SAS Certification Prep Guide: Statistical Business Analysis Using SAS9

Contents
About This Book
	What Does This Book Cover?
	Requirements and Details
		Exam Objectives
		Take a Practice Exam
		Registering for the Exam
	Syntax Conventions
	What Should You Know about the Examples?
		Software Used to Develop the Book's Content
		Example Code and Data
		SAS University Edition
	Where Are the Exercise Solutions?
	We Want to Hear from You
Chapter 1: Statistics and Making Sense of Our World
	Introduction
	What Is Statistics?
		The Two Branches of Statistics
	Variable Types and SAS Data Types
		Variable Types
			Table 1.1 Data for the Study of Diabetes
		SAS Data Types
	The Data Analytics Process
		Defining the Purpose
			Table 1.2  Examples of Analyses by Purpose for Various Industries
		Data Preparation
			Sampling
			Cleaning the Data
			Exploring the Data
		Analyzing the Data and Roadmap to the Book
			Table 1.3  Summary of Statistical Models for Business Analysis Certification by Variable Role
		Conclusions and Interpretation
	Getting Started with SAS
		Diabetic Care Management Case
		Ames Housing Case
			Table 1.4  List of Data Sets Used in the Book by Chapter
		Accessing the Data in the SAS Environment
			Program 1.1 PROC CONTENTS of the Diabetes Care Management Case Data Set
			SAS Log 1.1 PROC CONTENTS of the Diabetes Care Management Case Data Set
			Output 1.1 PROC CONTENTS of the Diabetes Care Management Case Data Set
	Key Terms
Chapter 2: Summarizing Your Data with Descriptive Statistics
	Introduction
	Measures of Center
		Mean
			Figure 2.1 Time to Process Online Orders (in Hours)
		Median
		Mode
			Table 2.1 Number of Deaths for Top Ten Causes – 2014 United States
	Measures of Variation
		Range
			Table 2.2 Time to Process Orders (in Hours) by Retailer
			Figure 2.2 Time to Process Orders (in Hours)
		Variance
			Table 2.3 Descriptive Statistics for Time to Process Orders
			Table 2.4 Calculations for Variance as Average Squared Deviations
		Standard Deviation
	Measures of Shape
		Skewness
			Figure 2.3  Examples of Symmetric and Asymmetric Distributions
			Table 2.5 Sum of Z3 Values for Calculating Skewness
		Kurtosis
			Figure 2.4  Examples of Kurtosis as Compared to the Normal Distribution
			Table 2.6 Sum of Z4 Values for Calculating Kurtosis
	Other Descriptive Measures
		Percentiles, the Five-Number-Summary, and the Interquartile Range (IQR)
			Percentiles
			The Five-Number-Summary and the Interquartile Range (IQR)
				Figure 2.5 Time to Process Online Orders (in Hours) for Retailer 2
		Outliers
	The MEANS Procedure
		Procedure Syntax for PROC MEANS
			Program 2.1 PROC MEANS of Process Time and Amount Spent for Retailer 1
			Output 2.1 PROC MEANS of Process Time and Amount Spent for Retailer 1
		Customizing Output with the VAR statement and Statistics Keywords
			Program 2.2 PROC MEANS with Additional Descriptive Statistics of Process Time for Retailer 1
			Output 2.2  PROC MEANS with Additional Descriptive Statistics of Process Time for Retailer 1
			Key Words for Generating Desired Statistics
				Table 2.7  Keywords for Requesting Statistics in the MEANS Procedure
		Comparing Groups Using the CLASS Statement or the BY Statement
			PROC MEANS Using the CLASS Statement
				Program 2.3 PROC MEANS of Process Time for Retailers 1 and 2 Using the CLASS Statement
				Output 2.3 PROC MEANS of Process Time for Retailers 1 and 2 Using the CLASS Statement
			PROC MEANS Using the BY Statement
				Program 2.4 PROC MEANS of Process Time for Retailers 1 and 2 Using the BY Statement
				Output 2.4 PROC MEANS of Process Time for Retailers 1 and 2 Using the BY Statement
				Program 2.5 Analysis of Process Time for Retailers 1 and 2 Using BY DESCENDING
				Output 2.5 Analysis of Process Time For Retailers 1 and 2 Using BY DESCENDING
		Multiple Classes and Customizing Output Using the WAYS and TYPES Statements
			Using Multiple Classes in the CLASS Statement
				Program 2.6 Three-Way Analysis of Ketones by Diabetes Status, Renal Disease, and Gender
				Output 2.6 Three-Way Analysis of Ketones by Diabetes Status, Renal Disease, and Gender
			The WAYS Statement for Multiple Classes
				Program 2.7 Two-Way Analysis of Ketones by Diabetes Status, Renal Disease, and Gender
				Output 2.7 Two-Way Analysis of Ketones by Diabetes Status, Renal Disease, and Gender
			The TYPES Statement for Multiple Classes
				Program 2.8 One- and Two-Way Analyses of Ketones by Diabetes Status, Renal Disease, and Gender
				Output 2.8 One- and Two-Way Analyses of Ketones by Diabetes Status, Renal Disease, and Gender
		Saving Your Results Using the OUTPUT Statement
			Program 2.9 Ketones for the Diabetic Care Management Case
			Output 2.9 Ketones for the Diabetic Care Management Case
			The CLASS Statement and the _TYPE_ and _FREQ_ Variables
				Program 2.10 Ketones by the Class Controlled_Diabetic
				Output 2.10 Ketones by the Class Controlled_Diabetic
				Program 2.11 Ketones by the Classes Controlled_Diabetic and Renal_Disease
				Output 2.11 Ketones by the Classes Controlled_Diabetic and Renal_Disease
				SAS Log 2.1 Ketone Analysis by Two Classes
				Program 2.12 Ketones by the Classes Controlled_Diabetic, Renal_Disease, and Gender
				Output 2.12 Ketones by the Classes Controlled_Diabetic, Renal_Disease, and Gender
				Table 2.8 TYPE Values and the Subgroups Produced by Three-Way Analyses
				SAS Log 2.2 Ketone Analysis by the Classes Controlled_Diabetic, Renal_Disease, and Gender
