The video provides a comprehensive overview of a regression analysis workflow and emphasizes the importance of dealing with empirically testable assumptions after the analysis. It begins with formulating a hypothesis, followed by data collection and exploration to understand relationships. It then estimates an initial regression model involving independent and dependent variables and briefly discusses its results. The focus then shifts to diagnostics, favoring graphs over statistical tests to provide a more informative look at issues such as heteroskedasticity.

In the diagnosis phase, the video demonstrates the use of different plots, starting with the regular QQ plot to assess the distribution of residuals and identify outliers. This is followed by the residuals versus adjusted plot to detect nonlinearity and heteroskedasticity in the data. The leverage versus squared residuals plot helps identify influential observations. The added variables plot is then used to examine the relationship between the dependent variable and each independent variable and isolate their respective contributions. Based on this diagnosis, adjustments are made to the regression model, such as by correcting for nonlinearity or heteroskedasticity, and retests are performed until a satisfactory model is achieved. The video concludes by interpreting the regression coefficients in the context of the research, using the Prestige dataset with "prestige" as the dependent variable and "education", "income", and "female percentage" as independent variables.

Slides: https://osf.io/6agb4

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