Advanced Statistical Methods

✍ Scribed by Sahana Prasad

• Publisher: Springer
• Year: 2024
• Tongue: English
• Leaves: 241
• Category: Library

✦ Table of Contents

Acknowledgments
About This Book
Contents
List of Figures
List of Tables
1 Regression
1.1 Difference Between Correlation and Regression
1.2 Different Types of Regression Analysis
1.3 Regression Lines
1.3.1 Definition
1.3.2 Types of Regression Lines
1.3.3 Fitting a Regression Line
1.3.4 Interpreting a Regression Line
1.3.5 Practical Applications
1.3.6 Properties of Regression Lines
1.4 Regression Equations
1.4.1 Definition
1.4.2 Components of a Regression Equation
1.4.3 Interpretation of Regression Coefficients
1.4.4 Different Regression Equations
1.4.5 Practical Applications
1.5 Simple Linear Regression
1.5.1 Properties of Regression Coefficients in Simple Linear Regression
1.5.2 Interpreting the Regression Coefficient
1.5.3 Estimating the Regression Equations from the Given Data in Case of Simple Linear Regression
1.5.4 Examples of Calculating Regression Equations from Given Data
1.5.5 Line of Best Fit
1.5.6 Evaluation of Model Goodness of Fit in Simple Regression: Understanding R-squared and Adjusted R-squared
1.6 Interpretation of the Standard Error of the Estimate
1.7 Significance of the Model
1.8 A Few Case Studies that Demonstrate the Application of Linear Regression
1.9 Polynomial Regression
1.9.1 Understanding Polynomial Regression
1.9.2 Benefits of Polynomial Regression
1.9.3 Challenges and Considerations
1.10 Multiple Regression
1.10.1 A Few Case Studies Where Multiple Linear Regression Has Been Applied
1.11 Logistic Regression
1.11.1 What is Logistic Regression?
1.11.2 Working Principle
1.11.3 Model Training and Optimization
1.11.4 Assumptions of Logistic Regression
1.11.5 Evaluation and Interpretation
1.11.6 Practical Applications
1.11.7 Logit Function
1.11.8 Binary Outcome
1.11.9 Probability and Odds
1.12 Which Regression to Use and When?
1.13 Caution While Using Regression Analysis
1.14 Outliers in Regression Analysis
1.14.1 Causes of Outliers in Regression Analysis
1.14.2 Impact of Outliers on Regression Analysis
1.14.3 Detecting Outliers in Regression Analysis
1.14.4 Handling Outliers in Regression Analysis
1.14.5 Removing Outliers on Regression Lines
2 Index Numbers
2.1 Introduction
2.2 Definitions
2.3 Important Uses of Index Numbers
2.3.1 Index Numbers in Analytics
2.3.2 Index Numbers in Nation Building
2.3.3 Index Numbers Are Economic Barometers
2.3.4 Index Numbers and Agriculture
2.4 The Base Year
2.5 Types of Index Numbers Based on Methods of Calculation
2.6 Price Relative
2.6.1 The Price, Quantity, and Value Index Numbers
2.7 Consumer Price Index Number—C.P.I.
2.7.1 How is the CPI Market Basket Determined?
2.7.2 Some Case Studies on Consumer Price Index (CPI) Numbers
2.7.3 The Weighting Pattern for 2019-Based CPI for General Households
2.7.4 Calculation of CPI
2.8 Wholesale Price Index Number (WPI)
2.8.1 Some Case Studies on WPI
2.9 Tax Price Index Numbers-TPI
2.9.1 Case Study: Tax Reform and Tax Price Index Numbers
2.10 Crime Index Numbers
2.10.1 Components of Crime Index Numbers
2.10.2 Significance of Crime Index Numbers
2.11 Environmental Quality Index
2.12 The Health Index
2.13 Education Index Number
2.14 Types of Index Number Based on Weights and Formula
2.14.1 Laspeyre’s Index—Output Inflator
2.14.2 Paasche’s Index—Output Deflator
2.14.3 Fisher’s Ideal Formula
2.14.4 Dorbish and Bowley
2.14.5 Marshall–Edgeworth’s Index
2.14.6 Kelly’s Index Number
2.14.7 Walsh’s Index Number
2.15 Criteria for a Good Index Number
2.15.1 Tests on Index Numbers
2.15.2 Time-Reversal Test (T.R.T.)
2.15.3 Factor Reversal Test (F.R.T.)
2.15.4 Unit Test
2.15.5 Circular Test
2.16 Shifting the Base Year
2.17 Chain Base Index and Link Relatives
2.18 Splicing of Index Numbers
2.19 Deflating Index Numbers
2.20 Note on Real Income
3 Time Series
3.1 Definition
3.2 Basic Concepts in Time Series Analysis
3.3 Uses of Time Series
3.4 Mathematical Models of Time Series
3.5 Descriptive Statistics Used in Regression Analysis
3.6 Stationary and Non-stationary Data
3.6.1 Stationarity
3.6.2 Non-stationarity
3.7 Linear and Non-linear Time Series
3.7.1 Linear Time Series
3.7.2 Non-linear Time Series
3.8 Components of Time Series
3.8.1 Trend/Secular Trend
3.9 Seasonal Variations
3.9.1 Methods of De-Seasonalizing Data
3.9.2 Ratio to Moving Averages Method
3.10 Time Series and Stochastic Processes
3.10.1 Difference Between Time Series and Stochastic Process
3.10.2 Examples of Stochastic Processes
3.11 What Are Lagged Values?
3.12 Graphical Representation of Time Series
3.13 General Overview of the Steps Involved in Time Series Data Processing
3.14 Graphical Representation of Time Series
3.15 Time Series Visualization: Techniques and Examples
3.16 Additional Topics
4 Vital Statistics
4.1 Introduction
4.2 Advantages of Vital Statistics
4.3 Common Terminologies Used in Vital Statistics
4.4 Sources of Data in Vital Statistics:
4.5 Measurement of Population
4.5.1 Calculation of Intercensal Estimates
4.6 Rates and Ratios of Vital Event
4.7 Mortality and Death Rates
4.7.1 Crude Mortality Rate or the Crude Death Rate
4.7.2 Cause-Specific Mortality Rate and Age-Specific Mortality Rate
4.7.3 Neonatal Mortality Rate
4.7.4 Maternal Mortality Rate (M.M.R)
4.7.5 Sex-Specific Mortality Rate
4.7.6 Race-Specific Mortality Rate
4.7.7 Age-Specific Death Rates
4.7.8 Standardized Death Rates
4.8 Birth Rates
4.8.1 Some Interesting Statistics About Birth Rates
4.8.2 Fertility Rates
4.9 Marriage and Divorce Statistics
4.10 Life Tables
4.10.1 Why Do We Need Life Tables?
4.10.2 Examples Where Life Tables Are Used
4.10.3 Other Applications of Life Tables
4.10.4 Limitations of Life Tables
4.11 Life Tables—Basic Notations
4.11.1 Life Expectancy
4.11.2 Abridged Life Table
4.11.3 Construction of Abridged Life Tables
4.11.4 Significance of Abridged Life Tables
4.11.5 Limitations
4.12 Case Studies Related to Vital Statistics