Statistics for Business and Economics: Excel/Minitab Enhanced Heinz Kohler

16. Simple Regression and Correlation

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16.1 INTRODUCTION

16.2 THE ORIGIN OF SIMPLE REGRESSION ANALYSIS

16.3 BASIC CONCEPTS OF REGRESSION ANALYSIS

Independent Versus Dependent Variables
Deterministic Versus Stochastic Relationships

Direct Versus Inverse Relationships

16.4 THE SCATTER DIAGRAM

16.5 DRAWING A REGRESSION LINE: THE EYEBALL APPROACH

16.6 DRAWING THE BEST REGRESSION LINE: LEAST SQUARES

16.7 ESTIMATED VERSUS TRUE REGRESSION LINE

The True Regression Line Conditions for Making Valid Inferences

16.8 REGRESSION DIAGNOSTICS

16.9 ESTIMATING THE AVERAGE VALUE OF Y, GIVEN X

Making a Point Estimate of µY * X
Establishing a Confidence Interval for µY * X from a Small Sample (n < 30)
Establishing a Confidence Band for µY * X
Establishing a Confidence Interval for µY * X from a Large Sample (n >= 30)

16.10 PREDICTING AN INDIVIDUAL VALUE OF Y, GIVEN X

Establishing a Prediction Interval for IY * X from a Small Sample (n < 30)
Establishing a Prediction Band for IY * X
Establishing a Prediction Interval for IY * X from a Large Sample (n >= 30)

16.11 MAKING INFERENCES ABOUT TRUE REGRESSION COEFFICIENTS

Establishing a Confidence Interval for b
Establishing a Confidence Interval for a

APPLICATION 16.1 Evaluating a New Food Product

APPLICATION 16.2 Of Bulls, Bears, and Beauty

APPLICATION 16.3 The Economy and the Ballot Box

16.12 SIMPLE CORRELATION ANALYSIS

The Coefficient of Determination
The Coefficient of Correlation

APPLICATION 16.4 The Uneven Burden of International Trade Restraints

APPLICATION 16.5 Snowfall and Unemployment

APPLICATION 16.6 Jukebox Economics

APPLICATION 16.7 Small Is Beautiful: The Relationship Between Height and Longevity

Other Coefficients

16.13 TESTING b WITH ANALYSIS OF VARIANCE

16.14 AN EXTENSION: CURVILINEAR REGRESSION

Approximating Curvilinear By Linear Regression Lines
Data Transformation

17. Multiple Regression and Correlation

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17.1 INTRODUCTION

17.2 LINEAR MULTIPLE REGRESSION WITH TWO EXPLANATORY VARIABLES

The Regression Plane
Least Squares Revisited

17.3 THE SAMPLE STANDARD ERROR OF THE ESTIMATE OF Y

17.4 MAKING INFERENCES

Crucial Assumptions
Estimating the Average Value of Y, Given X1 and X2

Predicting an Individual Value of Y, Given X1 and X2

Establishing Confidence Intervals for b1 and b2
Using t Values
Using p Values

17.5 ANOVA REVISITED: TESTING THE OVERALL SIGNIFICANCE OF A REGRESSION

17.6 MULTIPLE CORRELATION ANALYSIS

The Coefficient of Multiple Determination
The Coefficient of Multiple Correlation

The Adjusted Coefficient of Multiple Determination
Partial Correlation

17.7 LINEAR MULTIPLE REGRESSION WITH THREE OR MORE EXPLANATORY VARIABLES

Interpreting Computer Printout

APPLICATION 17.1 The Price of Heroin and the Incidence of Crime

APPLICATION 17.2 Housing Prices and Proposition 13

APPLICATION 17.3 An Economic Interpretation of Congressional Voting

APPLICATION 17.4 Determinants of the Natural Unemployment Rate in Canada

APPLICATION 17.5 Bankers Assess Credit Card Risk

APPLICATION 17.6 The Geography of Medicare

Predicting the Average or Individual Value of Y

17.8 DISCOVERING POSSIBLE VIOLATIONS OF ASSUMPTIONS

Normality
Homoscedasticity
Statistical Independence
Linearity

Uncorrelated Independent Variables

Part VII Supplementary Topics for Economics

18. Model Building With Multiple Regression

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18.1 ECONOMIC THEORY AND ECONOMETRICS

18.2 DUMMY VARIABLES

A Qualitative Variable With Two Categories
A Qualitative Variable With More Than Two Categories

APPLICATION 18.1 Whom Do Regulators Serve? The Case of the Education Industry

APPLICATION 18.2 Do Consumer Products Safety Regulators Reduce Injuries and Deaths?