				Table 2.9 TYPE, WAYS, Subgroups, and Number of Observations for One-, Two-, and Three-Way Analyses
			The CLASS Statement and Filtering the Output Data Set
				Program 2.13 Ketone Analysis by Four Classes
				SAS Log 2.3 Ketone Analysis by Four Classes
				Output 2.13 Filter of Output File for Only One-Way Analyses (_TYPE_ = 1, 2, 4, 8)
			The NWAY Option and Comparisons to the WAYS and TYPES Statements
				Program 2.14 Three-Way Analysis of Ketones Using the NWAY Option
				Output 2.14 Three-Way Analysis of Ketones Using the NWAY Option
				Program 2.15 Alternative 1 for Three-Way Analysis of Ketones Using the NWAY Option
				Program 2.16 Three Class Variables Connected by the Asterisk (*) in the TYPES Statement
			The BY Statement and the _TYPE_ and _FREQ_ Variables
				Program 2.17 Ketones by Controlled_Diabetic
				Output 2.15 Ketones by Controlled_Diabetic
				Program 2.18 Ketones by Controlled_Diabetic for Two Classes
				Output 2.16 Ketones by Controlled_Diabetic for Two Classes
		Handling Missing Data with the MISSING Option
			Program 2.19 The MEANS Procedure of Glucose by AE_DURATION Including Missing Values
			Output 2.17a The MEANS Procedure of Glucose by AE_DURATION Including Missing Values
			Output 2.17b Glucose by AE_DURATION Including Missing Values
	Key Terms
	Chapter Quiz
Chapter 3: Data Visualization
	Introduction
	View and Interpret Categorical Data
		Frequency and Crosstabulation Tables Using the FREQ Procedure
			Procedure Syntax for PROC FREQ
				Figure 3.1 Diabetic Care Management Case Data
				Program 3.1 Frequency Tables of GENDER, AGE_RANGE, and CONTROLLED_DIABETIC
				Output 3.1 Frequency Tables of GENDER, AGE_RANGE, and CONTROLLED_DIABETIC
			PLOTS Options within the TABLES Statement
				Program 3.2 Frequency Table and Bar Chart of GENDER
				Output 3.2 Frequency Table and Bar Chart of GENDER
			Crosstabulations for Illustrating Associations between Two Categorical Variables
				Program 3.3 Crosstabulation of Gender by Diabetes Status
				Output 3.3a Crosstabulation of Gender by Diabetes Status
				Output 3.3b Crosstabulation of Gender by Diabetes Status: Frequency Pots of Gender by Diabetes Status
				Program 3.4 Cross Tabs and Frequency Plots of Diabetes Status and Renal Disease
				Output 3.4  Cross Tabs and Frequency Plots of Diabetes Status and Renal Disease
			MISSING Option within the TABLES Statement
				Program 3.5 Crosstabulation of Diabetes Status and Primary Medication with Missing Obs Excluded
				Output 3.5 Crosstabulation of Diabetes Status and Primary Medication with Missing Obs Excluded
				Program 3.6 Crosstabulation of Diabetes Status and Primary Medication with Missing Obs Included
				Output 3.6 Crosstabulation of Diabetes Status and Primary Medication with Missing Obs Included
	View and Interpret Numeric Data
		Histograms Using the UNIVARIATE Procedure
			Figure 3.2 Histogram for Numeric Data
			Procedure Syntax for PROC UNIVARIATE
				Program 3.7 Univariate Statistics on BMI for 200 Diabetic Patients
				Output 3.7 Univariate Statistics on BMI for 200 Diabetic Patients
				Table 3.1 Summary Data for the Variable BMI
				Program 3.8 Histogram of the Variable BMI
				Output 3.8 Histogram of the Variable BMI
			Q-Q Plots Using the UNIVARIATE Procedure
				Table 3.2 Expected Z-Scores for Number of Texts
				Figure 3.3 Q-Q Plot for Number of Texts
			Interpreting the Q-Q Plots
				Program  3.9 Q-Q Plot for the Variable BMI
				Output 3.9 Q-Q Plot for the Variable BMI
			Box-and-Whisker Plot Using the UNIVARIATE Procedure
				Calculating Quartiles for Five-Number Summary
				Figure 3.4 Box Plot for Number of Texts
				Interpreting the Box Plot
				Program 3.10 Distribution and Probability Plot for BMI
				Output 3.10 Distribution and Probability Plot for BMI
			UNIVARIATE Procedures Using the INSET Statement
				Program 3.11 Histogram with Descriptive Statistics of BMI
				Output 3.11  Histogram with Descriptive Statistics of BMI
			UNIVARIATE Procedures Using the CLASS Statement
				Program 3.12 Histogram of Pounds with Descriptive Statistics by Gender
				Output 3.12 Histogram of Pounds with Descriptive Statistics by Gender
	Visual Analyses Using the SGPLOT Procedure
		Procedure Syntax for PROC SGPLOT
		Exploring Bivariate Relationships with Basic Plots, Fits, and Confidence
			The SCATTER and REG Statements
				Program 3.13 Scatter Plot of Systolic and Diastolic Blood Pressure
				Output 3.13 Scatter Plot of Systolic and Diastolic Blood Pressure
				Program 3.14 Regression Line and Confidence Limits on Bivariate Scatter Plot
				Output 3.14 Regression Line and Confidence Limits on Bivariate Scatter Plot
				Program 3.15 Scatter Plot of Price by Quantity Sold
				Output 3.15 Scatter Plot of Price by Quantity Sold
				Program 3.16 Scatter Plot of Weight and Blood Pressure by Gender
				Output 3.16a Scatter Plot of Weight and Blood Pressure by Gender
				Output 3.16b Scatter Plot of Weight by Systolic Blood Pressure by Gender
		Exploring Other Relationships Using SGPLOT
			Program 3.17 Vertical Bar Charts for Diabetes Status
			Output 3.17  Vertical Bar Charts for Diabetes Status
			Program 3.18 Bar Chart of Diabetes Status by Renal Disease
			Output 3.18a Bar Chart of Diabetes Status by Renal Disease
			Output 3.18b Numbers with Renal Diseases by Diabetes Status
			Program 3.19 Bar Charts for Diastolic and Systolic BP by Diabetes Status
			Output 3.19 Bar Charts for Diastolic and Systolic BP by Diabetes Status
