"Applied Linear Statistical Models" is not a formal class at ETSU, but the material here might overlap some with the Statistical Methods sequence (STAT 5710 and 5720). The book and these notes are broken into six parts. Links to the parts are given on my main Applied Linear Statistical Models webpage.

Copies of the classnotes are on the internet in PDF format as given below. The notes and supplements may contain hyperlinks to posted webpages; the links appear in red fonts. The "Examples, Exercises, and Proofs" files were prepared in Beamer. The "Printout of Examples, Exercises, and Proofs" are printable PDF files of the Beamer slides without the pauses. These notes have not been classroom tested and may have typographical errors.

Chapter 1. Linear Regression with One Predictor Variable.

• 1.1. Relations between Variables. Section 1.1 notes
• 1.2. Regression Models and Theory Uses. Section 1.2 notes
• 1.3. Simple Linear Regression Model with Distribution of Error Terms. Section 1.3 notes
• 1.4. Data for Regression Analysis. Section 1.4 notes
• 1.5. Overview of Steps in Regression. Section 1.5 notes
• 1.6. Estimation of Regression Function. Section 1.6 notes
• Supplement. Examples, Exercises, and Proofs from Section 1.6. Beamer file of Section 1.6 proofs
• Supplement. Printouts of Examples, Exercises, and Proofs from Section 1.6. Print file of Section 1.6 proofs
• 1.7. Estimation of Error Terms Variance σ². Section 1.7 notes
• 1.8. Normal Error Regression Model. Section 1.8 notes
• Supplement. Examples, Exercises, and Proofs from Section 1.8. Beamer file of Section 1.8 proofs
• Supplement. Printouts of Examples, Exercises, and Proofs from Section 1.8. Print file of Section 1.8 proofs
• Study Guide 1

Chapter 2. Inferences in Regression and Correlation.

• 2.1. Inferences Concerning β₁ (partial). Section 2.1 notes
• Supplement. Examples, Exercises, and Proofs from Section 2.1. Beamer file of Section 2.1 proofs (prepared in Beamer).
• Supplement. Printouts of Examples, Exercises, and Proofs from Section 2.1. Print file of Section 2.1 proofs
• 2.2. Inferences Concerning β₀.
• 2.3. Some Considerations on Making Inferences Concerning β₀ and β₁.
• 2.4. Interval Estimation of E{Y_n}.
• 2.5. Prediction of New Observations.
• 2.6. Confidence Band for Regression Line.
• 2.7. Analysis of Variance Approach to Regression Analysis.
• 2.8. General Linear Test Approach.
• 2.9. Descriptive Measures of Linear Association between X and Y.
• 2.10. Considerations in Applying Regression Analysis.
• 2.11. Normal Correlation Models.
• Study Guide 2.

Chapter 3. Diagnostics and Remedial Measure.

• 3.1. Diagnostics for Predictor Variable.
• 3.2. Residuals.
• 3.3. Diagnostics for Residuals.
• 3.4. Overview of Tests Involving Residuals.
• 3.5. Correlation Test for Normality.
• 3.6. Tests for Constancy of Error Variance.
• 3.7. F Test for Lack of Fit.
• 3.8. Overview of Remedial Measures.
• 3.9. Transformations.
• 3.10. Case Example - Plutonium Measurement.
• 3.11. Normal Correlation Models.
• Study Guide 3.

Chapter 4. Simultaneous Inferences and Other Topics in Regression Analysis.

• 4.1. Joint Estimation of β₀ and β₁.
• 4.2. Simultaneous Estimation of Mean Responses.
• 4.3. Simultaneous Prediction Intervals for New Observations.
• 4.4. Regression through Origin.
• 4.5. Effects of Measurement Errors.
• 4.6. Inverse Predictions.
• 4.7. Choice of X Levels.
• Study Guide 4.

Chapter 5. Matrix Approach to Simple Linear Regression Analysis. Chapter 5 Introduction notes

• 5.1. Matrices.
• 5.2. Matrix Addition and Subtraction.
• 5.3. Matrix Multiplication.
• 5.4. Special Types of Matrices.
• 5.5. Linear Dependence and Rank of Matrix.
• 5.6. Inverse of a Matrix.
• 5.7. Some Basic Results for Matrices.
• 5.8. Random Vectors and Matrices. Section 5.8 notes
• Supplement. Examples, Exercises, and Proofs from Section 5.8. Beamer file of Section 5.8 proofs (prepared in Beamer).
• Supplement. Printouts of Examples, Exercises, and Proofs from Section 5.8. Print file of Section 5.8 proofs
• 5.9. Simple Linear Regression Model in Matrix Terms. Section 5.9 notes
• 5.10. Least Squares Estimation of Regression Parameters.
• 5.11. Fitted Values and Residuals.
• 5.12. Analysis of Variance Results.
• 5.13. Inferences in Regression Analysis.
• Study Guide 5.

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