Multiple Regression Analysis

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Multiple Regression Analysis

• Bernhard Kittel
• Center for Social Science Methodology
• University of Oldenburg

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The Art of Summarizing Relationships
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The Straight Line
1998 G. Meixner
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The Straight Line
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The Art of Summarizing Relationships
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Regression Analysis Issues
Y a Xb e (s.e.)
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The Art of Summarizing Relationships

• Assumptions
• Diagnostics
• Residual structures
• Modeling Issues
• Categorical variables
• Time series

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Day 1 2 The Model and its Assumptions

• Linearity
• Identifiability
• Independent variables exogenous
• Identically, independently, and normally
  distributed errors

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Day 3 4Diagnostics

• Do the assumptions hold?
• Multicollinearity
• Residual analysis
• Outlying influential data
• Heteroskedasticity

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Day 5 6Modeling Issues

• Beyond linear models?
• Functional forms
• Squares, roots, inverses, logarithms
• Categorical factors
• Dummy variables
• Conditional effects
• Interactive models

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Day 7Binary response variables

• How should we deal with dichotomous dependent
  variables?
• Probability models Logit
• Maximum likelihood estimation
• Interpretation

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Day 8 9Longitudinal data

• How should we deal with repeated observations?
• Autocorrelation
• Time series analysis
• Panel data analysis

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Day 10Potentials Limits of Multiple Regression

• Equilibrium analysis
• Statistical sophistication vs. measurement
  precision
• Temporality in variables and effects
• Levels of aggregation

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The Art of Summarizing Relationships