	Key Terms
	Chapter Quiz
Chapter 4: The Normal Distribution and Introduction to Inferential Statistics
	Introduction
	Continuous Random Variables
		Normal Random Variables
			Figure 4.1 Distributions of Adult Weights for Three Populations
		The Empirical Rule
			Figure 4.2 Visualization of the Empirical Rule
			Figure 4.3 Empirical Rule Applied to Height of Diabetic Males
			Program 4.1 Actual Percentage of Males Having Heights within 1, 2, and 3 Standard Deviations from the Mean
			Output 4.1 Actual Percentage of Males Having Heights within 1, 2, and 3 Standard Deviations from the Mean
		The Standard Normal Distribution
			Figure 4.4 Proportion of Z-values Less Than -1.15, P(Z < -1.15)
			Table 4.1 Excerpt from Standard Normal Cumulative Area  (for Z ≤ 0)
			Figure 4.5 Proportion of Z-values Less Than 1.15, P(Z < +1.15)
			Table 4.2 Excerpt from Standard Normal Cumulative Area (for Z ≥ 0)
			Figure 4.6 Proportion of Z-Values Greater Than 1.15, P(Z > +1.15)
			Figure 4.7 Proportion of Z-Values between -1.00 and +1.00, P(-1.00 < Z < +1.00)
			Figure 4.8 Proportion of Z-Values between -1.96 and +1.96, P(-1.96 < Z < +1.96)
		Applying the Standard Normal Distribution to Answer Probability Questions
			Figure 4.9 Proportion of Americans Exceeding Recommended Daily Sugar Consumption
			Figure 4.10 Proportion of College Students Spending More Than 14 Hours Using Digital Devices
	The Sampling Distribution of the Mean
		Characteristics of the Sampling Distribution of the Mean
			Figure 4.11 Distribution of Wait-Times at a Casual-Dining Restaurant
			Program 4.2 Description of the Sampling Distribution of Mean Wait-Times
			Output 4.2 Description of the Sampling Distribution of Mean Wait-Times
		The Central Limit Theorem
			Figure 4.12 Sampling Distribution of Average Wait-Times by Sample Size
		Application of the Sampling Distribution of the Mean
			Figure 4.13 Sample Distribution of the Mean Based upon a Sample Size of 50
			Figure 4.14 Probability That Z > +1.77
			Effects of Sample Size on the Sampling Distribution
				Figure 4.15 Sampling Distribution of the Mean for Two Sample Sizes
	Introduction to Hypothesis Testing
		Defining the Null and Alternative Hypotheses
			Figure 4.16 Rejection Region for a Two-Tailed Test
			Figure 4.17 Rejection Region for a Lower-Tailed Test
			Figure 4.18 Rejection Region for an Upper-Tailed Test
		Defining and Controlling Errors in Hypothesis Testing
	Hypothesis Testing for the Population Mean (σ Known)
		Two-Tailed Tests for the Population Mean (µ)
			Figure 4.19 Rejection Region for a Two-Tailed Test at α = 0.05
			Table 4.3 Finding Z-Value Associated with 0.025 Area in the Lower Tail
			Figure 4.20 Critical Values for a Two-Tailed Test at α = 0.05
		One-Tailed Tests for the Population Mean (µ)
			Figure 4.21 Critical Value for a One-Tailed Test at α = 0.05
			Figure 4.22 Test Statistic Compared to the Critical Value
			Table 4.4 Critical Values Based upon α-Level and One-Tailed versus Two-Tailed Tests
		Hypothesis Testing Using the P-Value Approach
			Figure 4.23 p-Value for a One-Tailed Test
		The P-Value for the Two-Tailed Hypothesis Test
			Figure 4.24  p-Value for a Two-Tailed Test
	Hypothesis Testing for the Population Mean (σ Unknown)
		One-Tailed Tests for the Population Mean (µ)
			Figure 4.25  The t-Distribution for Various Sample Sizes
			Table 4.5  Descriptive Statistics of BMI for 25 Female Diabetic Patients
			Table 4.6 Excerpt from the t-Table
			Figure 4.26 t-Test Statistic Compared to the Critical Value
			Procedure Syntax for PROC TTEST
				Program 4.3 t-Test of BMI for Female Diabetics
				Output 4.3  t-Test of BMI for Female Diabetics
		Confidence Intervals for Estimating the Population Mean
		Confidence Interval for the Population Mean (σ Known)
			Figure 4.27 Confidence Intervals as Related to the Sampling Distribution
			Effects of Level of Confidence and Sample Size on Confidence Intervals
		Confidence Interval for the Population Mean (σ Unknown)
	Key Terms
	Chapter Quiz
Chapter 5: Analysis of Categorical Variables
	Introduction
	Testing the Independence of Two Categorical Variables
		Hypothesis Testing and the Chi-Square Test
			Table 5.1 Expected Frequency Count of Online Shopping by Gender
			Table 5.2 Observed and Expected Frequencies Count of Online Shopping by Gender
			Figure 5.1 Bivariate Bar Charts of Gender and Online Shopping
		The Chi-Square Test Using the FREQ Procedure
			Procedure Syntax for PROC FREQ
				Program 5.1 Testing Association between Bonus and Kitchen Quality
				Output 5.1a Testing Association between Bonus and Kitchen Quality
				Output 5.1b Testing Association between Bonus and Kitchen Quality: Bivariate Bar Charts of Bonus and Kitchen Quality
			Assumptions
	Measuring the Strength of Association between Two Categorical Variables
		Cramer’s V
		The Odds Ratio
			Table 5.3 General Form of the 2x2 Contingency Table
		Using Chi-Square Tests for Exploration Prior to Predictive Analytics
			Program 5.2 Testing Association between Bonus and Corner Lot
			Output 5.2a Testing Association between Bonus and Corner Lot
			Output 5.2b Testing Association between Bonus and Corner Lot: Bivariate Bar Charts of Bonus and Corner Lot
	Key Terms
	Chapter Quiz
Chapter 6: Two-Sample t-Test
	Introduction
	Independent Samples
		The Pooled Variance t-Test
		Assumptions
		Procedure Syntax of PROC TTEST Procedure
			Program 6.1 Independent Samples t-Test for Mean Differences in Above Ground Living Area
