Applied Regression Modeling: A Business Approach

by Iain Pardoe

Table of contents

• Introduction
  • Statistics in business
  • Learning statistics

1. Foundations
   1. Identifying and summarizing data
   2. Population distributions
   3. Selecting individuals at random—probability
   4. Random sampling
      1. Central limit theorem—normal version
      2. Student's t-distribution
      3. Central limit theorem—t version
   5. Interval estimation
   6. Hypothesis testing
      1. The rejection region method
      2. The p-value method
      3. Hypothesis test errors
   7. Random errors and prediction
   8. Chapter summary and problems
2. Simple linear regression
   1. Probability model for X and Y
   2. Least squares criterion
   3. Model evaluation
      1. Regression standard error
      2. Coefficient of determination—R²
      3. Slope parameter
   4. Model assumptions
      1. Checking the model assumptions
   5. Model interpretation
   6. Estimation and prediction
      1. Confidence interval for the population mean, E(Y)
      2. Prediction interval for an individual Y-value
   7. Chapter summary, review example, and problems
3. Multiple linear regression
   1. Probability model for (X₁, X₂, ...) and Y
   2. Least squares criterion
   3. Model evaluation
      1. Regression standard error
      2. Coefficient of determination—R²
      3. Regression parameters—global usefulness test
      4. Regression parameters—nested model test
      5. Regression parameters—individual tests
   4. Model assumptions
      1. Checking the model assumptions
   5. Model interpretation
   6. Estimation and prediction
      1. Confidence interval for the population mean, E(Y)
      2. Prediction interval for an individual Y-value
   7. Chapter summary and problems
4. Regression model building I
   1. Transformations
      1. Natural logarithm transformation for predictors
      2. Polynomial transformation for predictors
      3. Reciprocal transformation for predictors
      4. Natural logarithm transformation for the response
      5. Transformations for the response and predictors
   2. Interactions
   3. Qualitative predictors
      1. Qualitative predictors with two levels
      2. Qualitative predictors with three or more levels
   4. Chapter summary and problems
5. Regression model building II
   1. Influential points
      1. Outliers
      2. Leverage
      3. Cook's distance
   2. Regression pitfalls
      1. Autocorrelation
      2. Multicollinearity
      3. Excluding important predictor variables
      4. Overfitting
      5. Extrapolation
      6. Missing Data
   3. Model building guidelines
   4. Model interpretation using graphics
   5. Chapter summary and problems
6. Case studies
   1. Home prices
      1. Data description
      2. Exploratory data analysis
      3. Regression model building
      4. Results and conclusions
      5. Further questions
   2. Vehicle fuel efficiency
      1. Data description
      2. Exploratory data analysis
      3. Regression model building
      4. Results and conclusions
      5. Further questions
7. Extensions
   1. Generalized linear models
      1. Logistic regression
      2. Poisson regression
   2. Discrete choice models
   3. Multilevel models
   4. Bayesian modeling

• Appendix A Computer software help
  • SPSS
  • Minitab
  • SAS
  • R and S-PLUS
  • Excel
• Appendix B Critical values for t-distributions
• Appendix C Notation and formulas
  • Univariate data
  • Simple linear regression
  • Multiple linear regression
• Appendix D Mathematics refresher
  • The natural logarithm and exponential functions
  • Rounding and accuracy
• Appendix E Brief answers to selected problems
• References
• Glossary
• Index