Added variable plot or partial regression plot

The video explains added variable plots, also known as partial regression plots, which are vital diagnostic tools in regression analysis. It begins by illustrating the concept using the prestige data set, demonstrating how these plots are constructed for each independent variable. The focus is on the first plot, revealing how it is a scatter plot with a regression line, representing data points for education and prestige, conditional on other variables.

The video then delves into the methodology behind these plots, showcasing the use of R code for computation. The process involves regressing one independent variable against others, then doing the same with the dependent variable, excluding the one in focus. The residuals from these regressions are then plotted against each other. This approach effectively isolates the relationship between the two variables of interest, filtering out the influence of other variables in the model.

Additionally, the video explains the significance of these plots in interpreting the unique relationship between variables, using a Venn diagram for better understanding. It highlights that the regression coefficient obtained from an added variable plot is identical to that obtained from regressing residuals against each other. This insight is crucial for understanding complex relationships in data, especially when dealing with non-linear models. The usefulness of added variable plots extends beyond diagnostics to include interpretation, as emphasized in the video with real-world application examples. The concept that regression analysis often boils down to examining the relationship between residuals is also touched upon, offering a deeper understanding of control variables in regression models.

Slides: https://osf.io/rs8v4