APPLICATION 18.3 Does Photocopying Harm Authors and Publishers?

APPLICATION 18.4 Determinants of Air Fares

APPLICATION 18.5 Women's Wages and the Crowding Hypothesis

18.3 SELECTING AN IDEAL SET OF PREDICTOR VARIABLES

The Forward-Selection Method
The Backward-Elimination Method

The Best Subsets Approach

18.4 MULTIPLE-EQUATIONS MODELS

The General Model of Demand and Supply
An Econometric Model of Demand and Supply
Endogenous Variables and Predetermined Variables

18.5 SIMULTANEOUS EQUATIONS BIAS

Correlation Between Explanatory Variable and Error Term
A Graphical Illustration of Simultaneous Equations Bias

18.6 INDIRECT LEAST SQUARES-AN INTRODUCTION

The Rationale for ILS
Finding Reduced-Form Equations

18.7 THE IDENTIFICATION PROBLEM

The Counting Rule
A Graphical Illustration of the Identification Problem

18.8 INDIRECT LEAST SQUARES-AN EXTENDED EXAMPLE

APPLICATION 18.6 An Econometric Model of the United States Economy

18.9 TWO-STAGE LEAST SQUARES

Overidentification
Instrumental Variable Techniques

An Extended Example of 2SLS

APPLICATION 18.7 CEO Incentive Contracts and Corporate Performance

18.10 SECOND THOUGHTS ON ORDINARY LEAST SQUARES

Similar Results From OLS
Recursive Models

APPLICATION 18.8 A Macroeconomic Model of the Chinese Economy

19. Time Series and Forecasting

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19.1 BASIC CONCEPTS

19.2 THE COMPOSITION OF A TIME SERIES

The Trend
Cyclical Fluctuations
Seasonal Fluctuations
Irregular Variations

APPLICATION 19.1 The Role of Time Series in Social Experiments

APPLICATION 19.2 The Importance of Proper Timing

19.3 FORECASTING AND MOVING AVERAGES

The Raw Data
Computing Moving Averages

APPLICATION 19.3 The Slutsky-Yule Effect

Forecasting With Moving Averages

APPLICATION 19.4 The Dangers of Extrapolation

19.4 FORECASTING AND EXPONENTIAL SMOOTHING

Single-Parameter Exponential Smoothing
A Graphical Exposition of Single-Parameter Exponential Smoothing
Two-Parameter Exponential Smoothing
A Graphical Exposition of Two-Parameter Exponential Smoothing

19.5 FORECASTING AND LEAST-SQUARES REGRESSION

Consulting a Scatter Diagram
Forecasting With a Linear Regression Line

From Annual to Quarterly Data
Forecasting With a Curvilinear Regression Line

APPLICATION 19.5 Fitting Trends With Logarithms

Dealing With Serial Correlation

19.6 FORECASTING AND THE USE OF SEASONAL INDEXES

The Ratio-To-Moving-Average Method
Deseasonalizing Data
Making Forecasts

Computer Applications
The Dummy-Variable Method

19.7 FORECASTING AND BAROMETRIC INDICATORS

Anticipatory Surveys

20. Index Numbers

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20.1 THE NATURE OF INDEX NUMBERS

20.2 SIMPLE PRICE INDEXES

An Intertemporal Index
An Interspatial Index

20.3 UNWEIGHTED COMPOSITE PRICE INDEXES

An Unweighted Average of Simple Price Indexes
An Unweighted Aggregative Price Index

20.4 WEIGHTED AGGREGATIVE PRICE INDEXES

The Laspeyres Price Index
The Paasche Price Index
The Index Number Problem

Other Weighted Aggregative Price Indexes

20.5 FISHER'S QUALITY TESTS AND HIS IDEAL INDEX

The Time-Reversal Test
The Factor-Reversal Test
The Circularity Test

Testing the Laspeyres Index
Fisher's Ideal Index

20.6 MANIPULATING INDEX-NUMBER TIME SERIES

Shifting the Base
Splicing Two Short Series Into a Longer Series

Combining Two Specialized Series Into a More Comprehensive Series
Creating Chain Indexes

