Decision Analytics

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Introduction 1 What's in the Book 1 Why Use Excel? 3 1 Components of Decision Analytics 5 Classifying According to Existing Categories 5 Using a Two-Step Approach 6 Multiple Regression and Decision Analytics 6 Access to a Reference Sample 8 Multivariate Analysis of Variance 9 Discriminant Function Analysis 10 Logistic Regression 12 Classifying According to Naturally Occurring Clusters 13 Principal Components Analysis 13 Cluster Analysis 14 Some Terminology Problems 16 The Design Sets the Terms 17 Causation Versus Prediction 18 Why the Terms Matter 18 2 Logistic Regression 21 The Rationale for Logistic Regression 22 The Scaling Problem 24 About Underlying Assumptions 25 Equal Spread 25 Equal Variances with Dichotomies 27 Equal Spread and the Range 28 The Distribution of the Residuals 29 Calculating the Residuals 30 The Residuals of a Dichotomy 30 Using Logistic Regression 31 Using Odds Rather Than Probabilities 32 Using Log Odds 33 Using Maximum Likelihood Instead of Least Squares 34 Maximizing the Log Likelihood 35 Setting Up the Data 35 Setting Up the Logistic Regression Equation 36 Getting the Odds 38 Getting the Probabilities 39 Calculating the Log Likelihood 40 Finding and Installing Solver 41 Running Solver 41 The Rationale for Log Likelihood 43 The Probability of a Correct Classification 44 Using the Log Likelihood 45 The Statistical Significance of the Log Likelihood 48 Setting Up the Reduced Model 50 Setting Up the Full Model 51 3 Univariate Analysis of Variance (ANOVA) 53 The Logic of ANOVA 54 Using Variance 54 Partitioning Variance 55 Expected Values of Variances (Within Groups) 56 Expected Values of Variances (Between Groups) 58 The F-Ratio 61 The Noncentral F Distribution 64 Single Factor ANOVA 66 Adopting an Error Rate 66 Computing the Statistics 67 Deriving the Standard Error of the Mean 70 Using the Data Analysis Add-In 72 Installing the Data Analysis Add-In 73 Using the ANOVA: Single Factor Tool 73 Understanding the ANOVA Output 75 Using the Descriptive Statistics 75 Using the Inferential Statistics 76 The Regression Approach 79 Using Effect Coding 80 The LINEST() Formula 82 The LINEST() Results 83 LINEST() Inferential Statistics 85 4 Multivariate Analysis of Variance (MANOVA) 89 The Rationale for MANOVA 89 Correlated Variables 90 Correlated Variables in ANOVA 91 Visualizing Multivariate ANOVA 92 Univariate ANOVA Results 93 Multivariate ANOVA Results 93 Means and Centroids 95 From ANOVA to MANOVA 96 Using SSCP Instead of SS 98 Getting the Among and the Within SSCP Matrices 102 Sums of Squares and SSCP Matrices 104 Getting to a Multivariate F-Ratio 105 Wilks' Lambda and the F-Ratio 107 Converting Wilks' Lambda to an F Value 108 Running a MANOVA in Excel 110 Laying Out the Data 110 Running the MANOVA Code 111 Descriptive Statistics 112 Equality of the Dispersion Matrices 113 The Univariate and Multivariate F-Tests 115 After the Multivariate Test 116 5 Discriminant Function Analysis: The Basics 119 Treating a Category as a Number 120 The Rationale for Discriminant Analysis 122 Multiple Regression and Discriminant Analysis 122 Adjusting Your Viewpoint 123 Discriminant Analysis and Multiple Regression 125 Regression, Discriminant Analysis, and Canonical Correlation 125 Coding and Multiple Regression 127 The Discriminant Function and the Regression Equation 129 From Discriminant Weights to Regression Coefficients 130 Eigenstructures from Regression and Discriminant Analysis 133 Structure Coefficients Can Mislead 136 Wrapping It Up 137 6 Discriminant Function Analysis: Further Issues 139 Using the Discriminant Workbook 139 Opening the Discriminant Workbook 140 Using the Discriminant Dialog Box 141 Why Run a Discriminant Analysis on Irises? 144 Evaluating the Original Measures 144 Discriminant Analysis and Investment 145 Benchmarking with R 147 Downloading R 147 Arranging the Data File 148 Running the Analysis 149 The Results of the Discrim Add-In 152 The Discriminant Results 153 Interpreting the Structure Coefficients 155 Eigenstructures and Coefficients 156 Other Uses for the Coefficients 159 Classifying the Cases 162 Distance from the Centroids 163 Correcting for the Means 164 Adjusting for the Variance-Covariance Matrix 167 Assigning a Classification 169 Creating the Classification Table 170 Training Samples: The Classification Is Known Beforehand 171 7 Principal Components Analysis 173 Establishing a Conceptual Framework for Principal Components Analysis 174 Principal Components and Tests 174 PCA's Ground Rules 175 Correlation and Oblique Factor Rotation 176 Using the Principal Components Add-In 177 The Correlation Matrix 179 The Inverse of the R Matrix 179 The Sphericity Test 182 Counting Eigenvalues, Calculating Coefficients and Understanding Communalities 183 How Many Components? 184 Factor Score Coefficients 186 Communalities 186 Relationships Between the Individual Results 187 Using the Eigenvalues and Eigenvectors 187 Eigenvalues, Eigenvectors, and Loadings 188 Eigenvalues, Eigenvectors, and Factor Coefficients 190 Getting the Eigenvalues Directly from the Factor Scores 191 Getting the Eigenvalues and Eigenvectors 192 Iteration and Exhaustion 193 Rotating Factors to a Meaningful Solution 196 Identifying the Factors 197 The Varimax Rotation 200 Classification Examples 202 State Crime Rates 202 Physical Measurements of Aphids 206 8 Cluster Analysis: The Basics 209 Cluster Analysis, Discriminant Analysis, and Logistic Regression 209 Euclidean Distance 211 Mahalanobis' D2 and Cluster Analysis 214 Finding Clusters: The Single Linkage Method 215 The Self-Selecting Nature of Cluster Analysis 220 Finding Clusters: The Complete Linkage Method 223 Complete Linkage: An Example 224 Other Linkage Methods 227 Finding Clusters: The K-means Method 228 Characteristics of K-means Analysis 228 A K-means Example 229 Benchmarking K-means with R 233 9 Cluster Analysis: Further Issues 235 Using the K-means Workbook 235 Deciding on the Number of Clusters 237 The Cluster Members Worksheet 239 The Cluster Centroids Worksheet 241 The Cluster Variances Worksheet 242 The F-Ratios Worksheet 244 Reporting Process Statistics 247 Cluster Analysis Using Principal Components 248 Principal Components Revisited 249 Clustering Wines 253 Cross-Validating the Results 256 Index 259

Conrad Carlberg has written eleven books about quantitative analysis with Excel, including Statistical Analysis: Microsoft (R) Excel 2010 and Predictive Analytics: Microsoft (R) Excel. His company, found at www.conradcarlberg.com, focuses on the quantitative analysis of data that companies routinely collect in their sales, employee, customer management and other operations database systems. Carlberg holds a Ph.D. in statistics from the University of Colorado and has 25 years' experience applying advanced analytical techniques. Conrad Carlberg lives near San Diego with his wife, not too far from the beach, but high enough that the rise in the sea level is unlikely to convert their home to waterfront property. Two cats round out the indoor menagerie; the three rabbits are required to stay outside.

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