			Output 6.1a  Independent Samples t-Test for Ames Housing, Above Ground Living Area by Bonus
			Testing the Equal Variance Assumption Using the Folded F-Test
		Verifying the Assumptions of a Two-Sample t-Test
			Output 6.1b Normal Probability Plots for Above Ground Living Area by Bonus
			Supplemental Plots for Data Visualization
				Output 6.1c Histograms and Box Plots for Above Ground Living Area by Bonus
			Testing the Normality Assumption Using the Kolmogorov-Smirnov Test
				Program 6.2 Kolmogorov-Smirnov Test of Normality for Above Ground Living Area by Bonus
				Output 6.2 Kolmogorov-Smirnov Test of Normality for Above Ground Living Area by Bonus
		Satterthwaite t-Test for Unequal Variances
			Program 6.3 Independent Samples t-Test for Mean Differences in Total Basement Area
			Output 6.3 Independent Sample t-Test for Ames Housing, Total Basement Area by Bonus
			Summary of Steps for the t-Test of Two Independent Populations
	Paired Samples
		Assumptions
		The Paired-Sample t-Test Using the PAIRED Statement in the TTEST Procedure
			Table 6.1 Whitley County, Indiana, 2012 and 2016 Tax Assessed Property Values Sample Data
			Program 6.4 Kolmogorov-Smirnov Test of Normality Assumption on the Difference Score Using the UNIVARIATE Procedure
			Output 6.4a Kolmogorov-Smirnov Test of Normality Assumption on the Difference Score Using the UNIVARIATE Procedure
			Output 6.4b Paired t-Test Results for Differences in Tax Assessed Property Values
			Output 6.4c Accompanying Plots for the Paired-Sample t-Test
	Key Terms
	Chapter Quiz
Chapter 7: Analysis of Variance (ANOVA)
	Introduction
	One-Factor Analysis of Variance
		The One-Factor ANOVA Model
		Constructing the Test Statistic: Estimating Variance among Groups and Variance within Groups
			Table 7.1 Deviations within and across Groups
			Table 7.2 Squared Deviations within and across Groups
			Figure 7.1 The F-Distribution
			Table 7.3 General Form of the Analysis of Variance Table
		The GLM Procedure for Investigating Mean Differences
			Program 7.1 Descriptive Statistics for Computer Anxiety by Academic Major
			Output 7.1 Exploration of Computer Anxiety by Academic Major
			Program 7.2 One-Way ANOVA for Testing Differences in Computer Anxiety
			Output 7.2 One-Way ANOVA for Testing Differences in Computer Anxiety
		Predicted Values and Residuals Using the OUTPUT Statement
			Program 7.3 Predicted Values and Residuals for Computer Anxiety Scores
			Output 7.3 Predicted Values and Residuals for Computer Anxiety Scores
		Measures of Fit
		The Normality Assumption and the PLOTS Option
			Output 7.4 Fit Diagnostics for the One-Way Analysis of Variance
		Levene’s Test for Equal Variances and the MEANS Statement
			Program 7.4 The MEANS Statement for Additional Tests of Computer Anxiety Scores
			Output 7.5 Levene’s Homogeneity of Variance Test for Computer Anxiety Scores
		Post Hoc Tests:  The Tukey-Kramer Procedure and the MEANS Statement
			Output 7.6 Tukey-Kramer for Testing Pairwise Differences in Computer Anxiety
		Other Post Hoc Procedures, the LSMEANS Statement, and the Diffogram
			Output 7.7 LSMEANS Statement for Testing Pairwise Differences in Computer Anxiety
			Output 7.8 Dunnett Adjustment for Testing Pairwise Differences in Computer Anxiety
			Program 7.5 Complete Analysis of Difference in Computer Anxiety Scores Across Academic Majors
	The Randomized Block Design
		The ANOVA Model for the Randomized Block Design
		Example and Interpretation of the Randomized Block Design
			Program 7.6  Exploration of Computer Anxiety by Academic Major and Block
			Output 7.9 Exploration of Computer Anxiety by Academic Major and Block
			Table 7.4 The ANOVA Table for the Randomized Block Design
			Program 7.7 Randomized Block Design for Testing Differences in Computer Anxiety
			Output 7.10 Randomized Block Design for Testing Differences in Computer Anxiety
		Post Hoc Tests Using the LSMEANS Statement
			Output 7.11 LSMEANS Statement for Testing Pairwise Differences in Computer Anxiety When Blocking
		Assessing the Assumptions of a Randomized Block Design Using the PLOTS Option
		Unbalanced Designs, the LSMEANS Statement, and Type III Sums of Squares
			Table 7.5 Cell Means and Sample Sizes for Computer Anxiety Scores
	Two-Factor Analysis of Variance
		The Two-Factor ANOVA Model
			Table 7.6 General Form of the Two-Factor ANOVA Table
		Example and Interpretation of the Two-Factor ANOVA
			Program 7.8 Exploration of Computer Anxiety by Academic Major and Gender
			Output 7.12  Descriptive Statistics for Computer Anxiety by Academic Major and Gender
			Figure 7.2 Mean Computer Anxiety Scores by Academic Major and Gender
			Program 7.9 Two-Factor ANOVA for Testing Differences in Computer Anxiety
			Output 7.13a Two-Factor ANOVA for Testing Differences in Computer Anxiety
			Output 7.13b Least Squares Means for Major by Gender Interaction Effects
			Output 7.13c  Diffogram of MAJOR by GENDER Means
		Analyzing Simple Effects When Interaction Exists Using the LSMEANS Statement with the SLICE Option
			Output 7.13d  Analysis of Simple Effects in the Presence of Interaction
		Assessing the Assumptions of a Two-Factor Analysis of Variance
	Key Terms
	Chapter Quiz
Chapter 8: Preparing the Input Variables for Prediction
	Introduction
	Missing Values
		Complete-Case Analysis
		Using Imputation with a Missing Value Indicator
			Program 8.1 Ames Housing Data with Missing Values
