1. 8- Multiple Regression Analysis: The Problem of Inference The Normality Assumption Once Again Example 8.1: U.S. Personal Consumption and Personal Disposal Income Relation, 1956-1970 Hypothesis Testing in Multiple Regression: General Comments Hypothesis Testing about Individual Partial Regression Coefficients Testing the Overall Significance of the Sample Regression Testing the Equality of Two Regression Coefficients Restricted Least Squares: Testing Linear Equality Restriction Comparing Two Regression: Testing for Structural Stability of Regression Models Testing the Functional Form of Regression: Choosing between Linear and Log-Linear Regression Models Prediction with Multiple Regression The Troika of Hypothesis Tests: The Likelihood Ratio (LR), Wald (W), and Lagrange Multiplier (LM) Tests Summary and Conclusions

2. 9- The Matrix Approach to Linear Regression Mode 9- The Matrix Approach to Linear Regression Mode l The k-Variable Linear Regression Model Assumption of the Classical Linear Regression Model in Matrix Notation OLS Estimation The Coefficient of Determination R 2 in Matrix Notation The Correlation Matrix Hypothesis Testing About Individual Regression Coefficients in Matrix Notation Testing the Overall Significance of Regression: Analysis of Variance in Matrix Notation Testing Linear Restrictions: General F Testing Using Matrix Notation Prediction Using Multiple Regression: Matrix formulation Summary of the matrix Approach: An Illustrative Example Summary and Conclusions

3. The nature of Multicollinearity The nature of Multicollinearity Estimation in the Presence of Perfect Multicollinearity Estimation in the Presence of Perfect Multicollinearity Estimation in the Presence of “ High ” but “ Imperfect ” Multicollinearity Estimation in the Presence of “ High ” but “ Imperfect ” Multicollinearity Multicollinearity: Much Ado about Nothing ? Multicollinearity: Much Ado about Nothing ? Theoretical Consequences of Multicollinearity Theoretical Consequences of Multicollinearity Practical Consequences of Multicollinearity Practical Consequences of Multicollinearity An Illustrative Example: Consumption Expenditure in Relation to Income and Wealth An Illustrative Example: Consumption Expenditure in Relation to Income and Wealth Detection of Multicollinearity Detection of Multicollinearity Remedial Measures Remedial Measures Is Multicollinearity Necessarily Bad? Maybe Not If the Objective Is Prediction Only Is Multicollinearity Necessarily Bad? Maybe Not If the Objective Is Prediction Only Summary and Conclusions Summary and Conclusions Relaxing the Assumptions of the Classical Model 10- Multicollinearity and Micronumerosity