Multiple Regression Analysis Bernhard Kittel Center for Social Science Methodology University of Oldenburg

The Art of Summarizing Relationships

The Straight Line 1998 G. Meixner

The Straight Line

The Art of Summarizing Relationships

Regression Analysis: Issues E(b) =  → Case selection Var(b) → Number of cases Y =  + X  +  (s.e.) Measurement Error Model Specification Ontological Assumptions

The Art of Summarizing Relationships  Assumptions  Diagnostics  Residual structures  Modeling Issues  Categorical variables  Time series

Day 1 & 2: The Model and its Assumptions  Linearity  Identifiability  Independent variables exogenous  Identically, independently, and normally distributed errors

Day 3 & 4: Diagnostics  Do the assumptions hold? –Multicollinearity –Residual analysis Outlying & influential data –Heteroskedasticity

Day 5 & 6: Modeling Issues  Beyond linear models? –Functional forms Squares, roots, inverses, logarithms –Categorical factors Dummy variables –Conditional effects Interactive models

Day 7: Binary response variables  How should we deal with dichotomous dependent variables? –Probability models: Logit –Maximum likelihood estimation –Interpretation

Day 8 & 9 Longitudinal data  How should we deal with repeated observations? –Autocorrelation –Time series analysis –Panel data analysis

Day 10: Potentials & Limits of Multiple Regression  Equilibrium analysis  Statistical sophistication vs. measurement precision  Temporality in variables and effects  Levels of aggregation

The Art of Summarizing Relationships