			Output 8.1 Ames Housing Data with Missing Values
			Program 8.2 Ames Housing with Imputed Data
			Output 8.2  Ames Housing with Imputed Data
	Categorical Input Variables
		Sparse Events and Quasi-Complete Separation
		Greenacre’s Method Using the CLUSTER Procedure
			Table 8.1  Contingency Table of Bonus by Neighborhood
			Program 8.3 Combining Neighborhoods from Ames Data Housing Using Greenacre’s Method
			Output 8.3a Chi-square for Bonus by Neighborhood
			Output 8.3b  Proportion of Houses with Bonus by Neighborhood
			Output 8.3c  Results of Cluster Analysis on Ames Neighborhoods
			Output 8.3d  Dendrogram of Cluster Analysis Results by Neighborhoods
			Output 8.3e  Contents of the Cluster History
			Output 8.3f  Log P-Value Information and the Cluster History
			Output 8.3g  Plot of Log P-Value by Number of Clusters
			Output 8.3h  List of Neighborhoods by Cluster
			Table 8.2  Contingency Table of Bonus by Clustered Neighborhoods
	Variable Clustering
		The VARCLUS Procedure for Variable Reduction
			Table 8.3  Correlation Matrix for Variables Q1 through Q6
			Procedure Syntax for PROC VARCLUS
				Program 8.4 The VARCLUS Procedure for Reducing Ames Housing Inputs
				Output 8.4a Summary Information for VARCLUS Procedure for Ames Housing Input Data
				Output 8.4b Cluster Summary for 2 Clusters for Ames Housing Input Data
				Output 8.4c Cluster Summary for 23 Clusters for Ames Housing Input Data
				Output 8.4d  R-Squared with Own Cluster and Next Closest Cluster for Ames Housing Input Data
				Output 8.4e Summary of Cluster Splitting by Stage
				Output  8.4f Dendrogram Illustration of Cluster Splits for Ames Housing Input Data
		Cluster Representative and Best Variable Selection
			Table 8.4 Reduced Set of Inputs After Deleting Redundant Variables for Ames Housing
	Variable Screening
		The CORR Procedure for Detecting Associations
			Program 8.5 Description of Input Variables Screened for Relevance for Ames Housing Data
			Output 8.5a Summary of Input Variables Screened for Relevance for Ames Housing Data
			Output 8.5b ODS Output of Spearman Data
			Output 8.5c Spearman’s and Hoeffding’s D Correlation Data Sorted by Spearman’s Rank
			Output 8.5d Rank of Spearman’s Correlation by Rank of Hoeffding’s D
		Using the Empirical Logit to Detect Non-Linear Associations
			Program 8.6 Plot of Empirical Logit by Bsmt_Unf_SF
			Output 8.6a Value of Bsmt_Unf_SF and Bin Variables for the First Eight Houses in Ames Housing
			Output 8.6b Total Frequency, Number of Houses Earning a Bonus, and Average Bsmt_Unf_SF  by Bin
			Output 8.6c Empirical Logit by the Variable Bsmt_Unf_SF
	Key Terms
	Chapter Quiz
Chapter 9: Linear Regression Analysis
	Introduction
	Exploring the Relationship between Two Continuous Variables
		Exploring the Relationship between Two Continuous Variables Using a Scatter Plot
			Program 9.1 Scatter Plot of Sale Price by Above Ground Living Area
			Output 9.1 Scatter Plot of Sale Price and Above Ground Living Area
			Program 9.2 Scatter Plot of Sale Price and Age at Time of Sale
			Output 9.2 Scatter Plot of Sale Price and Age at Time of Sale
			Program 9.3 Scatter Plot of Sale Price and Square Footage
			Output 9.3 Scatter Plot of Sale Price and Square Footage
		Quantifying the Degree of Association between Two Continuous Variables Using Correlation Statistics
			Figure 9.1 Scatter Plot of Perfect Positive, Perfect Negative, and No Relationship
		Producing Correlation Coefficients Using the CORR Procedure
			Program 9.4 Correlation Coefficient and Descriptive Statistics for Ames Housing
			Output 9.4 Correlation Coefficients and Descriptive Statistics for Ames Housing
			Program 9.5 Correlation Coefficients with Sale Price for Ames Housing
			Output 9.5a Correlation Coefficients with Sale Price for Ames Housing
			Output 9.5b Scatter Plots for Sale Price with Potential Predictors
		Testing the Hypothesis for a Bivariate Linear Relationship Using the CORR Procedure
		Understanding Potential Misuses of the Correlation Coefficient
	Simple Linear Regression
		Fitting a Simple Linear Regression Model Using the REG Procedure
			Figure 9.2 Fitting the Line Closest to All Points
			Program 9.6 Linear Regression for Predicting Sale Price with Ground Living Area
			Output 9.6 Linear Regression Output for Predicting Saleprice with Ground Living Area
		Measures of Fit for the Linear Regression Model
			The Coefficient of Determination (R2)
			The Standard Error of the Regression (Se)
			Using Measures of Fit to Compare Models
				Table 9.1 Measures of Fit for Simple Linear Regression
		Hypothesis Testing for the Slope
			The t-Test for Slope
			The F-Test for Slope
				Table 9.2 Analysis of Variance (ANOVA) Table for Linear Regression
		Producing Confidence Intervals
			Program 9.7 Confidence Interval for Effect of Gr_Liv_Area on Sale Price
			Output 9.7  Confidence Interval for Effect of Gr_Liv_Area on SalePrice
	Multiple Linear Regression
		Fitting a Multiple Linear Regression Model Using the REG Procedure
			Program 9.8 Multiple Linear Regression for Predicting Sale Price with Six Predictors
			Output 9.8 Multiple Linear Regression for Predicting SalePrice with Six Predictors
		Measures of Fit for the Multiple Linear Regression Model
			Adjusted R-Square
				Output 9.9 Multiple Linear Regression for Predicting SalePrice with Five Predictors
				Table 9.3 Measures of Fit for Multiple Linear Regression
		Quantifying the Relative Impact of a Predictor
