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
y  Xb  ε
b  X' X  X' y
1
Regression Analysis: Issues
Measurement Error
Model Specification
E(b) = b → Case selection
Y = a + Xb + e
(s.e.)
Var(b) → Number of cases
Ontological Assumptions
The Art of Summarizing Relationships
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Assumptions
Diagnostics
Residual structures
Modeling Issues
Categorical variables
Time series
Day 1 & 2:
The Model and its Assumptions
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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