The video provides a comprehensive overview of a workflow for regression analysis, emphasizing the importance of addressing empirically testable assumptions post-analysis. It begins with formulating a hypothesis, followed by data collection and exploration to understand relationships. An initial regression model is then estimated, involving independent and dependent variables, and its results are briefly reviewed. The focus then shifts to diagnostics, favoring plots over statistical tests for a more informative view of issues like heteroskedasticity.
In the diagnostic phase, the video demonstrates the use of various plots, starting with the normal Q-Q plot to assess the distribution of residuals and identify outliers. This is followed by the residuals versus fitted plot to detect nonlinearity and heteroskedasticity in the data. The leverage versus residual squared plot helps identify influential observations. The added-variable plot is then used to examine the relationship between the dependent variable and each independent variable, isolating their unique contributions. Based on these diagnostics, adjustments are made to the regression model, such as addressing nonlinearity or heteroskedasticity, and retesting until a satisfactory model is achieved. The video concludes with the interpretation of regression coefficients in the context of the research, using the prestige dataset with 'prestige' as the dependent variable and 'education', 'income', and 'share of women' as independent variables.
Slides: osf.io/6agb4