			Program 9.9 Measures of Relative Predictor Importance in Multiple Linear Regression
			Output 9.10  Measure of Relative Predictor Impact in Multiple Linear Regression
		Checking for Collinearity Using VIF, COLLIN, and COLLINOINT
			The Variance Inflation Factor (VIF) for Detecting Collinearity
			The Condition Index (C) for Detecting Collinearity
				Program 9.10 VIF and Condition Numbers for Detecting Collinearity
				Output 9.11 VIF and Condition Numbers for Detecting Collinearity
		Fitting a Simple Linear Regression Model Using the GLM Procedure
			Program 9.11 PROC GLM for Prediction Using One Categorical Variable
			Output 9.12a PROC GLM for Prediction Using One Categorical Variable
			Output 9.12b Tukey Procedure for Detecting Differences in Mean Sale Price
			Program 9.12 PROC REG for Prediction Using One Categorical Variable
			Output 9.13 PROC REG for Prediction Using One Categorical Variable
	Variable Selection Using the REG and GLMSELECT Procedures
		The REG Procedure for Variable Selection
			All Possible Subsets
				Program 9.13 Best Subsets Regression Models Ranked by Adjusted R-Square
				Output 9.14 Best Subsets Regression Models Ranked by Adjusted R-Square
				Program 9.14 Best Subsets Regression Models Ranked by Mallows’ Cp
				Output 9.15a Mallows’ Cp Plot for Variable Selection
				Output 9.15b Best Subsets Regression Models Ranked by Mallows’ Cp
			Backward Elimination
				Program 9.15 Backward Elimination for the Ames Housing Case
				Output 9.16a Backward Elimination Step 0
				Output 9.16b Backward Elimination Step 1
				Output 9.16c Backward Elimination Step 2
				Output 9.16d Backward Elimination Step 7
				Output 9.16e Summary of Backward Elimination
				Output 9.16f Plot of Adjusted R-Square by Backward Elimination Step
			Forward Selection
				Program 9.16 Forward Selection for the Ames Housing Case
				Output 9.17a Forward Selection Step 1
				Output 9.17b Forward Selection Step 2
				Output 9.17c Forward Selection Step 7
				Output 9.17d Summary of Forward Selection
				Output 9.17e Plot of Adjusted R-Square by Forward Selection Step
			Stepwise Selection
				Program 9.17 Stepwise Selection for the Ames Housing Case
				Program 9.18 Three Variable Selection Methods for the Ames Housing Case
		The GLMSELECT Procedure for Variable Selection
			Program 9.19 PROC GLMSELECT with Stepwise Selection for the Ames Housing Case
			Output 9.18a PROC GLMSELECT for Stepwise Selection Step 1
			Output 9.18b PROC GLMSELECT for Stepwise Selection Step 2
			Output 9.18c Summary for Stepwise Selection in PROC GLMSELECT
			Output 9.18d The Selected Model from Stepwise Selection in PROC GLMSELECT
			Other Features of the GLMSELECT Procedure
				Table 9.4 Default SLENTRY and SLSTAY Settings by Model Selection Method.
			Cautionary Note on Sequential Selection Methods
	Assessing the Validity of Results Using Regression Diagnostics
		The Assumptions of Linear Regression
		Residual Analysis for Checking Assumptions
			Figure 9.3 Fit Plot and Residual Plot for Illustrating a Linear Trend with Constant Variance
			Figure 9.4 Residual Plot Illustrating a Curvilinear Trend
			Figure 9.5 Residual Plot Illustrating Unequal Variance
			Figure 9.6 Residual Plot Illustrating Autocorrelation
			Program 9.20 Linear Regression Analysis Diagnostics Panel
			Output 9.19a Linear Regression on Revenue with Diagnostics Panel
			Output 9.19b Predicted Revenue and Residuals Using the Predictor AdExpense
			Program 9.21 Linear Regression Analysis Using Transformed Ad Expense (LnAdExp)
			Output 9.20 Linear Regression on Revenue Using Transformed Ad Expense (LnAdExp)
			Program 9.22 Diagnostics for Multiple Linear Regression
			Output 9.21a Multiple Linear Regression for Predicting SalePrice
			Output 9.21b Residual by Predicted Plot and Q-Q Plot of Residuals for SalePrice
			Output 9.21c Panel of Residual by Regressors for SalePrice
			Studentized Residuals
				Program 9.23 Residuals and Studentized Residuals by AdExpense for Saleprice
				Output 9.22a Residual and Studentized Residuals by AdExpense for SalePrice
				Output 9.22b Residuals and Studentized Residuals by AdExpense for Saleprice
		Using Statistics to Identify Potential Influential Observations
			Program 9.24 Comparing Regression Lines Based on Influence of Obs 15
			Output 9.23 Comparing Regression Lines Based on Influence of Obs 15
			Leverage (hii)
			Discrepancy (RSTUDENTi)
			Influence
				Program 9.25 Identifying Suspicious Observations Using Measures of Influence
				Output 9.24a Linear Regression Output for SalePrice with Influential Observation
				Output 9.24b Leverage by RStudent Plot
				Output 9.24c Cook’s D and DFFITS Plots for Detecting Influence
				Output 9.24d Deletion Statistics for Detecting Influence
				Output 9.25 Influence Statistics Using the INFLUENCE Option
				Program 9.26 DFBETA Plots for Assessing Local Influence
				Output 9.26 DFBETA Plots for Assessing Local Influence
				Program 9.27 Regression Diagnostics for the Ames Housing Case
				Output 9.27a Influence Panels and Influential Observations for Ames Housing
				Output 9.27b Observations Flagged as Influential for Ames Housing
			Recommendations for Handling Influential Observations
	Concluding Remarks
	Key Terms
	Chapter Quiz
Chapter 10: Logistic Regression Analysis
	Introduction
	The Logistic Regression Model
		Development of the Logistic Regression Model
			Figure 10.1 Scatter Plot of Gr_Liv_Area by Bonus
