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389 | (1) |
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11.6 Computer Session: Markov Processes and Autoregressive Time Series |
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389 | (16) |
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11.6.1 Weather Generation: Rainfall Models |
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389 | (2) |
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391 | (1) |
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11.6.3 AR(p) Modeling and Forecast |
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392 | (3) |
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11.6.4 ARIMA(p, d, q) Modeling and Forecast |
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395 | (3) |
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11.6.5 Computer Exercises |
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398 | (2) |
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400 | (3) |
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403 | (2) |
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Chapter 12 Geostatistics: Kriging |
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405 | (24) |
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405 | (1) |
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405 | (8) |
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413 | (1) |
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12.4 Data Transformations |
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414 | (1) |
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414 | (1) |
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12.6 Computer Session: Geostatistics, Kriging |
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415 | (14) |
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415 | (2) |
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417 | (5) |
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12.6.3 Regular Grid Data Files |
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422 | (3) |
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425 | (3) |
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12.6.5 Computer Exercises |
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428 | (1) |
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428 | (1) |
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Chapter 13 Spatial Auto-Correlation and Auto-Regression |
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429 | (26) |
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13.1 Lattice Data: Spatial Auto-Correlation and Auto-Regression |
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429 | (1) |
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13.2 Spatial Structure and Variance Inflation |
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429 | (1) |
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13.3 Neighborhood Structure |
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429 | (3) |
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13.4 Spatial Auto-Correlation |
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432 | (2) |
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432 | (1) |
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433 | (1) |
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434 | (1) |
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13.5 Spatial Auto-Regression |
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434 | (2) |
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436 | (1) |
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13.7 Computer Session: Spatial Correlation and Regression |
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437 | (18) |
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437 | (1) |
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438 | (2) |
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13.7.3 Neighborhood Structure |
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440 | (1) |
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13.7.4 Structure Using Distance |
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441 | (4) |
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13.7.5 Structure Based on Borders |
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445 | (1) |
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13.7.6 Spatial Auto-Correlation |
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446 | (2) |
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13.7.7 Spatial Auto-Regression Models |
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448 | (3) |
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13.7.8 Neighborhood Structure Using Tripack |
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451 | (1) |
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13.7.9 Neighborhood Structure for Grid Data |
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452 | (1) |
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13.7.10 Computer Exercises |
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453 | (1) |
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454 | (1) |
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Chapter 14 Multivariate Analysis I: Reducing Dimensionality |
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455 | (46) |
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14.1 Multivariate Analysis: Eigen-Decomposition |
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455 | (1) |
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14.2 Vectors and Linear Transformation |
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455 | (1) |
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14.3 Eigenvalues and Eigenvectors |
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455 | (4) |
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14.3.1 Finding Eigenvalues |
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457 | (1) |
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14.3.2 Finding Eigenvectors |
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458 | (1) |
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14.4 Eigen-Decomposition of a Covariance Matrix |
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459 | (6) |
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459 | (2) |
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461 | (4) |
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14.5 Principal Components Analysis (PCA) |
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465 | (4) |
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14.6 Singular Value Decomposition and Biplots |
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469 | (3) |
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472 | (3) |
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14.8 Correspondence Analysis |
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475 | (4) |
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479 | (1) |
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14.10 Computer Session: Multivariate Analysis, PCA |
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480 | (21) |
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14.10.1 Eigenvalues and Eigenvectors of Covariance Matrices |
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480 | (1) |
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14.10.2 PCA: A Simple 2x2 Example Using Eigenvalues and Eigenvectors |
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481 | (2) |
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14.10.3 PCA: A 2 × 2 Example |
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483 | (2) |
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14.10.4 PCA Higher-Dimensional Example |
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485 | (1) |
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14.10.5 PCA Using the Rcmdr |
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486 | (4) |
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490 | (3) |
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14.10.7 Factor Analysis Using Rcmdr |
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493 | (2) |
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14.10.8 Correspondence Analysis |
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495 | (4) |
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14.10.9 Computer Exercises |
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499 | (1) |
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500 | (1) |
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Chapter 15 Multivariate Analysis II: Identifying and Developing Relationships among Observations and Variables |
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501 | (20) |
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501 | (1) |
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15.2 Multigroup Discriminant Analysis (MDA) |
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501 | (1) |
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15.3 Canonical Correlation |
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502 | (3) |
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15.4 Constrained (or Canonical) Correspondence Analysis (CCA) |
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505 | (1) |
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506 | (2) |
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15.6 Multidimensional Scaling (MDS) |
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508 | (1) |
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509 | (1) |
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15.8 Computer Session: Multivariate Analysis II |
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509 | (12) |
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15.8.1 Multigroup Linear Discriminant Analysis |
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509 | (5) |
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15.8.2 Canonical Correlation |
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514 | (1) |
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15.8.3 Canonical Correspondence Analysis |
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515 | (1) |
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516 | (2) |
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15.8.5 Multidimensional Scaling (MDS) |
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518 | (2) |
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15.8.6 Computer Exercises |
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520 | (1) |
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520 | (1) |
Bibliography |
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521 | (4) |
Index |
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525 | |