20.7 MAJOR U. S. PRICE INDEXES

The Consumer Price Index
The Producer Price Index
Stock Price Indexes

Implicit Price Deflators

20.8 MAJOR USES OF PRICE INDEXES

Evaluating Economic Policy
Deflating Current-Dollar Time Series
Escalators

20.9 QUANTITY INDEXES

The Index of Industrial Production
The Index-Number Problem Revisited

APPLICATION 20.1 Measuring Soviet Economic Growth

APPLICATION 20.2 Comparing U. S. With Soviet Real GNP

20.10 THE VAIN PURSUIT OF THE UNQUANTIFIABLE

The United Nations Human Development Index
Constructing the Index

HDI Data From Around the World
A Word of Caution

Part VIII Supplementary Topics for Business

21. Hypothesis Testing: Nonparametric Techniques

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21.1 PARAMETRIC VERSUS NONPARAMETRIC TESTS

Types of Nonparametric Tests

21.2 THE WILCOXON RANK-SUM TEST

The Test Statistic
An Illustration The Sampling Distribution of W

21.3 THE MANN-WHITNEY TEST

The Test Statistic
The Sampling Distribution of U

21.4 THE SIGN TEST

The Test Statistic
The Sampling Distribution of S

An Important Variation: A Sign Test Concerning the Population Median

21.5 THE WILCOXON SIGNED-RANK TEST

The Test Statistic
The Sampling Distribution of T

APPLICATION 21.1 The Gains From Takeover Deregulation

21.6 THE NUMBER-OF-RUNS TEST

The Test Statistic
The Sampling Distribution of RH

APPLICATION 21.2 Examining the 1971 Draft Lottery

21.7 THE KRUSKAL-WALLIS TEST

21.8 THE KOLMOGOROV-SMIRNOV ONE-SAMPLE TEST

Goodness of Fit to the Binomial Distribution
Goodness of Fit to the Poisson Distribution

Goodness of Fit to the Normal Distribution

21.9 SPEARMAN'S RANK-CORRELATION TEST

The Test Statistic
The Sampling Distribution of Rho

APPLICATION 21.3 Searching for Leviathan

22. Quality Control

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22.1 INTRODUCTION

22.2 THE PRODUCTION PROCESS

APPLICATION 22.1 Striving for Reliability—The Case of the Apollo Mission

22.3 ACCEPTANCE SAMPLING

Types of Sampling Plans
Producer's Risk and Consumer's Risk

Managing Risk Levels

22.4 STATISTICAL PROCESS CONTROL

The Inevitability of Variation
Hypothesis Testing for Quality

Alternative Types of Control Charts
X bar Charts: Parameters Known

X bar Charts: Parameters Unknown
P
Charts
nP Charts, R Charts, and c Charts
Interpreting Control Charts

APPLICATION 22.2 Control Charts— A Brief Historical Tour

22.5 OTHER METHODS OF QUALITY CONTROL

Quality Circles and Team Work

APPLICATION 22.3 Team Work in Sweden

Guaranteed Employment

APPLICATION 22.4 Guaranteed Employment in Japan

The Total Quality Movement

APPLICATION 22.5 U.S. Quality Programs Show Mixed Results

23. Decision Theory

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23.1 INTRODUCTION

23.2 BASIC CONCEPTS

Actions, Events, Payoffs
The Payoff Table
The Decision Tree

23.3 DECISION MAKING WITHOUT PROBABILITIES

Maximin or Minimax
Maximax or Minimin
Minimax Regret

Criticisms of Nonprobabilistic Techniques

23.4 DECISION MAKING WITH PROBABILITIES: PRIOR ANALYSIS

Maximum Likelihood
Expected Monetary Value

Expected Opportunity Loss

APPLICATION 23.1 The Decision to Seed Hurricanes—A Second Look

Expected Utility

APPLICATION 23.2 When Decision Analysis Came of Age

23.5 DECISION MAKING WITH PROBABILITIES: POSTERIOR ANALYSIS

Gathering New Information
Applying Bayes' Theorem
Finding the Optimal Strategy

23.6 THE VALUE OF INFORMATION

The Expected Value of Perfect Information

APPLICATION 23.3 The Value of Perfect Information: The Case of the U.S. Cattle Industry

The Expected Value of Sample Information
The Efficiency of Sample Information

23.7 PREPOSTERIOR ANALYSIS

Extensive-Form Analysis
Normal Form Analysis
Pros and Cons

APPLICATION 23.4 Sequential Sampling

23.8 THE GREAT CONTROVERSY: CLASSICAL VERSUS BAYESIAN STATISTICS

An Example
The Unresolved Issue

Subject Index

Name Index