			Program 10.1 Scatter Plot of Binned Living Area by Proportion of Successes
			Output 10.1 Scatter Plot of Binned Living Area by Proportion of Successes
			The Logit Transformation
			Estimating the Logistic Regression Parameters
		Syntax for the Logistic Regression Procedure
			Program 10.2 Simple Logistic Regression
			Output 10.2a Model Information and Response Profile for Simple Logistic Regression
			Output 10.2b Model Convergence, Fit Statistics, and Testing Global Null
			Output 10.2c Analysis of Maximum Likelihood Estimates
			Estimating the Odds Ratio from the Parameter Estimates
				Output 10.2d Odds Ratio Estimate for Gr_Liv_Area Based upon Default UNITS=1
				Output 10.3 Odds Ratio Estimate for Gr_Liv_Area Based upon UNITS=100
			Additional Measures of Fit
				Output 10.2e  Association of Predicted Probabilities and Observed Responses
			Assumptions of Logistic Regression
		Plots for Probabilities of an Event and for the Odds Ratios
			Figure 10.2  Plot of Gr_Living Area by Probability for Bonus=1
			Program 10.3 Odds Ratio with 95% Confidence Interval for Gr_Liv_Area (UNITS=100)
			Output 10.4 Plot of Odds Ratio with 95% Confidence Interval for Gr_Liv_Area (UNIT=1)
			Program 10.4 Odds Ratio with 95% Confidence Interval for Gr_Liv_Area (UNITS=100)
			Output 10.5 Plot of Odds Ratio with 95% Confidence Interval for Gr_Liv_Area (UNITS=100)
			Program 10.5 UNITS Statement and ODDSRATIO Statement
	Logistic Regression with a Categorical Predictor
		Effect Coding Parameterization
			Program 10.6 Logistic Regression for One Categorical Predictor Using Effect Coding
			Output 10.6 Logistic Regression for One Categorical Predictor Using Effect Coding
		Reference Cell Coding Parameterization
			Program 10.7 Logistic Regression for One Categorical Predictor Using Reference Coding
			Output 10.7 Logistic Regression for One Categorical Predictor Using Reference Coding
			Program 10.8 CLASS Statement with Dummy Coded Variable
	The Multiple Logistic Regression Model
		Multiple Logistic Regression by Example
			Program 10.9 Multiple Logistic Regression for Ames Housing Using Reference Coding
			Output 10.8a Class Level Information Using Reference Coding
			Output 10.8b Fit Statistics and Global Null Test for Multiple Logistic Regression
			Output 10.8c Test 3 Analysis of Effects for Multiple Logistic Regression
			Output 10.8d Maximum Likelihood Estimates and Odds Ratios for Multiple Logistic Regression
		Variable Selection
			Backward Elimination
				Program 10.10 Backward Elimination for Ames Housing
				Output 10.9a   Effects Eligible for Removal for Step 1 of Backward Elimination
				Output 10.9b  Effects Eligible for Removal for Step 2 of Backward Elimination
				Output 10.9c  Effects Eligible for Removal for Steps 3 through 5 of Backward Elimination
				Output 10.9d Summary of Effects Removed in Backward Elimination
			Forward Selection
				Program 10.11 Forward Selection for Ames Housing
				Output 10.10a Effects Eligible for Entry for Step 1 of Forward Selection
				Output 10.10b  Summary of Effects Entered in Forward Selection
			Stepwise Selection
				Program 10.12 Stepwise Selection for Ames Housing
				Output 10.11a  Effects Eligible for Entry for Step 1 of Stepwise Selection
				Output 10.11b  Effects Eligible for Removal After Step 1 of Stepwise Selection
				Output 10.11c  Effects Eligible for Entry for Step 2 of Stepwise Selection
				Output 10.11d  Summary of Effects Entered or Removed in Stepwise Selection
				Table 10.1 Summary of Effects Entered or Removed in Stepwise Selection
			Customized Options within the Sequential Methods
				Output 10.12 Summary of Effects Removed in Backward Elimination Using the STOP= Option
				Output 10.13 Summary of Effects Entered in Forward Selection Using START= Option
			Best Subset Selection
				Program 10.13 Score Chi-Square Statistics for the Best Subsets of Size 1 through 8
				Output 10.14 Score Chi-Square Statistics for the Best Subsets of Size 1 through 8
		Modeling Interaction
			Figure 10.3 Mean Plots by Degree and Occupational Area
			Program 10.14 Testing Main Effects and Interactions for Ames Housing
			Output 10.15 Testing Main Effects and Interactions for Ames Housing
			Output 10.16 Example of Failed Model Convergence
			Program 10.15  Backward Model Selection for Ames Housing
			Output 10.17a Step 0 of Backward Elimination for Main and Interactions Effects
			Output 10.17b Interaction Effects Eligible for Removal for Step 1 of Backward Elimination
			Output 10.17c Interaction Effects Eligible for Removal for Step 2 of Backward Elimination
			Output 10.17d Effects Eligible for Removal for Step 3 of Backward Elimination
			Output 10.17e Final Model Selected Using Backward Elimination
			Program 10.16 Odds Ratios with Plots for Main Effects and Conditional Effects
			Output 10.18a Odds Ratios with Plots for Main Effects and Conditional Effects
			Output 10.18b Probabilities for High_Kitchen_Quality by Fullbath_2plus for Overall_Quality=1
	Scoring New Data
		The SCORE Statement with PROC LOGISTIC
			Program 10.17 Predicted Class for New Observations Using the SCORE Statement in PROC LOGISTIC
			Output 10.19 Predicted Class for New Observations Using the SCORE Statement in PROC LOGISTIC
		Using the PLM Procedure to Call Score Code Created by PROC LOGISTIC
			Program 10.18 Predicted Class for New Observations Using PROC PLM with the SCORE Statement
			Output 10.20 Predicted Class for New Observations Using PROC PLM with the SCORE Statement
