Multiple regression

Gist

Like the Linear regression but you add more predictors

Mathematics

Interpretations

Note that it is not necessary to “hold constant” all other variables to be able to interpret the effect of one predictor. It is sufficient to hold constant the weighted sum of all the variables other than $X_j$. And in many cases it is not physically possible to hold other variables constant while varying one, e.g., when a model contains $X$ and $X^2$ ^[1]

References

[^1] Gelman, A., & Hill, J. (2007). Data analysis using regression and multilevel/hierarchical models. Cambridge university press.

• explanatory variables allow one to address primary research questions
• explanatory variables control for important covariates
• potential interactions have been investigated
• variables are centered where interpretations can be enhanced
• unnecessary terms have been removed
• LINE assumptions and the presence of influential points have both been checked using residual plots
• the model tells a “persuasive story parsimoniously”
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