		The CODE Statement within PROC LOGISTIC
			Program 10.19 Predicted Class for New Observations Using PROC PLM with the SCORE Statement
			Output 10.21 Predicted Class for New Observations Using PROC PLM with the SCORE Statement
			Program 10.20 SAS Scoring Code Created by the PLM Procedure
		The OUTMODEL and INMODEL Options with PROC LOGISTIC
			Program 10.21 Model Saved as SAS Data Set Created by the OUTMODEL Option in PROC LOGISTIC
			Output 10.22 Model Saved as SAS Data Set Created by the OUTMODEL Option in PROC LOGISTIC
	Key Terms
	Chapter Quiz
Chapter 11: Measure of Model Performance
	Introduction
	Preparation for the Modeling Phase
		Honest Assessment of a Classifier
		PROC SURVEYSELECT for Creating Training and Validation Data Sets
			Program 11.1 Partitioning Ames Housing Data into Training and Validation Data Sets
			Output 11.1a PROC FREQ on Bonus for Ames Housing Data
			Output 11.1b PROC SURVEYSELECT Using Ames Housing Data
			Output 11.1c  PROC FREQ on Bonus for Ames Training and Validation Data
			Log 11.1 Partial Log for PROC SURVEYSELECT Using Ames Housing Data
		Recommendations for the Model Preparation Stage
	Assessing Classifier Performance
		Measures of Performance Using the Classification Table
			Table 11.1 General Form of the Classification Table
			The CTABLE Option for Producing Classification Results
				Program 11.2 Classification Tables for Ames Training and Validation Data Sets
				Output 11.2a Classification Table for Ames Training Data
				Table 11.2  Classification Table for Ames Training Data
				Output 11.2b  Classification Table for Ames Validation Data
			Assessing the Performance and Generalizability of a Classifier
			The Effect of Cutoff Values on Sensitivity and Specificity Estimates
				Output 11.3  Classification Table for Multiple Cutoff Values for Ames Training Data
				Figure 11.1  Performance Measures by Cutoff Values for Ames Training Data
				Program 11.3 Classification Table Using Cutoff=0.20 for Ames Validation Data
				Output 11.4 Classification Table for Cutoff = 0.20 for Ames Validation Data
		Measure of Performance Using the Receiver-Operator-Characteristic (ROC) Curve
			Figure 11.2  ROC Curve for Ames Training Data
			Producing an ROC Curve Using the SCORE Statement with the OUTROC Option
				Program 11.4 ROC Curves for Ames Housing Training and Validation Data
				Output 11.5a:  Training and Validation ROC Curves for Ames Housing Data
				Output 11.5b:  ROC Information for Ames Validation Data
		Model Comparison Using the ROC and ROCCONTRAST Statements
			Program 11.5 Comparing Two Models Using Validation ROC Curves for Ames Housing
			Output 11.6a:  ROC Curves for Two Models Applied to Ames Validation Data
			Output 11.6b:  ROC Contrast Results for Two Models Applied to Ames Validation Data
		Measures of Performance Using the Gains and Lift Charts
			The Gains Chart
				Program 11.6 Gains Information for Ames Validation Data
				Output 11.7a Gains Information for Ames Validation Data
				Output 11.7b  Gains Chart for Ames Validation Data
			The Lift Chart
				Output 11.8  Lift Chart for Ames Validation Data
	Adjustment to Performance Estimates When Oversampling Rare Events
		The PEVENT Option for Defining Prior Probabilities
			Program 11.7 Use of PEVENT Option to Define Prior Probabilities
			Output 11.9a  The Logistic Regression Model for Ames Training Data
			Output 11.9b  Classification Table for PEVENT = 0.02 and PEVENT = 0.4053
			Table 11.3  Classification Table for Ames Housing Training Data Labeled for Bayes’ Theorem
		Manual Adjustment of the Classification Matrix
			Table 11.4  General Classification Table Adjusted for Oversampling
		Scoring the Validation Data Using Adjusted Posterior Probabilities
			Manually Adjusting Posterior Probabilities to Account for Oversampling
				Program 11.8 Posterior Probabilities Manually Adjusted for Oversampling
				Output 11.10  Classification Table for Ames Housing Validation Data Adjusted for Oversampling
			Manually Adjusted Intercept Using the Offset
				Program 11.9 Posterior Probabilities Using Manually Adjusted Intercept
				Program 11.10 Adjusting the Model Intercept Using the OFFSET Option
				Output 11.11 Logistic Regression Model for Ames Training with Intercept Adjusted for Oversampling
			Automatically Adjusted Posterior Probabilities to Account for Oversampling
				Program 11.11 Comparison of the Three Approaches to Adjusting for Oversampling
				Output 11.12  Posterior Probabilities for Ames Validation Data Using Three Approaches
	The Use of Decision Theory for  Model Selection
		Decision Cutoffs and Expected Profits for Model Selection
			Table 11.6  Profit Matrix for Classification Decisions
			Table 11.7  Profit Matrix for Ames Housing
			Program 11.12 Classification Results and Profit Information for Ames Validation Data
			Output 11.13a  Classification Matrix for Ames Validation Data Based upon 0.10 Cutoff
			Output 11.13b  Average Expected Profit for Ames Validation Data Based upon 0.10 Cutoff
			Output 11.13c  Line Listing for Several Houses in the Ames Validation Data Set
		Using Estimated Posterior Probabilities to Determine Cutoffs
			Program 11.13 Average Profit for Ames Validation Data by Depth and Cutoff
			Output 11.14a  Average Profit for Ames Validation Data by Depth and Cutoff
			Output 11.14b  Maximum Average Profit for Ames Validation Data
	Key Terms
	Chapter Quiz
References